Open Access
Add to BibSonomy
Abstract
The linear photogalvanic effect (LPGE) is investigated by using the non-equilibrium Green’s function (NEGF) technique combined with density functional theory (DFT) in monolayer Na2MgSn. We consider the cases of three different central regions, which are pure Na2MgSn, Na-vacancy, and Pb-substituted. It is found that both pure and defective Na2MgSn monolayers induce photoresponse under linearly polarized light. The photoresponse varies periodically as a form of either sinusoidal or cosinoidal function of the polarization angle. In the near-infrared and visible ranges, the photoresponse is more sensitive to the long wave range of visible light. In the case of single-atom defects, the photoresponse with Na-vacancy is larger than that of pb-substitution defects. Compared with the other two central regions, the maximum extinction ratio (ER) of Na-vacancy is larger, so it has higher polarization sensitivity. When the location of Na-vacancy is adjusted, the photoresponse changes obviously, and the Na 1*- vacancy has the largest photoresponse. With the increase of the Na-vacancy concentration, the photoresponse changes nonlinearly but is smaller than that of a single vacancy. A small bias voltage can greatly improve the photoresponse. Our results suggest an effective method to enhance the photoresponse and show the promise of Na2MgSn monolayers in optical detection.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
17 August 2023: A correction was made to the funding.
1. Introduction
Photoelectric materials directly convert light energy into electricity, which has attracted wide attention in the field of materials and energy, so as in solving of energy shortage and environmental crisis. Because of their unique crystal structure, layered photoelectric materials possess excellent photoelectric properties through artificial modulation. Compared with the conventional mechanism, the photogalvanic effect (PGE) [1–3] can generate photoresponse without external bias voltage due to lacking of center symmetry.
The crystal and atomic structures of intermetallic compounds [4–6] are different from those of primary metals and can form new ordered superlattice structures. Interatomic bond includes metal bond, ionic bond, covalent bond and molecular bond, resulting in many unique properties. Some intermetallic compounds are semiconductors, despite their metallic bonding properties. Yamada et al. [7] synthesized layered intermetallic compound Na2MgSn semiconductor experimentally, and theoretically calculated its crystal structure, electronic and physical properties. The reported band gap is about 0.17 eV. Mg and Sn atoms are located in the same plane, forming a strongly bonded graphene-like honeycomb structure, with two layers of Na atoms filling in between adjacent Mg-Sn layers. There are 8 atoms in the Na2MgSn unit cell. In the hexagonal system, lattice constant a = 5.0486(11) Å, c = 10.0950(2) Å. Wang et al. [8] showed that Na2MgSn is a mechanically stable soft material, which is brittle. Zhou et al. [9] found that Na2MgSn is a potential thermoelectric material in their theoretical study.
Under the irradiation of polarized light, the transition of excited electrons from the valence band is unbalanced, resulting in continuous photocurrent [10–12]. Because of these advantages, PGE has been extensively studied in electron gas [13–16], semiconductor quantum well [17,18], two-dimensional perovskites [19], topological insulators [20,21], and Weyl semi-metals [22–24]. Based on our previous work [25–28], this paper will study the PGE of monolayer Na2MgSn, which has not been reported so far. Na2Mgsn has a graphene-like honeycomb structure, and the upper and lower intercalation of Na atoms enhances spatial inversion symmetry. It means that symmetry breaking results in the lowest energy electron-hole pair being spatially separated, which will effectively reduce the probability of electron-hole pair recombination, which is conducive to the generation of sustained photocurrent. Inspired by advances in graphene research, there are several ways to prepare monolayer nanosheets, including mechanical stripping [29,30], electrochemical stripping [31,32], and chemical vapor deposition [33,34]. The proposed scheme has potential application in chip-based QKD [35], coherent Ising machines [36]. In addition, monolayer molecular devices are being actively studied [37–39].
The actions of intercalations are weakly bound and Na-vacancy is inevitable. With the improvement of nanofabrication technology, it is possible to artificially add or replace atoms in materials, and thus to control the materials’ electronic, optical and other properties [40,41].
In this paper, the linear photogalvanic effect in the near infrared to visible ranges (1379 nm - 376 nm) is investigated under the conditions of perfect monolayer Na2MgSn, Na-vacancy, and Sn replaced by Pb atom. Extinction ratio was calculated to prove the polarization sensitivity of Na2MgSn. The effects of Na-vacancy position, concentration and bias voltage on photoresponse are also studied taking the location and concentration of Na-vacancy and bias voltage on photoresponse into consideration. This work can provide more theoretical guidance for the photogalvanic research of simple layered intermetallic compounds and the design of photodetectors.
