Electrically tunable valley polarization and valley coherence in monolayer WSe<sub>2</sub> embedded in a van der Waals heterostructure [Invited]

Chitraleema Chakraborty; Arunabh Mukherjee; Liangyu Qiu; A. Nick Vamivakas

doi:10.1364/OME.9.001479

1. Introduction

Two-dimensional (2D) materials have been the subject of intense research during the past decade owing to their exotic optical properties and their potential to be integrated with photonic and opto-electronic circuitry [1–6]. In particular, transition metal dichalcogenides (TMDCs) are highly desirable due to their layer dependent bandgap, large exciton binding energy [7, 8] stabilizing excitons at room temperature and possibility to serveas sources of quantum light [9–14]. Of additional interest is that the momentum index of electronic excitations can give rise to a binary pseudospin. Valleytronics, in analogy to spintronics, is the concept of using the valley index of charge carriers in these materials as an information bearing entity. In TMDCs, due to inversion symmetry breaking and valley dependent optical selection rules, each K valley in the momentum space can be uniquely addressed using circularly polarized light of opposite helicity and this gives rise to valley contrasted photoluminescence (PL). To utilize the valley degree of freedom in valleytronic devices, electrical as well as optical approaches to its manipulation are necessary.

There is precedence for the electric field control of the valley degree of freedom. Electrically switchable valley polarization has been demonstrated in the electroluminescence (EL) of monolayer semiconductors [15, 16] as well as in the PL in bilayers [17, 18]. However, no significiant tunability of valley coherence or valley polarization has been observed for polarization resolved PL in TMDC monolayers. The primary reason is that in monolayer TMDCs the two valley excitons are coupled by the electron-hole Coulomb exchange interaction that limits the exciton valley depolarization [19].

A convenient approach to control the valley DOF is to use the applied electrical field in a van der Waals heterostructure. van der Waals heterostructures, the layering of 2D materials, have come to play an important role in 2D material science and technology. The demonstration of interlayer excitons [20], light-emitting diodes [21, 22], quantum-confined Stark effect [23] and even efficient charging [24, 25] have been realized using assembled van der Waals materials. In this work we leverage a van der Waals heterostructure to demonstrate electrical tunability of the valley polarization and valley coherence in a monolayer TMDC. We show that the exchange induced valley depolarization can be controlled by the application of an external electric field by modifying the overlap of the electron and hole wave functions in the heterostructure device. Critical in our device is the ability to minimize electrostatic doping and only apply electric fields across the 2D semiconductor layer WSe $_{2}$ .

Fig. 1 (a) Schematic of the van der Waals heterostructure used to form a vertical field effect diode. Inset: Band diagram of the monolayer under a vertically applied electric field. (b) Voltage controlled PL spectra. The neutral exciton X $^{0}$ and negative charged exciton, the trion, X $^{- 1}$ are indicated.

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2. Design and optical characterization of the van der Waals device

Our device [Fig. 1(a)] is composed of a five-layer van der Waals heterostructure [26] with a monolayer WSe $_{2}$ encapsulated between two dielectric layers of hBN, and two few-layer graphene (FLG) serving as the top and bottom transparent electrodes. The FLG layers are in contact with pre-patterned gold electrodes on a n-doped Si substrate with 285 nm of SiO $_{2}$ on top. All the layers were mechanically exfoliated from bulk crystals on viscoelastic PDMS substrate followed by an all dry transfer on the Si/SiO $_{2}$ using the same PDMS layer as a stamp [27]. All experiments are conducted at 4.2K in an Attodry 1000 cryostat. The sample is optically excited by focusing a laser of wavelength 675 nm into a diffraction limited spot using an objective of 0.82 NA. Excitation power is 20 $μ W$ . Voltage is applied through a Keithley sourcemeter. The device is operated at a bias below the onset of tunnel conductivity to obtain maximum field effect without signal from electroluminescence or charging crossover in the device [21].

A similar device geometry, incorporating different dielectrics on either side of the monolayer, was used to demonstrate the quantum-confined Stark effect of excitons in monolayer [28] and few layer MoS $_{2}$ [29]. And, such a device has also been used to demonstrate electroluminescence [21], controlled charging [24, 25] and Stark effect in single photon emitters [23] hosted by 2D materials. In our device, application of an electric field leads to band realignment [inset Fig. 1(a)] and a concurrent modulation in the separation of the electron-hole wavefunctions of the exciton which impacts the electron-hole exchange interaction.

