Abstract

Black phosphorus (BP) has recently attracted significant attention for its brilliant physical and chemical features. The remarkable strong light-matter interaction and tunable direct wide range band-gap make it an ideal candidate in various application regions, especially saturable absorbers. In this paper, ultrasmall black phosphorus quantum dots (BPQDs), a unique form of phosphorus nanostructures, with average size of 5.7 ± 0.8 nm are synthesized. Compared with BP nanosheets (BPNs) with similar thickness, the ultrafast nonlinear optical (NLO) absorption properties and excited carrier dynamics are investigated in wide spectra. Beyond the saturation absorption (SA), giant two photon absorption (TPA) is observed in BPQDs. BPQDs exhibit quite different excitation intensity and wavelength dependent nonlinear optical (NLO) response from BPNs, which is attributed to the quantum confinement and edge effects. The BPQDs show broadband photon-induced absorption (PIA) under the probe wavelength from 470 nm to 850 nm and a fast and a slow decay time are obtained as long as 92 ± 10 ps and 1100 ± 100 ps, respectively. The substantial independence for ultra-long time scales of pump intensity and temperature reveals that the carrier recombination mechanism may be attributed to a defect-assisted Auger capture process. These findings will help to develop optoelectronic and photonic devices operating in the infrared and visible wavelength region.

© 2017 Optical Society of America

1. Introduction

Two-dimensional (2D) layered materials, such as graphene and transition-metal dichalcogenides (TMDs), have triggered a surge of research interest in both fundamental studies and potential applications owing to their intriguing properties [1–4]. However, graphene suffers drawbacks from its zero-bandgap nature while TMDs are subject to limitations due to their relatively larger and indirect (multilayer) bandgap, which restricts their applications in near infrared region. Recently, considerable efforts have been devoted to the exploration of black phosphorus (BP), a new 2D layered material with large direct bandgap tunable from 0.3 to ∼2 eV and high carrier mobility (104 cm2 V−1 s−1) [5,6], which shows great potential to compensate the shortcomings of graphene and TMDCs.

Given that bulk BP shows quite low optical transmittance with strong absorption and scattering loss, it is of great significance to get thinner BP nanostructures so that efficient light-matter interaction could occur inside BP with low transmission loss. To fully take advantage of the excellent properties of BP, kinds of BP nanostructures have been prepared with sorts of methods [7–15]. As a matter of fact, great efforts have also been made to study the ultrafast NLO properties of various forms of BP nanostructures. The wavelength-dependent relaxation times of BPNs were determined to be 360 femtosecond (fs) to 1.36 picosecond (ps) with photon energies from 1.55 to 0.61 eV by pump-probe technique [10]. Ultrafast NLO response of multi-layer BPNs has been investigated with Z-scan measurement technique at the wavelengths of 400 nm, 515 nm, 800 nm, 1030nm, 1562nm, 1910 nm and 2100nm [11]. BPNs exhibit significant SA response under femtosecond excitation at all the wavelengths above, which confirms that ultrathin BPNs are potentially useful as broadband optical elements in ultrafast photonics devices.

The realization of mode-locked pulse generation by erbium fiber lasers with BPNs based saturable absorber were also reported by several groups at 1550 nm [12,13]. Our group has done some work on the NLO properties of BPNs [14,15]. The reverse saturable absorption (RSA) and giant two photon absorption (TPA) of BPNs at 800 nm excitation were observed for the first time [14]. Y. W. Wang et al. reported ultrafast recovery time (τ = 24 ± 2 fs) in BP suspension at the pump-probe wavelength of 1550 nm [16]. R. Long et al. predicted that the nonradiative electron-hole recombination rate would be reduced by defects in monolayer BP [17]. J. Q. He et al. demonstrated strong anisotropic transport in BP, where the photocarrier lifetime was determined as long as 100 ps [18]. S. F. Ge et al. performed angle-resolved transient reflection spectroscopy to study BP’s anisotropic properties, with the lifetime of hot carrier cooling and recombination measured to be hundreds of ps [19]. In addition, we realized both Q-switching and model-locked pulsed lasers and obtained harmonic mode-locking operation at 2 μm with BPNs saturable absorbers [20,21]. Besides the 2D layered structure, 1D BP nanoribbons have also been explored, and their intriguing electronic properties have made BP nanoribbons promising candidates for field-effect transistors, solar-cells, single electron transistors (SET), gas sensing, and photodetectors [22,23]. Most recently, BPQDs, another form of BP nanostructures, have been successfully synthesized and show great ultraviolet-visible absorption spectroscopy [8,9]. BPQDs exhibit unique electronic and optical properties due to the quantum confinement and edge effects [24].

Although the SA response of 800nm excitation has been observed and the model-locked pulsed laser was generated with BPQDs saturation absorbers at 1567.5 nm [9], the accurate knowledge of NLO characteristics and excited carrier dynamics of BPQDs in wide spectrum are relatively absent and the underlying mechanism in such finite-sized QDs is still unclear. Since the remarkable strong light-matter interaction and tunable direct wide range band-gap of BPQDs make them ideal candidates in various application regions especially saturable absorbers (SA) lasers, it’s of great importance to make certain the irradiance-dependence, wavelength-dependence and temperature-dependence of BPQDs’ excited carrier dynamics and the underlying recombination mechanism of BPQDs.

In this paper, the ultrafast NLO response of BPQDs is experimentally studied in a wide spectra from 800 nm to 2μm. The intensity and wavelength dependence of NLO properties of BPQDs are also investigated. Beyond the SA response at 800 nm excitation reported before [9], giant TPA response is observed meanwhile at all wavelengths utilized in this paper. The ultrafast pump-probe technology is performed to study the excited carrier dynamics of BPQDs. Broadband photon-induced absorption (PIA) appears at the excitation of probe photon wavelength from 470 nm to 850 nm. A fast and a slow decay time are extracted through the experimental data as long as 92 ± 10 ps and 1100 ± 100 ps, respectively, which infers that BPQDs are potential candidates for ultrafast Q-switched picosecond and nanosecond lasers. Meanwhile, the ultra-long exciton lifetime shows remarkable independence of pump intensity and environmental temperature, inferring that the recombination mechanism of BPQDs’ may be attributed to defect-assisted Auger capture process. Furthermore, the wavelength at which BPQDs performs largest difference absorption (ΔA/A0) slightly red-shifts with increasing experimental temperature. The results of our work provide deep insight into the NLO absorption and excited carrier dynamics of BPQDs, which is essential for their potential applications in the field of photonics, optoelectronics and electronic devices.

2. Experimental implementation

2.1 Sample characterization

The ultrasmall BPQDs are prepared in large scale from BP powder by using a solvothermal methods [8,9]. In our experiments, a simple, effective and productive technique has been adopted to prepare high-quality BPQDs. In the synthesis process, 10 mg of BP powder is added into 30 mL of N-methyl-2-pyrrolidone (NMP) in a glass vial and then ground for 1 hour. After sealed carefully, the glass vial is sonicated in an ice-bath at the power of 150W for 4 hours. The resultant dispersion is centrifuged for 20 minutes at a speed of 7000 rpm. The supernatant containing BPQDs and some few-layer BPNs is decanted gently. The BPNs are mostly contained in the bottom suspended sediment. And the supernatant is centrifuged once again for 40 minutes at the speed of 12000 rpm. In the following, the top supernatant is filtered through a 100nm-size membrane. Then the BPQDs and the BPNs are transferred into the glass vials, as shown in the inset of Figs. 1(a) and 1(b), respectively. As proved by previous research, BP nanostructures prepared by different methods or dissolved in different solvents show different optical properties [11]. With this method, 2D BPNs and 0D BPQDs can be obtained simultaneously. Then the different optical properties of BPNs and BPQDs could be contrastive studied carefully without the problems mentioned above.