2. Calculations and methods
LPGE occurs when the central region is shined by linearly polarized light. The photocurrent $J_\textrm{L}^{(ph)}$ in the left lead can be given by [42,43]
Here, $G_{1,2,3}^{ > / < (ph)}$ is the greater /lesser Green function with photon-electron interaction. $G_0^{r/a}$ and $G_0^{ > / < }$ are individually the retarded/advanced and greater/lesser Green’s functions without photons. ${e_{1(2)\alpha ,\beta ,\gamma }}$ is the Cartesian component of the unit vector ${e_{1(2)}}$ determined by the light polarization and ${p_{\alpha ,\beta ,\gamma }}$ is the Cartesian component of the electron momentum. The polarization vector of the linearly polarized light can be written as $\hat{e} = \cos \theta {\hat{e}_1} + \sin \theta {\hat{e}_2}$, where $\theta$ the angle between the polarization and the transport directions (z-axis) in our calculation. In Eq. (2), C0 can be written as ${C_0} = {e^2}\hbar {I_\omega }\sqrt {{\mu _r}{\varepsilon _r}} /(2Nm_0^2\omega \varepsilon C)$, where ${\mu _r}$ is the relative magnetic susceptibility, ${\varepsilon _r}$ the relative dielectric constant, $\varepsilon$ the dielectric constant, N the number of photons, ${m_0}$ the bare electron mass, $\omega$ the photon frequency, C the speed of light, and ${I_\omega }$ the photon flux determined by the number of photons per unit area per unit time. The photoresponse function is $R = J_\textrm{L}^{(ph)}/e{I_\omega }$ in which R is in the unit of $a_0^2/\textrm{phonon}$ and $a_0^{}$ the Bohr radius.
The NEGF-DFT numerical calculations have been implemented in NanoDcal [44], and double Zeta polarization atomic orbital bases are used to expand all physical quantities. Local density approximation is used to deal with interchange and correlation. Atomic cores are defined by the standard norm conserving nonlocal pseudopotentials. The cutoff energy is 80 Hartree. The k-point mesh of 7 × 2 is employed in the band structure calculation and 12 × 1 is employed in the calculation of photoresponse transport from the left probe to the right probe.
3. Results and discussions
Figure 1 shows the monolayer Na2MgSn photodetector in the zigzag transport direction, where the left and right leads are individually extended to ${\pm} \infty$ along the transmission direction z, whereas the x and y axes are along the vacuum and periodic directions, respectively. The polarization angle $\theta$ of the linearly polarized light is formed with respect to the z direction. The purple, green, gray, and blue balls individually represent the Na, Mg, Sn and the Pb atoms. The bond lengths of Na-Mg, Na-Sn and Mg-Sn are 3.40 Å, 3.40 Å and 2.86 Å, respectively. The dash lines at the left and right ends separate two leads from the central region, which contains 44 atoms. Vertical linearly polarized light shines on the y-z plane of the central region, and the photocurrent flows along the z direction as shown in Fig. 1(b). Three configurations are discussed here, namely Pure Na2MgSn, Na-vacancy, and Pb substituted. The symmetry of the pristine Na2MgSn monolayer and Pb-Substituted is Cs, and the symmetry of the Na-Vacancy is C1.
Fig. 1. The top (a) and side (b) views of the monolayer Na2MgSn photodetector in zigzag devices. The purple, green, gray, and blue spheres represent the Na, Mg, Sn and the Pb atoms, respectively. The red space is Na-vacancy. The blue space means one Sn atom is substituted by one Pb atom.