Fig. 2 (a) Energy and (b) PL intensity of the neutral exciton (X $^{0}$ ) and trion (X $^{-}$ ) as a function of voltage extracted by peak fitting from Fig. 1(b).

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3. Voltage-controlled PL emission

Figure 1(b) shows the evolution of the PL spectra as a function of the electric field (applied voltage). We observe the neutral excitons (X $^{0}$ ) emission at $\sim 1.74$ eV. Because the WSe $_{2}$ monolayer is n-doped, we also observe emission from trions which are negatively charged excitons (X $^{-}$ ) at $\sim 1.71$ eV, without any external electrostatic doping. These peak assignments are consistent with previous reports [30]. To extract the peak energy and the emission intensity as a function of voltage, we peak fit linecuts at each voltage and plotthem in Fig. 2. In Fig. 2(a), the extracted energies of the neutral exciton and trion versus applied voltage are plotted. Both the features show a quadratic shift due to the quantum confined Stark effect. The maximum shift in energy of the neutral exciton and trion peak is ∼1.1 meV and ∼ 1.8 meV respectively. The data in Fig. 2(a) is fit to a second order polynomial equation in electric field [28]:

E = E_{0} - μ F - α F^{2}

where E₀ is the zero-field transition energy, F is the effective electric field on the excitons, and μ and α are the dipole moment and polarizability, respectively, between the ground and excited states.

F is calculated from the applied voltage (V) using $F = (V - V_{b i}) / t$ , where V $_{b i}$ is the built-in voltage and t is the thickness for the surrounding h-BN environment. The h-BN layers are approximately 15 nm thick. The built-in voltage (V $_{b i}$ ) is calculated using an approach described previously [28]. From the fit, the values of polarizability volume of the neutral exciton and trion are $- 4.7 \pm 0.7 Å^{3}$ and $- 14.5 \pm 0.8 Å^{3}$ . These values are more thantwo orders of magnitude smaller than the maximum obtained values for quantum emitters [23]. The dipole moment of the trion is found to be $0.33 \pm 0.01 D$ . The dipole moment of the neutral exciton was set to zero to account for the built-in voltage [28].

The change is energy is accompanied by a corresponding change in intensity which is a hallmark of the quantum confined Stark effect. Both the neutral exciton and trion emission intensity decreases with voltage as presented in Fig. 2(b). Although thechange in intensity of both the species follow a different slope, we do not see a crossover from neutral exciton to trion in the voltage regime unlike electrostatically gated monolayers. However, it is possible that there is a change in the local charge environment due to the applied electric field which could affect the two exciton states differently.

Fig. 3 (a) Circular polarization resolved PL spectra at 0V. Black (Gray) curve is co-(cross-) polarized PL signal. Excitation is $σ^{+}$ polarized. (b) Exciton and trion degree of circular polarization (DoCP) as a function of voltage. (c) Illustration depicting valley depolarization due to the electron-hole exchange interaction.

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It is well known that the excitons and trions inherit the valley properties of the free electrons and holes and exhibit valley polarization and coherence [30]. Figure 3(a) presents the valley polarized PL spectra in the absence of applied voltage. The trion and the neutral exciton features show maximum valley polarization. However, the valley polarization and coherence is not perfect due, in part, to the Coulomb exchange interaction [Fig. 3(d)] between the electron and hole. This mechanism is known to be the primary depolarization mechanism for neutral excitons in monolayers [19]. The relevance of this interaction in valley polarization can be studied using an electric or magnetic field. The magnetic field induces a valley splitting with subsequent valley polarization. The effect of magnetic field on the valley polarization [31] and coherence [32] in monolayer WSe $_{2}$ PL have been reported earlier.