 

Fig. 1 TEM of the (a) BPQDs and (b) BPNs. Insets are photographs of BPQDs and BPNs in glass vials, respectively. (c) AFM image of BPQDs. (d) Height profile of the red line marked in (c). (e) Statistical analysis of the height of 85 BPQDs determined by AFM. (f) Magnified TEM image. (g) Statistical analysis of the sizes of 100 BPQDs measured from TEM images (h) UV/Vis Absorbance spectrum of BPQDs prepared in this paper. Raman spectra of (i) BPQDs and (j) BPNs [15].

Download Full Size | PPT Slide | PDF

The morphology of the as-prepared BPQDs was characterized by transmission electron microscopy (TEM) and atomic force microscopy (AFM) technology. The results of AFM measurement are shown in Figs. 1(c) and 1(e). The measurement of several quantum dots in Fig. 1(c) illustrates that the thickness of the two BPQDs is about 5.1 and 6.9 nm, respectively, as shown in the height profile of Fig. 1(d). In fact, AFM would usually overestimate the lateral dimensions due to the finite size of AFM tips, especially for samples down to few nanometers. Therefore, we utilize TEM for diameter measurement, as shown in Fig. 1(f). According to the statistical TEM and AFM analysis of quantitative BPQDs (Figs. 1(e) and 1(g)), the average lateral size was 5.7 ± 0.8 nm, and the average thickness was 5.6 ± 0.6 nm. Meanwhile, the thickness of BPNs is measured to be ~3.7 nm and the statistical results show that the thickness of BPNs is ~4 nm [15]. Thus it can be deduced that the BPQDs and BPNs prepared share similar thickness, however, the former is two dimensions confined while the latter is zero dimension confined.

UV/Vis absorption spectroscopy was used to investigate the optical property of BPQDs (Fig. 1(h)). The optical absorption spectrum acquired of the BPQDs shows a broad absorption band spanning the UV and NIR regions. Especially, there is a small absorption peak appearing at ~880 nm, revealing the optical band gap of as-prepared BPQDs to be ~1.4 eV. Furthermore, Raman spectroscopy of BPQDs and BPNs is shown in Figs. 1(i) and 1(j), respectively. Three prominent peaks can be attributed to one out-of-plane phonon Ag1 and two in-plane modes B2g and Ag2. Fig. 1(i) illustrates the Raman spectra of BPQDs while Fig. 1(j) corresponds to the counterpart of BPNs. Compared to BPNs, the Ag1, B2g and Ag2 modes of the BPQDs blue-shift by approximately 1.0, 1.6 and 2.2 cm−1, respectively. It was reported that the ratio of the Ag1/Ag2 phonon sensitively depends on sample degeneration as a result of oxidation [7]. The calculated results of the ratio Ag1/Ag2 are 0.69 and 0.63, respectively, which confirms the prepared BPQDs and BPNs samples to be unoxidizded [7].

2.2 Experimental setup

In order to investigate the NLO response and ultrafast excited carrier dynamics of BPQDs, femtosecond Z-scan and pump-probe technique are used in this paper. The experimental setup of Z-scan and pump-probe spectra system have been well described in our previous work [14,25]. The excitation laser at 800 nm is from a Ti: sapphire-type laser system with pulse width of 65 fs and repetition rate of 1 kHz. Then the laser goes through an optical parameter amplifier (OPA) and the excitation wavelength can be tunable optionally. Different from the solid sample measured before, the measurement of solution sample can be affected by optical tweezers effect seriously, especially near the focus [26]. Optical tweezers (originally called “single-beam gradient force trap”) are scientific instruments that use a highly focused laser beam to provide an attractive or repulsive force (typically on the order of piconewtons), depending on the refractive index mismatch to physically hold and move microscopic dielectric objects similar to tweezers. In Z-scan measurements for solution samples, the sample would be gradually gathered in the beam region because of optical tweezers effect. Thus the concentration of the sample in the area where laser passes through would increase during the whole process. Ensuring the solution sample be evenly excited by lasers and avoid the optical tweezers effect, a special spinning cuvette is used to contain the BPQDs and BPNs solutions. The details of the spinning cuvette can be found in our recent publication [25].

3. Results and discussion

3.1 Nonlinear optical absorption of BPQDs

The NLO absorption properties of BPQDs are investigated by OA Z-scan technique at the excitation of 800 nm, 1160 nm, 1300 nm, 1550 nm and 2μm. No obvious NLO response is found in the measurements of sapphire disks at these irradiances, which indicates that the NLO absorption and the transition arise mainly from BPQDs. The sample is firstly excited from lower intensities to higher and the nonlinear responses are recorded. After the measurement under the highest peak light intensity, the sample is put under lower intensity again and the similar results are obtained. Therefore, it can be deduced that BPQDs are not damaged even under the highest peak intensity in this paper.

The two different forms of BP nanostructures, namely BPQDs and BPNs, show quite different NLO responses. The NLO response under 1160 nm excitation is now taken for example. Fig. 2(a) shows the typical Z-scan results of the BPQDs excited by 1160 nm laser pulses with different irradiances. The excitation laser has a standard Gauss spot with the beam waist of ~100 μm, as shown in the inset of Fig. 2(a). According to our recent work, the NLO absorption of BPNs emerged at 11.59 GW/cm2 [15]. When the excitation on-focus intensity is above 11.59 GW/cm2, BPNs exhibit obvious SA response. That is, the total transmission increases monotonically as the intensity of the incident beam increases (z→0). When the intensity is 28.12 GW/cm2, the SA behavior becomes strongest. With higher excitation irradiance (above 282.9 GW/cm2), NLO absorption of the sample transforms from SA to RSA, where the transmittance reduces with the increasing intensity (z→0). However, BPQDs show obvious TPA response at all the excitation energy at 1160 nm, as shown in Fig. 2(a).

 

Fig. 2 (a) OA Z-Scan results for BPQDs, Inset: the photograph of the laser spot at focus. The scatters are experimental data and the solid lines show theoretical fit generated by the theory of Z-scan. (b) NLO absorption coefficient under different excitation irradiance at 1160 nm of BPQDs. Inset: Schematic of TPA process in BPQDs.