Figure 2 shows the electronic band structure of pure monolayer Na2MgSn with a band gap of 0.66 eV. Photon energies of (a) 0.9 eV, (b) 1.5 eV, (c) 1.7 eV, (d) 1.9 eV, (e) 2.9 eV, and (f) 3.1 eV are selected as special points to study the variation of photoresponse R with the polarization angle $\theta$. Pure Na2MgSn (black line), Na-vacancy (red line) and Pb-substituted (blue line) cases are shown in Fig. 3. It is found that R varies periodically with θ. Under different photon energies, the lines are in the form of sinusoidal or cosinoidal function. This result is consistent with the phenomenological model [45–47], which is used to explain the measured the dependence of the photoresponse on the polarization angles in PGE experiments. Generally, when the transmission direction is armchair shaped, the LPGE is stronger when the polarization direction is along or perpendicular to the transmission direction [26–28]. In this model, the transmission direction is along the zigzag direction. Figure 3 shows that the maximum photoresponse of pure Na2MgSn can be found for a polarization angle of 45°. Due to the introduction of defects, this angle is slightly adjusted. The fluctuation amplitude of the blue and red lines in all figures is greater than that of the black lines, indicating that the introduction of defects can enhance the photoresponse. The main reason is that the internal electric field becomes stronger due to the symmetry breaking caused by the defects. In addition, it can be seen that the photoresponse obtained in Fig. 3 (c) and (d)) is larger, which corresponds to the long wave range of visible light.
Fig. 3. The photoresponse R of the three different central regions varies with the polarization angle θ at the photon energies of (a) 0.9 eV, (b) 1.5 eV, (c) 1.7 eV, (d) 1.9 eV, (e) 2.9 eV, and (f) 3.1 eV respectively, pure Na2MgSn (black line), Na-vacancy (red line), Pb-substituted (blue line).
Figure 4 shows the variation of the maximum photoresponse Rmax of Na2MgSn devices as a function of photon energy in the near infrared and visible ranges, where pure Na2MgSn (black line), Na-vacancy (red line) and Pb-substitution (blue line) are shown. When the photon energy is less than 0.8 eV, the defect has little effect on the photoresponse. It can be seen that defects have a great impact on the enhancement of photoresponse. Pure Na2MgSn (black line) is always lower than the blue line and red line except for the individual points of 2.5 eV. In addition, the effect of vacancy defect is greater than that of substitution defect. At the photon energy of 1.8 eV, Na-vacancy Na2MgSn shows the maximum photoresponse Rmax =5.26, which is 94 times of the maximum photoresponse of pure Na2MgSn. Moreover, the long wave of visible light band can generate greater photoresponse. These results are consistent with those in Fig. 3. The introduction of defects enhances the degree of symmetry breaking, thus reducing the probability of electron-hole pair recombination, which is conducive to the generation of sustained photocurrent.
Fig. 4. The maximum photoresponse Rmax varies with the photon energy in three different central regions, which is pure Na2MgSn (black line), Na-vacancy (red line), and Pb-substituted (blue line).
Electron transmission spectrum (TS) as a function of electron energy is shown in Fig. 5. In the pure case, by radiating photons with energy of 2.5 eV, a large photoresponse is generated because of the greater probability of transition amplitude at TS peaks -1.40 eV and 1.10 eV (A, A’ in Fig. 5(a)) respectively. This is consistent with the peak of the black line in Fig. 4. The TS peaks at -1.16 eV and 1.54 eV (B, B’ in Fig. 5(6)) result in the Rmax at the photon energy of 2.7 eV for the Na-vacancy center region. For the Pb-substituted case, the peak value of TS is located at -0.98 eV and 0.72 eV (C, C’ in Fig. 5(c)). The electron transition probability is the greatest between these peaks, and then a large photoresponse appears at 1.7 eV, which is in consistent with the blue line in Fig. 4. These results show that the existence of defects can adjust the maximum photoresponse at different wavelengths because the defects alter the absorption properties of Na2MgSn.
Fig. 5. The electron transition spectrum for the (a) pure Na2MgSn, (b) Na-vacancy and (c) Pb-substituted, respectively. The electron transitions between valence bands and conduction bands are indicated by dotted lines with arrows. “A, A’, B, B’, C, C'“ denotes TS peaks.