An electric field applied along the growth direction of a quantum well can polarize the exciton, thus modifying the overlap between the electron and hole wave-functions (Fig. 1(a) [inset]) which influences the exchange interaction and the spin relaxation time [33]. Electric-field-dependent PL polarization has been observed in GaAs quantum wells, where the emitted polarization is related to the spin orientation and the spin depolarization timescales are affected by an electric field [34]. This study has been recently extended to TMDCs like MoS $_{2}$ [18] and WS $_{2}$ [17]. A modulation of the valley properties was observed only for bilayers in a back-gated device where large doping is realized along with field effect. For monolayers, modulation of valley polarized electroluminescence was achieved in WS $_{2}$ through spin injection via a dilute ferromagnetic semiconductor [16] and p-i-n heterojunction [35], and in WSe $_{2}$ using an electric double layer transistor [15] which also relied on charge injection via electrodes. However, for WSe $_{2}$ , the degree of circular polarization (DoCP) was not more than 10% in magnitude. On the contrary, WSe $_{2}$ monolayer exhibits a much higher DoCP in PL [30] when compared to EL. Furthermore, the hBN capped samples in our device offer an enhanced valley polarization than previously studied uncapped WSe $_{2}$ [30]. Our device architecture also allows us to apply a field perpendicular to the plane of the monolayer WSe $_{2}$ by biasing the top and the bottom FLGs relative to each other, thereby forming a parallel plate capacitor with a smaller charging effect than previously demonstrated in backgated bilayer WS $_{2}$ and MoS $_{2}$ [17, 18]. This allows us to deconvolute the effect of electric field from the effect of charging on the valley degree of freedom in the monolayer.

To study the valley polarization as a function of voltage, we measure circular polarization resolved PL spectra at each voltage. For polarization resolved spectroscopy, we use a combination of a linear polarizer (LP) and a quarter waveplate (QWP) to generate circularly polarized excitation light and another QWP/LP pair for a polarization analyzer at the collection port before feeding the signal to the input of the collection fiber. Figure 3(b) presents the DoCP as a function of voltage. Using a three-level model with incoherent pumping of excitonic population, the degree of circular polarization can be modeled [36] using:

D o C P = \frac{I_{+} - I_{-}}{I_{+} + I_{-}} \times 100 = \frac{1}{1 + 2 (γ_{v} / γ)}

where

I_{+} (I_{-})

is the intensity of the circularly polarized light with the same (opposite) helicity in the excitation and detection paths. The excitation laser in Fig. 3 is

σ^{+}

polarized. γ_v is the intervalley scattering rate and γ is the exciton recombination rate at the given valley.

From Fig. 3(b), it is evident that the electric field influences the valley polarization of the exciton and trion. We observe a quadratic relationship between the valley DoCP and the electric field similar to the energy shift as observed in Fig. 2(a). A maximum tunability of 5% and 8% is observed for the exciton and trion respectively. Thus, the valley polarization is directly proportional to the Stark shift of the two species. As mentioned previously, electric field can cause a change in the Coulomb exchange interaction [33] which controls the intervalley scattering rate (γ_v) in monolayer TMDCs. It also alters the oscillator strength of excitons and trions, as is evident from Fig. 2(b). The observation ofthe QCSE is a direct evidence of such modulation in our device. A modulation in the DoCP as a function of electric field suggests, as indicated in Eq. (2), that the intervalley scattering rate (γ_v) due to electron-hole exchange interaction is decreasing faster than γ as a function of electric field causing an increase in the DoCP.

Fig. 4 (a)-(b) Linear polarization resolved PL spectra at -8V and 8V respectively. Black (Grey) curve is co-(cross-) polarized signal with respect to the vertically polarized excitation laser. (c) DoLP as a function of voltage for the neutral exciton peak for H (solid blue triangle) and V (empty triangle) polarized excitation. (d) DoLP as a function of voltage for the trion peak for H (solid red triangle) and V (empty triangle) polarized excitation. (e) Illustration of the coherent superposition of thetwo valleys with no change in relative phase for the neutral exciton upon excitation with linearly polarized light (f) Illustration of an intervalley and intravalley trion with electron-hole (eh) and electron-electron (ee) exchange interactions. Linear excitation will also generate the time reversal partners.

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Finally, we study the electrical control of valley coherence. Quantum information processing with excitons in monolayer materials requires their coherent manipulation in the K and -K valleys, in addition to the inherent selective excitation. Valley coherence is demonstrated by the optical alignment of excitons, i.e., observation of a linearly polarized emission in the direction of the excitation polarization. A linearly polarized light source is a coherent superposition of circularly polarized $σ^{+}$ and $σ^{-}$ light. Therefore, it will simultaneously generate excitons in the K and -K valleys of momentum space [Fig. 4(e)] transferring the optical coherence to the photoexcited electron-hole pair generating valley quantum coherence [30]. Figures 4(a)-4(b) show polarization resolved (linear polarization) spectra at the two voltage extremes, i.e, -8V and 8V. The excitation laser was vertically (V) polarized for both cases. In the spectra we observe that the neutral exciton islinearly polarized consistent with previous observations [30]. By investigating the linearly polarized photoluminescence for orthogonally oriented, horizontally polarized, excitation, we find that the observed X $^{0}$ polarization is independent of crystal orientation [30].