Download Full Size | PPT Slide | PDF

With the theory of Z-scan technique [27], the absorption coefficient α(I) consists of two parts, which can be expressed as α(I)=α0+αNLI. Where α0 is the linear absorption coefficient and αNL is the nonlinear absorption coefficient. The transmission curve for OA Z-Scan measurement is given by:

Topen(z)=1122αNLI0Leff1+(z/z0)2
where Leff is the sample effective length, I0 is the on-axis peak intensity at the focus, z is the longitudinal displacement of the sample from the focus and z0 is the Rayleigh diffraction length. By fitting the experimental data with Eq. (1), the values of NLO absorption coefficient (αNL) of BPQDs are shown in Fig. 2(b). αNL of BPQDs at 1160 nm is about (2.2 ± 0.15) × 10−2 cm/GW at 105.3 GW/cm2, and shows a fast rise up to (8.64 ± 0.75) × 10−2 cm/GW at 274.73 GW/cm2. Then gradually declines to (2.68 ± 0.17) × 10−2 cm/GW at 1307.34 GW/cm2. However, different from the irradiance-dependence for BPQDs’ nonlinear coefficient, αNL of BPNs exhibit a monotonous decrease with the increase of incident irradiance [15].

To explain the different irradiance-dependence NLO properties of BPNs and BPQDs, the NLO absorption mechanism needs to be discussed carefully, which is schematically shown in Fig. 3. If the photon energy is larger than bandgap, linear absorption will occur when the excitation irradiance is relatively low. With sufficiently strong excitation, the population of the photo-generated carriers increases significantly, which can cause the states near half of the photon energy to be filled. Due to Pauli’s exclusion principle, it’s impossible to have two identical electrons filling the same state. Thus the absorption of photons decrease and SA process happens. However, with the increasing photon density, the probability of absorbing two photons simultaneously to transit to high states increased as well. Then TPA domains and RSA response is observed. As a result, BPNs exhibit RSA behavior under much higher irradiances at 1160nm. Similarly, when these higher states have been fully occupied, the saturation of TPA process can also be observed. That’s why the NLO absorption coefficient declines with the increasing excitation irradiance [15].

 

Fig. 3 Schematics of the single photon SA process of BPNs under the excitation of 1160 nm pulsed laser at (a) low excitation irradiance, (b) middle excitation irradiance, (c) high excitation energy and the schematics of TPA process of BPQDs under the excitation of 1160 nm pulsed laser at (d) low excitation irradiance, (e) middle excitation irradiance and (f) high excitation energy.

Download Full Size | PPT Slide | PDF

When it comes to BPQDs, according to the results of X. Niu et al. [28], the size-dependent of BPQDs’ absorption gap can be described to the following equation:

Eabs=1.46+0.30/r2+1.31/r
where r is the diameter of the BPQDs and Eabs respects for the absorption gap. As shown in Fig. 1(e), the diameter of BPQDs is 4.9 ~6.5 nm. The absorption gap of BPQDs is calculated to be 1.67~1.74 eV by applying the Eq. (2). However, the DFT calculation was performed on monolayer BP, while the sample thickness in this work was around 5nm, namely about 6 stacked layers of BP. Because of the strong layer-dependent electronic structure of BP, one would expect a significantly smaller energy gap for few-layer sample than monolayer sample of 1.5 eV. However, electrons are strongly confined in quantum dots by 3 dimensions while 2D materials just have only 1 dimension confinement effect. So it’s reasonable to estimate as-prepared BPQDs’ band gap to about 1.4 eV extracted from the absorbance spectra in Fig. 1(h), which is larger than the photon energy of 1160 nm (namely 1.07 eV). Thus the electron of valence band cannot be excited by a single photon at low excitation irradiance, resulting in small NLO absorption coefficient at low irradiance, as shown in Fig. 3. With increasing of the excitation irradiance, the photon density becomes so large that TPA dominates. After two-photo-excitation, hot carriers cool down and occupy the empty states at the edge of conduction band. When the excitation intensity is high enough, the empty band states which can be occupied by the hot carriers excited by two photons (2.14 eV) will be fully filled, resulting in the saturation of the nonlinear coefficient as shown in Fig. 2(b).

The wavelength dependence of NLO response of BPQDs is illustrated in Fig. 4. Both BPNs [15] and BPQDs exhibit giant TPA process at all the wavelengths in this work. However, SA induced by one photon absorption only takes place at some wavelengths. For example, BPNs exhibit one photon SA at all the wavelengths but 2μm [15], while SA behavior can merely be observed at 800nm for BPQDs. In addition, the excitation irradiances needed for SA and TPA are quite distinct at different excitation wavelengths.

 

Fig. 4 Z-Scan results of BPQDs at (a) 800nm, (b) 1300nm, (c) 1550nm and (d) 2μm pulsed laser under different excitation irradiances. The scatters are experimental data and the solid lines show theoretical fit.

Download Full Size | PPT Slide | PDF

To investigate the dependence of NLO response on excitation wavelength, Table 1 summarizes the linear and NLO absorption coefficients of BPNs [15] and BPQDs extracted through Z-Scan measurements. The imaginary part of the third-order NLO susceptibility Im χ3 can be approximately expressed [29,30]:

Imχ3=107cλn296π2αNL
where c is the speed of light, λ is the wavelength of the incident light and n is the refractive index. The figure of merit (FOM) is defined for eliminating the discrepancy caused by the linear absorption α0: FOM = |Imχ30|. At excitation of 800 nm, Imχ3 of the BPQDs ((−1.77 ± 0.09) × 10−8) is about three times as large as the BPNs ((−6.57 ± 0.15) × 10−8). At 1550nm and 2000nm, the value of Imχ3 of BPQDs is still twice as large as that of BPNs. But the Imχ3 of BPQDs is slightly smaller than BPNs at 1160nm and 1300nm. Besides, BPNs and BPQDs have the same sign of Imχ3 at 800 and 2000 nm for both of them perform SA and TPA in the experiments. As for other excitation wavelength (namely 1160, 1300 and 1550 nm) they have the opposite sign of Imχ3, which origins from different nonlinear process (SA and TPA) of BPNs and BPQDs. It can be found that the behavior of FOM is similar to Imχ3, which results from the similar values of the linear absorption index α0 at the excitation wavelengths using in the experiments.

Tables Icon

Table 1. Linear and NLO absorption coefficients of BPNs [15] and BPQDs Using Z-Scan Technique

To further reveal the saturable absorption properties of BPQDs, the Z-scan results can be fitted by using the reported equation [10]: T=Aexp((δT)/(1+I/Is)), where A represents for the linear coefficient, δT the saturable modulation depth and Is the saturable irradiance. Fitting the Z-scan results through above equation, saturable modulation depth δT is extracted to be ~40% and the saturable irradiance Is is 20.04 GW/cm2.

According to the Z-scan results in this paper, BPQDs perform obvious SA process at 800 nm, with the saturable modulation depth δΤ ~40% and the saturable irradiance Is ~20.04 GW/cm2, inferring them ideal candidates for saturable absorbers in Q-switched and mode locked pulsed laser regions. At the same time, BPQDs exhibit giant TPA process from 1160 ~2000 nm, indicating BPQDs as ideal materials in optical limiting and optical protecting regions. Especially, applications as Q-switched and mode locked pulsed lasers have restrict requirement for the optical and electrical properties of saturable absorbers. Such as appropriate modulation depth, relatively high saturable irradiance and the fast SA recovery time. The recovery time of saturable absorbers directly determines whether Q-switched or mode locked pulsed laser it fits best, which require ns, ps time scale and ps, fs time scale of recovery time, respectively. In order to obtain the ultrafast laser pulse, shorter recovery time of saturable absorbers makes more sense. Therefore it’s of great importance to further study the excited carrier dynamics of BPQDs, which is detailed discussed in next section.