As can be seen from Fig. 3, the photoresponse depends on the angle θ. Figure 6 shows the ER to test whether the Na2MgSn device is a candidate for the polarization detector. The polarization sensitivity can be described by ER, which can be defined as ${R_{/{/}}}/{R_ \bot }$ (black line) or ${R_ \bot }/{R_{/{/}}}$ (red line). In the three figures on the left, ${R_{/{/}}}$ and ${R_ \bot }$ are the magnitudes of the photoresponse at $\theta$= 0° and $\theta$= 90°. In the three figures on the right, ${R_{/{/}}}$ and ${R_ \bot }$ are the magnitudes of the photoresponse at $\theta$= 45° and $\theta$= 135°. Three kinds of central regions are considered here (a)(d) pure Na2MgSn, (b)(e) Na-vacancy, and (c)(f) Pb-substituted. When the orthogonal directions are 0° and 90°, the value of ${R_{/{/}}}/{R_ \bot }$ is larger than that of ${R_ \bot }/{R_{/{/}}}$ except for some special photon energies. As can be seen in Fig. 6(a), the maximum ER value of pure Na2MgSn is 109.95 when the photon energy is 2.0 eV. For the photodetectors with Na-vacancy (Fig. 6(b)) and Pb-substituted (Fig. 6(c)), the maximum ERs are 33.52 and 48.31 at 1.5 eV and 1.2 eV, respectively. In contrast, pure Na2MgSn is more suitable for high sensitivity photodetector. When the orthogonal directions are converted to 45° and 135°, the results change significantly. The red line peaks more significantly than the black line. The maximum ER of pure Na2MgSn in Fig. 6 (d) and Pb-substituted in Fig. 6 (f) is smaller than that in Fig. 6 (a) and (c). Na vacancy defect in Fig. 6 (e) has a stronger ER (605.91) at the photon energy 1.5 eV. When the photon energies is 2.7 eV, the maximum ER decreases to 165.24, which is still very competitive compared to all other cases. This outstanding extinction ratio is much larger than that (180) of 2D WSe2 [25] and (280) of MgBr2/CdCl2 van der Waals heterostructure photodetector [48]. In recent experiments, the 2D graphene/PdSe2/germanium heterojunction has shown an impressive extinction ratio of 73.8 at 365 nm [49]. In comparison, the proposed Na2MgSn photodetector which can be realized through the regulation of intercalation Na is superior to all these reported.
Fig. 6. The variation of ER of the photoresponse with photon energy for three different central regions. (a) (d) pure Na2MgSn; (b) (e) Na-vacancy; (c) (f) Pb-substituted. ${R_{/{/}}}/{R_ \bot }$ (black line) and ${R_ \bot }/{R_{/{/}}}$ (red line). From (a) to (c), ${R_{/{/}}}$ and ${R_ \bot }$ are the photocurrent at polarization angles of 0° and 90°. From (d) to (f), ${R_{/{/}}}$ and ${R_ \bot }$ are the photocurrent at polarization angles of 45°and 135°, respectively.
Figure 4 indicates that Na-vacancy contributes significantly to the improvement of photoresponse. In addition, the location and concentration of Na-vacancy will also affect the photoresponse. There are 22 Na atoms in the central region of our model. Figure 7 (a) Na 1#-vacancy, (b)Na 1*-vacancy, and (c)Na 1@-vacancy indicate that there is only one Na atom vacancy (red space) at different positions #, *, and @. Figure 7(d) Na 2-vacancy, (e) Na 4-vacancy, and (f) Na 6-vacancy are models with 2, 4 and 6 Na atomic vacancies. As can be seen from Fig. 4, the long wave range of visible light has a high excitation probability of photoresponse. Therefore, we choose the photon energies at 1.5 eV (black line), 1.7 eV (red line), and 1.9 eV (blue line) to irradiate the central region. From the comparison of Fig. 8(a) to (c), it is found that single-atom vacancies at different positions have a greater influence on photoresponse. In Fig. 8(a), the Na 1#-vacancy, Rmax = 7.42 occurs when the photon energy is 1.9 eV and θ= 45° (blue line). In Fig. 8(b), the Na 1*-vacancy, Rmax = 100 when the photon energy is 1.7 eV and $\theta$= 15°(red line). In Fig. 8(c) Na 1@-vacancy, the Rmax = 20.22 when the photon energy of 1.9 eV and $\theta$= 15° (blue line). In Na 1*-vacancy, the Rmax excited by 1.7 eV photon energy is much stronger than the other two cases. From Fig. 8(d) to (e), it can be found that all of the peaks occurred under the irradiation of 1.9 eV photon energy (blue line). The maximum photoresponse of two-vacancy, four-vacancy and six-vacancy are 3.07 at $\theta$ = 45° (Fig. 8(d)), 3.15 at $\theta$= 45° (Fig. 8(e)) and 4.21 at $\theta$= 75° (Fig. 8(f)), respectively. The results show that multi-vacancy does not excite higher photoresponse than the case of single-vacancy.