The valley coherence can be modeled using:

D o L P = \frac{I_{H} - I_{V}}{I_{H} + I_{V}} \times 100 ≃ \frac{1}{1 + 2 (γ_{v} + γ_{d e p}) / γ}

where

I_{H} (I_{V})

is the intensity of the H (V) polarized emission.

γ_{d e p}

is the pure dephasing rate from exciton-exciton collisions and γ is the exciton recombination rate at both valleys. Equation (3) is used to calculate valley coherence for both H and V polarized excitation. In Fig. 4(c), we see a monotonic increase in the magnitude of valley coherence for the neutral exciton for both excitation laser orientations (H and V). The long-range Coulomb exchange interaction couples the exciton states in the K and -K valleys and will, therefore, contribute to valley decoherence [37, 38] along with valley depolarization. In Fig. 3(b), we have seen that the valley polarization increases with increasing voltage on our device which suggests a decrease in the electron-hole exchange interaction along the same direction. This also explains the increase in valley coherence for excitons as it depends on γ_v [see Eq. (3)], which is being modulated by the electric field.

In contrast to the neutral exciton, we do not observe any significant influence on the trion valley coherence as a function of the electric field. This suggests that the $γ_{d e p}$ term for the trion is much higher than γ_v and the above Eq. (3), for trions, can be approximated as

D o L P ≃ \frac{γ^{X -}}{γ_{d e p}^{X -}}

where the superscripts indicate the trion (

X^{-}

). Although modulation of γ_v effects the exciton valley coherence it has no effect on the trion since it is dominated by the pure dephasing term (

γ_{d e p}^{X -}

) [39]. The pure dephasing can arise from scattering of trions via defects or impurities in its environment [39]. In our device, the modulation of the trion valley coherence is very small and within the fluctuation level in our experiment. Unlike neutral excitons, trions do not exhibit valley coherence in PL following linearly polarized excitation due to a fine structure splitting in the intervalley and intravalley trion states [30, 40]. The splitting originates from the exchange interaction of the extra electron in the trion with the electron-hole pair [Fig. 4(f)] and limits the detection of valley coherence via linearly polarized emission in trions [19, 30, 39, 40]. Unlike the neutral exciton the relative phase between the excitons in opposite valleys is not maintained for the inter- and intra-valley trions [30].

4. Conclusion

In conclusion, we have demonstrated all electrical manipulation of the valley polarization and valley coherence exhibited by excitons in monolayer WSe $_{2}$ by embedding the material in a van der Waals heterostructure. We have shown that the change in the valley polarization is related to modulating the electron-hole exchange interaction experienced by the exciton and trion species. Device engineering to generate a larger electric field should result in a higher degree of valley manipulation. In previous studies, resonant excitation has been used to improve the valley polarization of excitons and intra-valley trions [30, 41]. Resonant pumping in combination with electric field effect can be used in future to improvethe valley properties. We expect our device will provide a pathway for the dynamic electrical control of valley polarization and valley coherence in monolayer WSe $_{2}$ providing a promising platform for studying spin/valley physics as well as a new architecture for valleytronics devices.

Funding

National Science Foundation (NSF) (EFRI EFMA-1542707, CAREER DMR 1553788); AFOSR FA9550-16-1-0020; Cornell Center for Materials Research NSF MRSEC program (DMR-1719875).

Acknowledgments

A.N.V. acknowledges support from the Leonard Mandel Faculty Fellowship in Quantum Optics.

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Electrically tunable valley polarization and valley coherence in monolayer WSe₂ embedded in a van der Waals heterostructure [Invited]

Abstract

1. Introduction

2. Design and optical characterization of the van der Waals device

3. Voltage-controlled PL emission

4. Conclusion

Funding

Acknowledgments

References

Cited By

Figures (4)

Equations (4)

Optical Materials Express