3.2 Excited carrier dynamics of BPQDs

Typical results of ultrafast pump-probe experiments of BPQDs are shown in Fig. 5. At the temperature of 77K, differential absorption signal (ΔA/A0) of BPQDs is measured at different pump intensities. The pump wavelength is 400 nm (photon energy = 3.1 eV), guaranteeing the carriers of BPQDs be fully excited. Fig. 5(a) illustrates the map of ΔA/A0 as a function of both pump-probe delay and probe photon wavelength. The average pump power is set about 500 μW, in other words, the pump fluence is ~160 μJ/cm2. As shown in Fig. 5(a), the positive value of ΔA/A0 indicates strong intraband PIA in BPQDs. The PIA signal appears from 470 nm to 850 nm, verifying the broadband optical properties of BP nanostructures [9–13]. The PIA signal can be explained as follows. After the electrons are excited from valence band to conduction band by absorbing the energy of pump photons, as shown in Fig. 5(d), they can be further excited by the probe photons to higher states of conduction band, resulting in the extra absorption of the probe laser, namely the positive value of ΔA/A0 in Fig. 5. The continuous broadband PIA signal from 470 nm to 850 nm infers the BPQDs’ continuous band structure of conduction band from 1.4 eV to 2.5 eV as shown in the shadow of Fig. 5(d).

 

Fig. 5 (a) Differential absorption (ΔA/A0) map of BPQDs as a function of both delay time and probe photon wavelength with a pump wavelength of 400 nm at average power of 500 μW (pump fluence = 160 μJ/cm2) and probe with the supercontinum white light at the temperature of 77 K. (b) Time evolution of the photon-induced differential absorption (ΔA/A0) as a function of probe delay at wavelength of 545 nm, 601 nm, 657 nm and 716 nm. Inset: Max value of ΔA/A0 as the function of probe photon wavelength, showing that ΔA/A0 is strongest when the probe photon wavelength is ~546 nm (2.27 eV). (c) ΔA/A0 measured with pump power from 200μW to 800μW (pump fluence from 64 to 256 μJ/cm2). The red arrow points out the pump power increasing direction. The inset shows a linear relation between the peak signal and the pump intensity. (d) Schematic of the photon-induced intraband absorption process of BPQDs in pump-probe experiments.

Download Full Size | PPT Slide | PDF

To further study the wavelength dependence of BPQDs’ excited carrier dynamics, time evolution of the photon-induced differential absorption as a function of probe delay at wavelengths of 545 nm, 601 nm, 657 nm and 716 nm are shown in Fig. 5(b), as along four horizontal dash lines in Fig. 5(a). The largest peak value of ΔA/A0 appears at the probe wavelength of 545 nm. The more precise study of the peak value of ΔA/A0 is carried out as shown in the inset of Fig. 5(b), showing that the max value of ΔA/A0 reaches the largest at 546 nm (2.27 eV). It’s worth a mention that the above results reveal the average excited carrier dynamic properties of a large amount of BPQDs with all orientations, due to the nature of liquid exfoliated dispersions [7, 10].

The excited carrier dynamic relaxation process at pump wavelength of 400 nm and probe wavelength of 546 nm under different average pump intensities is presented in Fig. 5(c). The experimental temperature is set at 77K. The main figure shows the experimental data with the theoretically fitting curve for a single exponential relaxation process while the inset depicts a linear relation between the peak value of ΔA/A0 and the pump power. Dynamic relaxation process exhibits an exponential decay, and it can be fitted by exponential decay function: y=A1e(xx0)/τ1 +A2e(xx0)/τ2 +y0 [28,29], where τ1 and τ2represents the fast and slow relaxation time during dynamic relaxation process and is obtained as long as 92 ± 10 ps and 1100 ± 100 ps, respectively. We believe that the fast decay τ1 and the slow decay τ2 are correlated to the exciton recombination processes and τ1 has a relatively good agreement with the reported results for BPNs [15, 18,19], while τ2 seems much longer than the results reported. The detailed discussion of the fast decay τ1 and the slow decay τ2 can be found in the following. It can be seen from the experimental results that ΔA/A0 witnesses a sudden rise which is much faster than the following carrier recombination process, thus the carrier absorbing process can be seen as an instantaneous response [10]. Therefore the rise time can be neglected and the exponential decay function above can be applied.

To further reveal the carrier recombination mechanism, the temperature and pump intensity dependence of BPQDs’ excited carrier lifetime is further analyzed. As shown in Fig. 6(a), with the increasing pump intensity, the fast decay and the slow decay time of BPQDs basically remains at 100 ps and 1000 ps at the temperature of 77 K. The temperature-dependence of excited carrier dynamics of BPQDs is performed from 77 K to 350 K. The ΔA/A0 spectra at different temperatures is shown in and the carrier lifetime is extracted from the experimental data in Fig. 6(b). As shown in the inset of Fig. 6(a), the peak of ΔA/A0 spectra broadens, and slightly redshifts with increasing temperature, possibly due to the temperature-dependence of the band gap and valence band structure of BP nanostructures [31,32]. However, the carrier lifetime of BPQDs exhibits no obvious temperature dependence over the entire temperature range in this paper. Fig. 6(b) shows that the two decay time almost stay unchanged at different temperature. To further reveal the recombination mechanism of BPQDs, sight is first taken into the three time regions of the pump probe decay curve. Three temporal regions are observed and marked in Fig. 6(c): (1) Upon photon-excitation of the pump pulse, ΔA/A0 reaches its positive maximum value within ~3 ps. (2) A fast decay of the positive ΔA/A0 then occurs within ~100 ps, which corresponds to the fast decay time scale extracted in the pump probe experiments. (3) Finally, a slow decay of the positive ΔA/A0 lasts for more than 1000 ps. Combined with the temperature-dependence of the decay time, the recombination mechanism of BPQDs then can be deduced to be defect-assisted Auger process.

 

Fig. 6 (a) Carrier lifetime of BPQDs (exciton recombination time) under different pump power at the temperature of 77K. Inset: ΔA/A0 spectra of BPQDs under different temperature, showing a redshift of the spectra peak with the increasing temperature. (b) Carrier lifetime of BPQDs at different experimental temperature, where the pump power is 200 μW (pump fluence = 64 μJ/cm2). (c) shows three different temporal regions: (1) ΔA/A0 reaches its positive maximum value within ~3 ps. (2) A fast decay of the positive ΔA/A0 then occurs within ~100 ps. (3) Finally, a slow decay of the positive ΔA/A0 lasts for more than 1000 ps. (d) Schematic of defect-assisted Auger carrier capture process in the two temporal regions: (1) After photoexcitation, the carriers thermalize and cool and form a correlated electron−hole plasma. (2) Most of the holes and the electrons are captured by the fast defects within 100 ps time scale. (3) After all the photoexcited holes have been captured and the electrons have filled the traps completely, the direct and indirect electron-hole radiative recombination process then domains and lasts more than 1000 ps.