Applying a small bias voltage at both ends of the left and right electrodes usually improvesthe photoresponse. The effect of bias voltage on photoresponse R is shown in Fig. 9, where the bias voltage is individually set to be 0 eV (black line), 0.008 eV (red line), 0.012 eV (blue line), and 0.02 eV (green line). Comparing Fig. 9(a) to (c), it is found that under the same linearly polarized light and weak bias voltage, photoresponse of pure Na2MgSn and Pb-substituted is significantly enhanced, and is superior to that of Na-vacancy. In Fig. 9(a1), the Rmax of pure Na2MgSn with a bias of 0.02 eV is 105 times that of zero-bias Rmax at $\theta$= 90° when the photon energy is 1.5 eV. The magnitude of Rmax of Pb-substituted at 0.008 eV is 102 times that at zero-bias at $\theta$= 90° as shown in Fig. 9(c3). However, the bias voltage reduces the photoresponse in Na-vacancy at some special photon energies. In Fig. 9 (b2), for zero-bias voltage (the black line), the peak of R is 4.55 at $\theta$ = 30° whereas the maximum R is 4.09 when the bias voltage is 0.008 eV (red line). Due to the nonzero bias voltage, the photoresponse of the single-atom Na-vacancy structure is weakened at photon energy of 1.7 eV. In addition, the bias voltage also changes the polarization angle corresponding to maximum photoresponse. In Fig. 9(a2), R = 2.07 at $\theta$= 150° when the bias voltage is 0.008 eV (the red line), while R = 2.37 at $\theta$= 45° when the bias is 0.02 eV (the green line).
Fig. 9. Photoresponse R change with polarization angle θ when bias voltages are 0 eV (black line), 0.008 eV (red line), 0.012 eV (blue line), and 0.02 eV (green line). The photon energy are (a) 1.5 eV, (b) 1.7 eV, and (c) 1.9 eV, respectively. The first column is pure Na2MgSn, the second column is Na-vacancy, and the third column is Pb-substituted.
4. Conclusions
The LPGE is studied by using a quantum transport simulation method in the Na2MgSn monolayer with three different central regions, which are pure Na2MgSn, Na-vacancy, and Pb-substituted. Due to the breaking of structural symmetry which results in polarity and built-in electric field, both pure and defective Na2MgSn monolayers induce PGEs and generate photoresponse under linearly polarized light. Photoresponse varies periodically with polarization angle. In this paper, the photon energy varies from 0.9 eV (1379 nm) to 3.3 eV(376 nm). It is found that photoresponse is extremely sensitive to the long wave range of visible light (591 nm - 774 nm). Since the introduction of defective band creates favorable conditions for electron transitions, both single Na-vacancy and Pb-substituted defects enhance photoresponse, and that in Na-vacancy is more significant. The maximum ER of Na-vacancy defect is generally higher. The maximum ER is 605.91 when the photon energy is 1.5 eV (774 nm). The maximum ER is 165.24 when the photon energy is 2.7 eV (460 nm). A Na-vacancy defect case is more suitable for the development and application of high sensitivity polarization detectors. By adjusting the location of single Na-vacancy, it is found that the intensity of photoresponse changes obviously. In this study, Na 1*-vacancy has the largest photoresponse. When the concentration of Na-vacancy increases, the photoresponse changes nonlinearly, and is smaller than that of single vacancy. Photoresponse can also be further boosted by applying a small bias voltage.