Download Full Size | PPT Slide | PDF

The direct recombination mechanism is strongly dependent on temperature [33,34]. Electron and hole capture by defects in defect-assisted recombination occurs mainly by phonon-assisted processes and Auger process. The carrier capture rates in all phonon-assisted processes depend strongly on the lattice temperature [33]. In contrast, the rate of carrier capture by defects via Auger process is largely temperature independent and consistent with our experimental results [35,36]. Owing to the strong space confinement of QDs, electronic wave functions are forced to overlap and the dielectric screening is reduced, resulting in significant enhancement of carrier–carrier coulomb interactions [37,38]. Moreover, strong confinement also leads to discrete electron and hole levels, which will inhibit phonon emission (“phonon bottleneck”). Energy releasing from excited carriers or recombination of excitons will not dissipate as heat, but transfer to another carrier. These properties lead to various Auger processes [35,36]. Therefore it’s reasonable to assume that the carrier recombination mechanism in BPQDs in this paper may turn out to be defect-assisted Auger process. The excited carrier relaxation process in BPQDs is presented in the inset of Fig. 6(b) and consists of two main steps corresponding to the two temporal regions in the schematic. (1) After photoexcitation, the carriers thermalize and cool and form a correlated electron−hole plasma. (2) Most of the holes and the electrons are captured by the fast defects within 100 ps time scale. This step is fast and is responsible for the slow time scale observed in our experiments as long as ~100 ps. (3) After all the photoexcited holes have been captured and the electrons have filled the traps completely, the radiative electorom-hole recombination process then domains and lasts more than 1000 ps. Importantly, this process may be attributed to direct and indirect recombination. Since we used a 400nm (3.1eV) pump laser for the pump-probe measurement, such high photon energy is likely to excite the carriers into higher conduction bands, or causing electron relaxing into local conduction-band-minimal other than Z point in the Brillouin zone, which would subsequently result in an indirect recombination. Either of the cases can contribute to a slow recombination process, which is responsible for the slow time scale observed in our experiments as long as more than 1000 ps. According to the results of pump probe experiments, BPQDs are not suitable for mode locked pulsed lasers, but they can be used to obtain Q-switched lasers of ns pulse duration.

Actually, BPQDs and BPNs share similar thickness in our experiments, but their ultrafast NLO response and excited carrier dynamics differ a lot. The remarkable distinct nonlinear absorption properties and excited carrier dynamics of BPQDs and BPNs are attributed to their significant different low-dimensional confinements and giant TPA resonances. The energy levels of BP convert from continuous BPNs to discrete BPQDs, resulting in the different NLO behaviors of BPNs and BPQDs at different excitation wavelengths. In addition, the size and thickness of BPQDs have a greater impact on confinement effect than BPNs because BPQDs have quantum scale in all three dimensions, leading to the larger energy gap of BPQDs than BPNs even at the same thickness.

4. Summary

In conclusion, the ultrafast NLO properties and excited carrier dynamics of BPQDs are investigated by the femtosecond OA Z-scan technique and pump-probe technique in a wide spectra. The BPNs exhibit giant SA response at 1160 nm excitation, while BPQDs perform great TPA process with the TPA coefficient of (2.39 ± 0.2) × 10−2 cm/GW. The wavelength dependence of their NLO absorption have also been studied. With different excitation energy, BPNs performs both SA and TPA at the excitation of 800 nm, 1160 nm, 1300 nm, 1550 nm but merely TPA at 2μm [15]. In comparison, SA and TPA can be generated in succession only at the wavelength of 800nm for BPQDs. At the other wavelengths used in this paper, BPQDs exhibit only TPA response. In the pump-probe experiments, a fast and a slow decay time are extracted through the experimental data as long as 92 ± 10 ps and 1100 ± 100 ps, respectively, and stays almost constant at different pump intensities, which infers that BPQDs are fit for ultrafast Q-switched nanosecond lasers. The probe wavelength where peak value of ΔA/A0 reaches the largest is ~546 nm and slightly red-shifts with increasing experiment temperature. Furthermore, the remarkable independence of pump intensity and temperature for ultra-long carrier lifetime reveals that the carrier recombination mechanism may be attributed to defect-assisted Auger capture process. The remarkably distinct nonlinear absorption properties and excited carrier dynamics of BPQDs and BPNs are resulted from their significant different low-dimensional confinements and giant TPA resonances. This paper provides deep insight into broadband NLO and excited carrier dynamic properties of BPQDs, which is required for incorporating them into device designs, such as optical modulators and switches in this wavelength region, and other ultrafast photonics devices.

Funding

Scientific Research Foundation of National University of Defense Technology (No. zk16-03-59); Open Funding of Key Laboratory of Electro-Optical Countermeasures Test and Evaluation Technology (No. gkcp2016005).

References and links

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef]   [PubMed]  

2. X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012). [CrossRef]   [PubMed]  

3. D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016). [CrossRef]   [PubMed]  

4. L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013). [CrossRef]   [PubMed]  

5. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014). [CrossRef]   [PubMed]  

6. H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014). [CrossRef]   [PubMed]  

7. D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015). [CrossRef]   [PubMed]  

8. Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015). [CrossRef]   [PubMed]  

9. Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016). [CrossRef]  

10. K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016). [CrossRef]   [PubMed]  

11. S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015). [CrossRef]   [PubMed]  

12. L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016). [CrossRef]  

13. H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015). [CrossRef]  

14. X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of black phosphorus nanoplatelets with femtosecond pulsed Z-scan measurements,” Opt. Lett. 40(15), 3480–3483 (2015). [CrossRef]   [PubMed]  

15. R. Chen, Y. Tang, X. Zheng, and T. Jiang, “Giant nonlinear absorption and excited carrier dynamics of black phosphorus few-layer nanosheets in broadband spectra,” Appl. Opt. 55(36), 10307–10312 (2016). [CrossRef]   [PubMed]  

16. Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015). [CrossRef]  

17. R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016). [CrossRef]   [PubMed]  

18. J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015). [CrossRef]   [PubMed]  

19. S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015). [CrossRef]   [PubMed]  

20. H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Nanosecond passively Q-switched thulium/holmium-doped fiber laser based on black phosphorus nanoplatelets,” Opt. Mater. Express 6(2), 603–609 (2016). [CrossRef]  

21. H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Thulium/holmium-doped fiber laser passively mode locked by black phosphorus nanoplatelets-based saturable absorber,” Appl. Opt. 54(34), 10290–10294 (2015). [CrossRef]   [PubMed]  

22. J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014). [CrossRef]   [PubMed]  

23. L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014). [CrossRef]   [PubMed]  

24. K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009). [CrossRef]   [PubMed]  

25. K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater . 4(12), 1993–1997 (2016).

26. A. A. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, M. W. Berns, and H. Rubinsztein-Dunlop, “Escape forces and trajectories in optical tweezers and their effect on calibration,” Opt. Express 23(19), 24317–24330 (2015). [CrossRef]   [PubMed]  

27. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]  

28. X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016). [CrossRef]   [PubMed]  

29. K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013). [CrossRef]   [PubMed]  

30. S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015). [CrossRef]   [PubMed]  

31. D. Warschauer, “Electrical and optical properties of crystalline black phosphorus,” J. Appl. Phys. 34(7), 1853–1860 (1963). [CrossRef]  

32. M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991). [CrossRef]  

33. M. Lax, “Cascade capture of electrons in solids,” Phys. Rev. 119(5), 1502–1523 (1960). [CrossRef]  

34. B. K. Ridley, Quantum Processes in Semiconductors (Oxford University, 2013).

35. P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1992).

36. D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980). [CrossRef]  

37. J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008). [CrossRef]   [PubMed]  

38. S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985). [CrossRef]   [PubMed]  

References

  • View by:
  • |
  • |
  • |

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
    [Crossref] [PubMed]
  2. X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
    [Crossref] [PubMed]
  3. D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
    [Crossref] [PubMed]
  4. L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
    [Crossref] [PubMed]
  5. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
    [Crossref] [PubMed]
  6. H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014).
    [Crossref] [PubMed]
  7. D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
    [Crossref] [PubMed]
  8. Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
    [Crossref] [PubMed]
  9. Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
    [Crossref]
  10. K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
    [Crossref] [PubMed]
  11. S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
    [Crossref] [PubMed]
  12. L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
    [Crossref]
  13. H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
    [Crossref]
  14. X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of black phosphorus nanoplatelets with femtosecond pulsed Z-scan measurements,” Opt. Lett. 40(15), 3480–3483 (2015).
    [Crossref] [PubMed]
  15. R. Chen, Y. Tang, X. Zheng, and T. Jiang, “Giant nonlinear absorption and excited carrier dynamics of black phosphorus few-layer nanosheets in broadband spectra,” Appl. Opt. 55(36), 10307–10312 (2016).
    [Crossref] [PubMed]
  16. Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
    [Crossref]
  17. R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
    [Crossref] [PubMed]
  18. J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
    [Crossref] [PubMed]
  19. S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
    [Crossref] [PubMed]
  20. H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Nanosecond passively Q-switched thulium/holmium-doped fiber laser based on black phosphorus nanoplatelets,” Opt. Mater. Express 6(2), 603–609 (2016).
    [Crossref]
  21. H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Thulium/holmium-doped fiber laser passively mode locked by black phosphorus nanoplatelets-based saturable absorber,” Appl. Opt. 54(34), 10290–10294 (2015).
    [Crossref] [PubMed]
  22. J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014).
    [Crossref] [PubMed]
  23. L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
    [Crossref] [PubMed]
  24. K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
    [Crossref] [PubMed]
  25. K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater.  4(12), 1993–1997 (2016).
  26. A. A. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, M. W. Berns, and H. Rubinsztein-Dunlop, “Escape forces and trajectories in optical tweezers and their effect on calibration,” Opt. Express 23(19), 24317–24330 (2015).
    [Crossref] [PubMed]
  27. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
    [Crossref]
  28. X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
    [Crossref] [PubMed]
  29. K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
    [Crossref] [PubMed]
  30. S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
    [Crossref] [PubMed]
  31. D. Warschauer, “Electrical and optical properties of crystalline black phosphorus,” J. Appl. Phys. 34(7), 1853–1860 (1963).
    [Crossref]
  32. M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
    [Crossref]
  33. M. Lax, “Cascade capture of electrons in solids,” Phys. Rev. 119(5), 1502–1523 (1960).
    [Crossref]
  34. B. K. Ridley, Quantum Processes in Semiconductors (Oxford University, 2013).
  35. P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1992).
  36. D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980).
    [Crossref]
  37. J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
    [Crossref] [PubMed]
  38. S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
    [Crossref] [PubMed]

2016 (9)

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

R. Chen, Y. Tang, X. Zheng, and T. Jiang, “Giant nonlinear absorption and excited carrier dynamics of black phosphorus few-layer nanosheets in broadband spectra,” Appl. Opt. 55(36), 10307–10312 (2016).
[Crossref] [PubMed]

R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
[Crossref] [PubMed]

H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Nanosecond passively Q-switched thulium/holmium-doped fiber laser based on black phosphorus nanoplatelets,” Opt. Mater. Express 6(2), 603–609 (2016).
[Crossref]

K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater.  4(12), 1993–1997 (2016).

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

2015 (11)

A. A. Bui, A. B. Stilgoe, N. Khatibzadeh, T. A. Nieminen, M. W. Berns, and H. Rubinsztein-Dunlop, “Escape forces and trajectories in optical tweezers and their effect on calibration,” Opt. Express 23(19), 24317–24330 (2015).
[Crossref] [PubMed]

H. Yu, X. Zheng, K. Yin, X. Cheng, and T. Jiang, “Thulium/holmium-doped fiber laser passively mode locked by black phosphorus nanoplatelets-based saturable absorber,” Appl. Opt. 54(34), 10290–10294 (2015).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of black phosphorus nanoplatelets with femtosecond pulsed Z-scan measurements,” Opt. Lett. 40(15), 3480–3483 (2015).
[Crossref] [PubMed]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

2014 (4)

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014).
[Crossref] [PubMed]

J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014).
[Crossref] [PubMed]

L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
[Crossref] [PubMed]

2013 (2)

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

2012 (1)

X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
[Crossref] [PubMed]

2009 (1)

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

2008 (1)

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

1991 (1)

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

1985 (1)

S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
[Crossref] [PubMed]

1980 (1)

D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980).
[Crossref]

1963 (1)

D. Warschauer, “Electrical and optical properties of crystalline black phosphorus,” J. Appl. Phys. 34(7), 1853–1860 (1963).
[Crossref]

1960 (1)

M. Lax, “Cascade capture of electrons in solids,” Phys. Rev. 119(5), 1502–1523 (1960).
[Crossref]

Abellan, G.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Akimov, A. V.

R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
[Crossref] [PubMed]

Baba, M.

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

Backes, C.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Bao, H. F.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Bao, Q.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Bao, Q. L.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Belle, B. D.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Bellus, M. Z.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Berner, N. C.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Berns, M. W.

Blau, W. J.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Boey, F.

X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
[Crossref] [PubMed]

Boland, C.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Britnell, L.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Bui, A. A.

Casiraghi, C.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Castro Neto, A. H.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Chemla, D. S.

S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
[Crossref] [PubMed]

Chen, C.

L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
[Crossref] [PubMed]

Chen, J.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Chen, R.

Chen, X. H.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Chen, Y.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Chen, Z.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Cheng, H.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Cheng, X.

Chiu, H. Y.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Chu, P. K.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Churchill, H. O. H.

H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014).
[Crossref] [PubMed]

Coleman, J. N.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Cucinotta, C. S.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Cui, Q.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Dai, J.

J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014).
[Crossref] [PubMed]

Doherty, E.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Dong, N.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Du, B.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Duesberg, G. S.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Eckmann, A.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Fan, D. Y.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref] [PubMed]

Fan, J.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Fang, W.

R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
[Crossref] [PubMed]

Feng, D.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Feng, J.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Feng, Y.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Fossard, F.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Fox, D.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Francoeur, S.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Frauenheim, T.

L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
[Crossref] [PubMed]

Ge, Q.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Ge, S.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Geim, A. K.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Georgiou, T.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Gholamvand, Z.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Gorbachev, R. V.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Grigorenko, A. N.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Guo, Z.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Guo, Z. N.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Hanlon, D.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Harvey, A.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Hauke, F.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

He, D.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

He, J.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Heureux, A. L. P.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Hirsch, A.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Huang, G.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Huang, H.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Huang, X.

X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
[Crossref] [PubMed]

Jalil, R.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Jarillo-Herrero, P.