Funding
National Natural Science Foundation of China (12264037, 12265022, 62075035); Natural Science Foundation of Inner Mongolia, China (2021MS03036, 2021MS01012); Fundamental Research Funds for Inner Mongolia University of Science & Technology (2023RCTD015); Basic and Applied Basic Research Foundation of Guangdong Province (2021B1515420001); Guangdong Province education department (2021KCXTD040).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
References
1. V.I. Belinicher, “Space-oscillating photocurrent in crystals without symmetry center,” Phys. Lett. A 66(3), 213–214 (1978). [CrossRef]
2. V.I. Belinicher and B.I. Sturman, “The photogalvanic effect in media lacking a center of symmetry,” Sov. Phys. Usp. 23(3), 199–223 (1980). [CrossRef]
3. E. Rabinowitch, “The photogalvanic effect II. The photogalvanic properties of the thionine-iron system,” J. Chem. Phys. 18(7), 560–566 (1940). [CrossRef]
4. J.B. Friauf, “The crystal structures of two intermetallic compounds,” J. Am. Chem. Soc. 49(12), 3107–3114 (1927). [CrossRef]
5. G.B. Bokii, B.K. Vul’f, and N.L. Smirnova, “Crystal structures of ternary metallic compounds,” J. Struct. Chem. 2(1), 68–105 (1961). [CrossRef]
6. J. Dshemuchadse and W. Steurer, “More statistics on intermetallic compounds - ternary phases,” Acta Crystallogr. A 71(3), 335–345 (2015). [CrossRef]
7. T. Yamada, V.L. Deringer, R. Dronskowski, and H. Yamane, “Synthesis, crystal structure, chemical bonding, and physical properties of the ternary Na/Mg stannide Na2MgSn,” Inorg. Chem. 51(8), 4810–4816 (2012). [CrossRef]
8. Y.F. Wang, Q.L. Xia, L.X. Pan, and Y. Yu, “First principles calculation on ternary stannide phase narrow band gap semiconductor Na2MgSn,” Trans. Nonferrous Met. Soc. China 24(6), 1853–1858 (2014). [CrossRef]
9. C. Wang, Y.B. Chen, S.H. Yao, and J. Zhou, “Low lattice thermal conductivity and high thermoelectric figure of merit in Na2MgSn,” Phys. Rev. B 99(2), 024310 (2019). [CrossRef]
10. V.M. Fridkin, E.P. Efremova, B.H. Karimov, V.A. Kuznezov, I.P. Kuzmina, and A.N. Lobachev, “The experimental investigation of the photovoltaic effect in some crystals without a center of symmetry,” Appl. Phys. 25(1), 77–80 (1981). [CrossRef]
11. S.D. Ganichev, E.L. Ivchenko, S.N. Danilov, J. Eroms, W. Wegscheider, D. Weiss, and W. Prettl, “Conversion of spin into directed electric current in quantum wells,” Phys. Rev. Lett. 86(19), 4358–4361 (2001). [CrossRef]
12. S.D. Ganichev, E.L. Ivchenko, and W. Prettl, “Photogalvanic effects in quantum wells,” Phys. E 14(1-2), 166–171 (2002). [CrossRef]
13. X.W. He, B. Shen, Y.H. Chen, Q. Zhang, K. Han, C.M. Yin, N. Tang, F.J. Xu, C.G. Tang, and Z.J. Yang, “Anomalous photogalvanic effect of circularly polarized light incident on the two-dimensional electron gas in AlxGa1−xN/GaN heterostructures at room temperature,” Phys. Rev. Lett. 101(14), 147402 (2008). [CrossRef]
14. S.H. Wang, H. Zhang, J. Zhang, S.Q. Li, D.B. Luo, J.Y. Wang, K.X. Jin, and J.R. Sun, “Circular photogalvanic effect in oxide two-dimensional electron gases,” Phys. Rev. Lett. 128(18), 187401 (2022). [CrossRef]
15. S.N. Danilov, L.E. Golub, T. Mayer, A. Beer, S. Binder, E. Monch, J. Minar, M. Kronseder, C.H. Back, and D. Bougeard, “Superlinear photogalvanic effects in (Bi0.3Sb0.7)2(Te0.1Se0.9)3: Probing three-dimensional topological insulator surface states at room temperature,” Phys. Rev. Appl. 21(6), 064030 (2021). [CrossRef]
16. L.E. Golub, E.L. Ivchenko, and B. Spivak, “Semiclassical theory of the circular photogalvanic effect in gyrotropic systems,” Phys. Rev. B 102(8), 085202 (2020). [CrossRef]
17. V.V. Bel’kov, S.D. Ganichev, E.L. Ivchenko, S.A. Tarasenko, W. Weber, S. Giglberger, M. Olteanu, H.P. Tranitz, S.N. Danilov, P. Schneider, W. Wegscheider, D. Weiss, and W. Prettl, “Magneto-gyrotropic photogalvanic effects in semiconductor quantum wells,” J. Phys.: Condens. Matter 17(21), 3405–3428 (2005). [CrossRef]
18. V.V. Bel’kov, S.D. Ganichev, P. Schneider, C. Back, M. Oestreich, J. Rudolph, D. Hagele, L.E. Golub, W. Wegscheider, and W. Prettl, “Circular photogalvanic effect at inter-band excitation in semiconductor quantum wells,” Solid State Commun. 128(8), 283–286 (2003). [CrossRef]
19. P. Huang, K. Taniguchi, M. Shigefuji, T. Kobayashi, M. Matsubara, T. Sasagawa, and H. Miyasaka, “Chirality-dependent circular photogalvanic effect in enantiomorphic 2D organic–inorganic hybrid perovskites,” Adv. Mater. 33(17), 2008611 (2021). [CrossRef]
20. M.V. Durnev and S.A. Tarasenko, “High-frequency nonlinear transport and photogalvanic effects in 2D topological insulators,” Ann. Phy. 531(6), 1800418 (2019). [CrossRef]
21. X. Sun, G. Adamo, M. Eginligil, H.N.S. Krishnamoorthy, N.I. Zheludev, and C. Soci, “Topological insulator metamaterial with giant circular photogalvanic effect,” Sci. Adv. 7(14), 5748 (2021). [CrossRef]
22. F. De Juan, A.G. Grushin, T. Morimoto, and J.E. Moore, “Quantized circular photogalvanic effect in Weyl semimetals,” Nat. Commun. 8(1), 15995 (2017). [CrossRef]
23. Y. Zhang, H. Ishizuka, J. van den Brink, C. Felser, B.H. Yan, and N. Nagaosa, “Photogalvanic effect in Weyl semimetals from first principles,” Phys. Rev. B 97(24), 241118 (2018). [CrossRef]
24. K. Sun, S.S. Sun, L.L. Wei, C. Guo, H.F. Tian, G.F. Chen, H.X. Yang, and J.Q. Li, “Circular photogalvanic effect in the Weyl semimetal TaAs,” Chin. Phys. Lett. 34(11), 117203 (2018). [CrossRef]
25. J. Liu, Y.H. Ma, F. Chi, L. M. Chao, and J.Y. Niu, “Linear photogalvanic effects in monolayer WSe2 with defects,” Opt. Express 31(8), 12026–12035 (2023). [CrossRef]
26. J. Liu, X. K. Ji, M. Sun, F. Chi, L.M. Chao, and Y.H. Ma, “Linear photogalvanic effects in Janus monolayer MoSSe with intrinsic defects,” Opt. Laser Technol. 159, 108946 (2023). [CrossRef]
27. M. Sun, J. Liu, and F. Chi, “Photogalvanic effects in Janus monolayer In2SSe with vacancy defects,” Phys. E 145, 115467 (2023). [CrossRef]
28. T. T. Wang and J. Liu, “Giant photogalvanic effect in Janus monolayer InSSe,” Opt. Commun. 492(20), 126945 (2021). [CrossRef]
29. H. Li, J. Wu, Z. Yin, and H. Zhang, “Preparation and applications of mechanically exfoliated single-layer and multilayer MoS2 and WSe2 Nanosheets,” Acc. Chem. Res. 47(4), 1067–1075 (2014). [CrossRef]
30. H. Li, G. Lu, and H. Zhang, “Mechanical exfoliation and characterization of single- and few-layer nanosheets of WSe2, TaS2, and TaSe2,” Small 9(11), 1974–1981 (2013). [CrossRef]
31. R.A. Wells, M. Zhang, Z.H. Chen, V. Boureau, M. Caretti, Y. Liu, J.H. Yum, H. Johnson, S. Kinge, and A. Radenovic, “High performance semiconducting nanosheets via a scalable powder-based electrochemical exfoliation technique,” ACS Nano 16(4), 5719–5730 (2022). [CrossRef]
32. N. Liu, P. Kim, J.H. Kim, J.H. Ye, S. Kim, and C.J. Lee, “Large-area atomically thin MoS2 nanosheets prepared using electrochemical exfoliation,” ACS Nano 8(7), 6902–6910 (2014). [CrossRef]