H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014).
[Crossref] [PubMed]

Jia, S.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Jiang, B.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Jiang, T.

Joo, J.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Khatibzadeh, N.

Kim, Y. J.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Klimov, V. I.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

Kong, L.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Kou, L.

L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
[Crossref] [PubMed]

Landsberg, P. T.

D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980).
[Crossref]

Lau, S. P.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Lax, M.

M. Lax, “Cascade capture of electrons in solids,” Phys. Rev. 119(5), 1502–1523 (1960).
[Crossref]

Lee, K.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Leonelli, R.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Lévesque, P. L.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Li, C.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Li, L.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Li, P. F.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Li, Y.

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Lin, S.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Lin, S. H.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Liu, J.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Loiseau, A.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Long, R.

R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
[Crossref] [PubMed]

Lotya, M.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Lu, S. B.

Lyding, J. W.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Lynch, P.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Magan, J. J.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

Mao, D.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Martel, R.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

McEvoy, N.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

McGuire, J. A.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

Miao, L. L.

Miller, D. A.

S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
[Crossref] [PubMed]

Mishchenko, A.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Morita, A.

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

Morozov, S. V.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Moynihan, G.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Mu, H.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Mu, H. R.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Nakamura, Y.

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

Nicolosi, V.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Nieminen, T. A.

Niu, X.

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

Novoselov, K. S.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

O’Brien, M.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

O’Neill, A.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

O’Regan, D. D.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Ou, X.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Pan, C. X.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Pietryga, J. M.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

Pokle, A.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Qi, X.

Qian, L.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Qin, Z.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Qiu, J.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Ramasse, Q. M.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Ribeiro, R. M.

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Ritter, K. A.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Robbins, D. J.

D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980).
[Crossref]

Rubinsztein-Dunlop, H.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Sanvito, S.

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Schaller, R. D.

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

Schmitt-Rink, S.

S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
[Crossref] [PubMed]

Shao, J.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

She, X.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Shen, C.

K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater.  4(12), 1993–1997 (2016).

Shi, G.

Shibata, K.

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

Shu, H.

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

Stilgoe, A. B.

Sun, D.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Sun, Z.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Szydlowska, B. M.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

Tang, D. Y.

Tang, N. Y.-W.

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Tang, S.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Tang, Y.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Wang, G.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

Wang, H.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Wang, J.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Wang, J. J.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

Wang, K.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Wang, Q.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Wang, Y.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Wang, Z.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Wang, Z. C.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Warschauer, D.

D. Warschauer, “Electrical and optical properties of crystalline black phosphorus,” J. Appl. Phys. 34(7), 1853–1860 (1963).
[Crossref]

Wei, K.

K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater.  4(12), 1993–1997 (2016).

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Wen, S. C.

Winters, S.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Wu, H.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Xiao, Q.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Xiao, S.

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Xie, G.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Xie, H.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Xu, Y.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Xu, Z.

Yang, D.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Ye, G. J.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Yim, C.

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Yin, K.

Yu, H.

Yu, X.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Yu, X. F.

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Yu, Y.

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Yuan, P.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Zeng, H.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Zeng, X. C.

J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014).
[Crossref] [PubMed]

Zhang, C.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Zhang, H.

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref] [PubMed]

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
[Crossref] [PubMed]

Zhang, J.

Zhang, L.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Zhang, S.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

Zhang, W.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Zhang, X.

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Zhang, Y.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

Zhang, Z.

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Zhao, C. J.

Zhao, H.

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

Zhao, J.

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Zhao, Q.

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

Zheng, X.

Acc. Chem. Res. (1)

J. A. McGuire, J. Joo, J. M. Pietryga, R. D. Schaller, and V. I. Klimov, “New aspects of carrier multiplication in semiconductor nanocrystals,” Acc. Chem. Res. 41(12), 1810–1819 (2008).
[Crossref] [PubMed]

ACS Nano (4)

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast saturable absorption of two-dimensional MoS2 nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref] [PubMed]

S. Zhang, N. Dong, N. McEvoy, M. O’Brien, S. Winters, N. C. Berner, C. Yim, Y. Li, X. Zhang, Z. Chen, L. Zhang, G. S. Duesberg, and J. Wang, “Direct observation of degenerate two-photon absorption and its saturation in WS2 and MoS2 monolayer and few-layer films,” ACS Nano 9(7), 7142–7150 (2015).
[Crossref] [PubMed]

J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Exceptional and anisotropic transport properties of photocarriers in black phosphorus,” ACS Nano 9(6), 6436–6442 (2015).
[Crossref] [PubMed]

K. Wang, B. M. Szydłowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref] [PubMed]

Adv. Opt. Mater (1)

K. Wei, X. Zheng, X. Cheng, C. Shen, and T. Jiang, “Observation of ultrafast exciton–exciton annihilation in CsPbBr3 quantum dots,” Adv. Opt. Mater.  4(12), 1993–1997 (2016).

Adv. Opt. Mater. (2)

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

H. R. Mu, S. H. Lin, Z. C. Wang, S. Xiao, P. F. Li, Y. Chen, H. Zhang, H. F. Bao, S. P. Lau, C. X. Pan, D. Y. Fan, and Q. L. Bao, “Black phosphorus–polymer composites for pulsed lasers,” Adv. Opt. Mater. 3(10), 1447–1453 (2015).
[Crossref]

Angew. Chem. Int. Ed. Engl. (1)

Z. Sun, H. Xie, S. Tang, X. F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, and P. K. Chu, “Ultrasmall black phosphorus quantum dots: Synthesis and use as photothermal agents,” Angew. Chem. Int. Ed. Engl. 54(39), 11526–11530 (2015).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Chem. Soc. Rev. (1)

X. Huang, X. Qi, F. Boey, and H. Zhang, “Graphene-based composites,” Chem. Soc. Rev. 41(2), 666–686 (2012).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

J. Appl. Phys. (2)

D. Warschauer, “Electrical and optical properties of crystalline black phosphorus,” J. Appl. Phys. 34(7), 1853–1860 (1963).
[Crossref]

M. Baba, Y. Nakamura, K. Shibata, and A. Morita, “Photoconduction of black phosphorus in the infrared region,” J. Appl. Phys. 30(2), 1178 (1991).
[Crossref]

J. Phys. C Solid State Phys. (1)

D. J. Robbins and P. T. Landsberg, “Impact ionisation and auger recombination involving traps in semiconductors,” J. Phys. C Solid State Phys. 13(12), 2425–2439 (1980).
[Crossref]

J. Phys. Chem. Lett. (4)

X. Niu, Y. Li, H. Shu, and J. Wang, “Anomalous size dependence of optical properties in black phosphorus quantum dots,” J. Phys. Chem. Lett. 7(3), 370–375 (2016).
[Crossref] [PubMed]

J. Dai and X. C. Zeng, “Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells,” J. Phys. Chem. Lett. 5(7), 1289–1293 (2014).
[Crossref] [PubMed]

L. Kou, T. Frauenheim, and C. Chen, “Phosphorene as a superior gas sensor: Selective adsorption and distinct I–V response,” J. Phys. Chem. Lett. 5(15), 2675–2681 (2014).
[Crossref] [PubMed]