33. L.L. Tan, Q.B Liu, Y.F. Ding, X.G. Lin, W. Hu, M.-Q. Cai, and H. Zhou, “Effective shape-controlled synthesis of gallium selenide nanosheets by vapor phase deposition,” Nano Res. 13(2), 557–563 (2020). [CrossRef]
34. H. Tan, Y. Fan, Y. Rong, B. Porter, and J.H. Warner, “Doping graphene transistors using vertical stacked monolayer ws2 heterostructures grown by chemical vapor deposition,” ACS Appl. Mater. Interfaces 8(3), 1644–1652 (2016). [CrossRef]
35. L.C. Kwek, L. Gao, W. Luo, Y.X. Wang, S.H. Sun, X.B. Wang, and A.Q. Liu, “Chip-based quantum key distribution,” AAPPS Bull. 31(1), 15 (2021). [CrossRef]
36. L. Bo, L. Liu, J.Y. Song, K. Wen, and C. Wang, “Recent progress on coherent computation based on quantum squeezing,” AAPPS Bull. 33(1), 7 (2023). [CrossRef]
37. Y.Y. Wang, J. Zhou, Y.L. Liu, W.F. Zhang, Z.H. Zhao, X.T. Li, Q.N. Chen, N. Liu, X. Shen, R.C. Yu, J.C. Nie, and R.F. Dou, “Tuning photoluminescence behaviors in strained monolayer belt-like MoS2 crystals confined on TiO2 (001) surface,” AAPPS Bull. 32(1), 31 (2022). [CrossRef]
38. A.S. Abbas, “Ultrawide-bandgap semiconductor of carbon-based materials for meta-photonics-heterostructure, lasers, and holographic displays,” AAPPS Bull. 33(1), 4 (2023). [CrossRef]
39. S. Guan, Shan, J.X. Xiong, Z. Wang, and J.W. Luo, “Progress of hidden spin polarization in inversion-symmetric crystals,” Sci. China Phys. Mech. 65(3), 237301 (2022). [CrossRef]
40. Y. Xie, L. Zhang, Y. Zhu, L. Liu, and H. Guo, “Photogalvanic effect in monolayer black phosphorus,” Nanotechnology. 26(45), 455202 (2015). [CrossRef]
41. Y.Q. Li, Y.X. Lu, P. Adelhelm, M.M. Titirici, and Y.S. Hu, “Intercalation chemistry of graphite: alkali metal ions and beyond,” Chem. Soc. Rev. 48(17), 4655–4687 (2019). [CrossRef]
42. .H. Kim, J. Hong, G. Yoon, H. Kim, K.Y. Park, M.S. Park, W.S. Yoon, and K. Kang, “Sodium intercalation chemistry in graphite,” Energ. Environ. Sci. 8(10), 2963–2969 (2015). [CrossRef]
43. F. Chu, M. Chen, Y. Wang, Y. Xie, B. Liu, Y. Yang, X. An, and Y. Zhang, “A highly polarization sensitive antimonene photodetector with a broadband photoresponse and strong anisotropy,” J. Mater. Chem. C. 6(10), 2509–2514 (2018). [CrossRef]
44. J. Taylor, H. Guo, and J. Wang, “Ab initio modeling of quantum transport properties of molecular electronic devices,” Phys. Rev. B 63(24), 245407 (2001). [CrossRef]
45. E.L. Ivchenko and G.E. Pikus, “New photogalvanic effect in gyrotropic crystals,” JETP. Lett. 27, 640–643 (1978).
46. S.D. Ganichev and W. Prettl, “Spin photocurrents in quantum wells,” J. Phys.: Condens. Matter. 15(20), R935–R983 (2003).
47. S.D. Ganichev, U. Rössler, W. Prettl, E.L. Ivchenko, V.V. Bel’kov, R. Neumann, K. Brunner, and G. Abstreiter, “Removal of spin degeneracy in p - SiGe quantum wells demonstrated by spin photocurrents,” Phys. Rev. B 66(7), 075328 (2002). [CrossRef]
48. Y.Z. Luo, Y.B. Hu, and Y.Q. Xie, “Highly polarization-sensitive, visible-blind and self-powered ultraviolet photodetection based on two-dimensional wide bandgap semiconductors: a theoretical prediction,” J. Mater. Chem. A 7(48), 27503–27513 (2019). [CrossRef]
49. D. Wu, J.W. Guo, J. Du, C.X. Xia, L.H. Zeng, Y.Z. Tian, Z.F. Shi, Y.T. Tian, X.J. Li, Y.H. Tsang, and J.S. Jie, “Highly polarization-sensitive, broadband, self-powered photodetector based on graphene/pdse2/germanium heterojunction,” ACS Nano 13(9), 9907–9917 (2019). [CrossRef]