R. Long, W. Fang, and A. V. Akimov, “Nonradiative electron–hole recombination rate is greatly reduced by defects in monolayer black phosphorus: Ab initio time domain study,” J. Phys. Chem. Lett. 7(4), 653–659 (2016).
[Crossref] [PubMed]

Laser Phys. Lett. (1)

L. Kong, Z. Qin, G. Xie, Z. Guo, H. Zhang, P. Yuan, and L. Qian, “Black phosphorus as broadband saturable absorber for pulsed lasers from 1 μm to 2.7 μm wavelength,” Laser Phys. Lett. 13(4), 045801 (2016).
[Crossref]

Nano Lett. (1)

S. Ge, C. Li, Z. Zhang, C. Zhang, Y. Zhang, J. Qiu, Q. Wang, J. Liu, S. Jia, J. Feng, and D. Sun, “Dynamical evolution of anisotropic response in black phosphorus under ultrafast photoexcitation,” Nano Lett. 15(7), 4650–4656 (2015).
[Crossref] [PubMed]

Nat. Commun. (1)

D. Hanlon, C. Backes, E. Doherty, C. S. Cucinotta, N. C. Berner, C. Boland, K. Lee, A. Harvey, P. Lynch, Z. Gholamvand, S. Zhang, K. Wang, G. Moynihan, A. Pokle, Q. M. Ramasse, N. McEvoy, W. J. Blau, J. Wang, G. Abellan, F. Hauke, A. Hirsch, S. Sanvito, D. D. O’Regan, G. S. Duesberg, V. Nicolosi, and J. N. Coleman, “Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics,” Nat. Commun. 6, 8563 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

K. A. Ritter, J. W. Lyding, F. Fossard, A. L. P. Heureux, N. Y.-W. Tang, P. L. Lévesque, A. Loiseau, R. Leonelli, S. Francoeur, and R. Martel, “The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons,” Nat. Mater. 8(3), 235–242 (2009).
[Crossref] [PubMed]

Nat. Nanotechnol. (2)

L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014).
[Crossref] [PubMed]

H. O. H. Churchill and P. Jarillo-Herrero, “Two-dimensional crystals: Phosphorus joins the family,” Nat. Nanotechnol. 9(5), 330–331 (2014).
[Crossref] [PubMed]

Nature (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. (1)

M. Lax, “Cascade capture of electrons in solids,” Phys. Rev. 119(5), 1502–1523 (1960).
[Crossref]

Phys. Rev. B Condens. Matter (1)

S. Schmitt-Rink, D. S. Chemla, and D. A. Miller, “Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures,” Phys. Rev. B Condens. Matter 32(10), 6601–6609 (1985).
[Crossref] [PubMed]

Science (1)

L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013).
[Crossref] [PubMed]

Small (1)

D. Mao, B. Du, D. Yang, S. Zhang, Y. Wang, W. Zhang, X. She, H. Cheng, H. Zeng, and J. Zhao, “Nonlinear saturable absorption of liquid-exfoliated molybdenum/tungsten ditelluride nanosheets,” Small 12(11), 1489–1497 (2016).
[Crossref] [PubMed]

Other (2)

B. K. Ridley, Quantum Processes in Semiconductors (Oxford University, 2013).

P. T. Landsberg, Recombination in Semiconductors (Cambridge University, 1992).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 TEM of the (a) BPQDs and (b) BPNs. Insets are photographs of BPQDs and BPNs in glass vials, respectively. (c) AFM image of BPQDs. (d) Height profile of the red line marked in (c). (e) Statistical analysis of the height of 85 BPQDs determined by AFM. (f) Magnified TEM image. (g) Statistical analysis of the sizes of 100 BPQDs measured from TEM images (h) UV/Vis Absorbance spectrum of BPQDs prepared in this paper. Raman spectra of (i) BPQDs and (j) BPNs [15].
Fig. 2
Fig. 2 (a) OA Z-Scan results for BPQDs, Inset: the photograph of the laser spot at focus. The scatters are experimental data and the solid lines show theoretical fit generated by the theory of Z-scan. (b) NLO absorption coefficient under different excitation irradiance at 1160 nm of BPQDs. Inset: Schematic of TPA process in BPQDs.
Fig. 3
Fig. 3 Schematics of the single photon SA process of BPNs under the excitation of 1160 nm pulsed laser at (a) low excitation irradiance, (b) middle excitation irradiance, (c) high excitation energy and the schematics of TPA process of BPQDs under the excitation of 1160 nm pulsed laser at (d) low excitation irradiance, (e) middle excitation irradiance and (f) high excitation energy.
Fig. 4
Fig. 4 Z-Scan results of BPQDs at (a) 800nm, (b) 1300nm, (c) 1550nm and (d) 2μm pulsed laser under different excitation irradiances. The scatters are experimental data and the solid lines show theoretical fit.
Fig. 5
Fig. 5 (a) Differential absorption (ΔA/A0) map of BPQDs as a function of both delay time and probe photon wavelength with a pump wavelength of 400 nm at average power of 500 μW (pump fluence = 160 μJ/cm2) and probe with the supercontinum white light at the temperature of 77 K. (b) Time evolution of the photon-induced differential absorption (ΔA/A0) as a function of probe delay at wavelength of 545 nm, 601 nm, 657 nm and 716 nm. Inset: Max value of ΔA/A0 as the function of probe photon wavelength, showing that ΔA/A0 is strongest when the probe photon wavelength is ~546 nm (2.27 eV). (c) ΔA/A0 measured with pump power from 200μW to 800μW (pump fluence from 64 to 256 μJ/cm2). The red arrow points out the pump power increasing direction. The inset shows a linear relation between the peak signal and the pump intensity. (d) Schematic of the photon-induced intraband absorption process of BPQDs in pump-probe experiments.
Fig. 6
Fig. 6 (a) Carrier lifetime of BPQDs (exciton recombination time) under different pump power at the temperature of 77K. Inset: ΔA/A0 spectra of BPQDs under different temperature, showing a redshift of the spectra peak with the increasing temperature. (b) Carrier lifetime of BPQDs at different experimental temperature, where the pump power is 200 μW (pump fluence = 64 μJ/cm2). (c) shows three different temporal regions: (1) ΔA/A0 reaches its positive maximum value within ~3 ps. (2) A fast decay of the positive ΔA/A0 then occurs within ~100 ps. (3) Finally, a slow decay of the positive ΔA/A0 lasts for more than 1000 ps. (d) Schematic of defect-assisted Auger carrier capture process in the two temporal regions: (1) After photoexcitation, the carriers thermalize and cool and form a correlated electron−hole plasma. (2) Most of the holes and the electrons are captured by the fast defects within 100 ps time scale. (3) After all the photoexcited holes have been captured and the electrons have filled the traps completely, the direct and indirect electron-hole radiative recombination process then domains and lasts more than 1000 ps.

Tables (1)

Tables Icon

Table 1 Linear and NLO absorption coefficients of BPNs [15] and BPQDs Using Z-Scan Technique

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

T open (z)=1 1 2 2 α NL I 0 L eff 1+ (z/ z 0 ) 2
E abs =1.46+0.30/ r 2 +1.31/r
Im χ 3 = 10 7 cλ n 2 96 π 2 α NL

Metrics