Abstract

Utilizing the spin or valley degree of freedom is a promising approach for realizing more energy-efficient information processing devices. Circularly polarized light can be used to generate spin/valley current in monolayer 2D transition metal dichalcogenides. We observe a geometrically dependent photocurrent in heterostructure ${{\rm MoS}_2}/{{\rm WSe}_2}$, where light with a different circular polarization generates photocurrents in opposite directions. Furthermore, we show that this photocurrent persists even at room temperature, and it can be controlled using an in-plane electric field and back gating. We explain the observed phenomena via valley-dependent valence band shift and the valley optical selection rule. This finding may facilitate the use of 2D heterostructures as a platform for opto-valleytronics and opto-spintronics devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The manipulation of the spin degree of freedom or valley degree of freedom can result in more energy-efficient information processing devices compared to the currently utilized charge-based approach [1,2]. The two-dimensional (2D) van der Waals heterostructure has emerged as a potential material class for realizing these devices [3,4]. This is due to the possibility of engineering the interlayer interaction [57] and tailoring the properties of different materials through the proximity effect [8,9].

However, an efficient method of generating spin/valley current in the 2D heterostructure is still lacking. Since the 2D heterostructure consists of monolayers, it is natural to try to extend the technique of the spin/valley current generation in the monolayer to the 2D heterostructure. Due to the large spin-orbit coupling and the valley optical selection rule in the monolayer transition metal dichalcogenide (TMD) [1014], the spin and valley current can be generated by using circularly polarized light. Such a method can be classified into two classes: the optical valley Hall effect [15,16], i.e., the generation of photocurrent transverse to an electrical bias, and the circular photogalvanic effect (CPGE) [1722], i.e., the generation of photocurrent due to the circularly polarized optical excitation. Since the longitudinal charge current is not needed in the CPGE, the spin/valley current generation method based on the CPGE is more energy-efficient compared to the valley Hall-based method [15,16,23].

Here, we report on an experimental observation of the geometrically dependent circular photocurrent due to the CPGE in the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure. The magnitude of the circular photocurrent depends on the distance to the metal electrode, while its polarity depends on which side of the electrode is optically excited. Such geometric circular photocurrent under a normal incidence optical excitation has not been observed in other systems. We also experimentally show that the geometric circular photocurrent can be controlled by using the in-plane electric field and the back gating.

Theoretically, the observed phenomena can be explained by considering the electrically induced valence band shift and the valley optical selection rule in the heterostructure system. Our theoretical simulation results show a good agreement with the experimental results. To the best of our knowledge, our finding is the first demonstration of the electrically tunable geometric circular photocurrent in the 2D TMD heterostructure. It demonstrates that the electrode geometry plays an important role in the photocurrent generation.

2. EXPERIMENTAL RESULTS

Figure 1(a) shows the microscopic image of the fabricated device. It consists of gold electrodes patterned on top of an ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure with ${{\rm SiO}_2}/{\rm Si}$ as the substrate. The ${{\rm MoS}_2}/{{\rm WSe}_2}$ structure is illustrated in Fig. 1(b). The ${{\rm MoS}_2}({{\rm WSe}_2})$ consists of Mo (W) atom located between the S (Se) atomic layers, creating a hexagonal lattice without the inversion symmetry. The inversion symmetry absence results in Berry curvatures to be nonzero and has opposite polarity at K and ${{\rm K}^\prime}$ valleys. As a result, these valleys couple to different circular polarizations [1014]. The type-II band alignment of ${{\rm MoS}_2}/{{\rm WSe}_2}$ [Fig. 1(c)] causes electrons to relax to the ${{\rm MoS}_2}$ layer while holes relax to the ${{\rm WSe}_2}$ layer, suppressing the electron–hole exchange interaction. Such suppression reduced the intervalley scattering [2426], which results in a significant valley polarization of the carrier even at room temperature [27]. Additionally, the suppression of the intervalley scattering could increase the carrier relaxation time. The carrier high valley polarization and the long relaxation time in ${{\rm MoS}_2}/{{\rm WSe}_2}$ can contribute to a sizable circular photocurrent.

 figure: Fig. 1.

Fig. 1. Device, experimental setup, and room temperature circular photocurrent map. (a) Optical image of the device; the device consists of gold electrodes patterned on top of ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure with ${{\rm SiO}_2}/{\rm Si}$ as the substrate. (b) Molecular structure of the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure; the monolayer ${{\rm WSe}_2}$ is stacked on top of the monolayer ${{\rm MoS}_2}$. (c) Carrier relaxation in the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure; the electrons relax quickly to the ${{\rm MoS}_2}$ layer while the holes relax to the ${{\rm WSe}_2}$. (d) Experimental setup; (e) circular photocurrent map with source: electrode 3 and drain: electrode 2 and (f) with source: electrode 6, and drain: electrode 5. A 720 nm 115 µW optical excitation is used at room temperature (295 K). The (+)/(−) indicates the current-collecting electrode, i.e., the current is positive if it flows from the (+) electrode to the (−) electrode. The source-drain bias is not applied.

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The setup for detecting and characterizing the circular photocurrent is shown in Fig. 1(d). The polarization state of the light is controlled either by changing the phase retardation of the liquid crystal modulator or the quarter-wave plate (QWP) axis orientation. The excitation can be scanned over the sample area using a galvo mirror system (not shown in the schematic) located before the polarizer. In the case that liquid crystal is used to modulate the circular polarization, the current is passed into a lock-in amplifier to get the circular photocurrent. In the case the QWP is used, the dark current is subtracted using a chopper and a lock-in amplifier. Here, the circular photocurrent (${I_{{\rm CPGE}}}$) is defined as the difference between the source-drain current under a left-circularly (${\sigma _ +}$) and a right-circularly (${\sigma _ -}$) polarized optical excitation: ${I_{{\rm CPGE}}} = {I_{{\rm SD}}}({\sigma _ +}) - {I_{{\rm SD}}}({\sigma _ -})$. The source-drain voltage, ${V_{{\rm SD}}}$, and the back-gate voltage, ${V_G}$, can be varied independently. All of the experiments were done under a normal incidence optical excitation, which rules out any contribution from the circular photon drag effect [17]. The excitation wavelength is 720 nm, which is near the ${{\rm WSe}_2}$ exciton transition [28], with its power around 100 to 115 µW (the dependence of the circular photocurrent on the excitation power and wavelength can be found in Supplement 1, Note 1 and Fig. S1).

First, we obtain the circular photocurrent map (i.e., ${I_{{\rm CPGE}}}$ versus the excitation location) at room temperature (295 K) under zero bias (${V_{{\rm SD}}} = {V_G} = 0\;{\rm V} $) with the circular polarization modulated by using a liquid crystal modulator. The results for two different electrode configurations are shown in Figs. 1(e) and 1(f), respectively. The reproducibility of the phenomenon is confirmed by testing a different sample using the same setup (Supplement 1, Note 2 and Fig. S2). The circular photocurrent shows a geometrical dependence. The magnitude of the circular photocurrent is much higher for the excitation near the edge of the metal electrodes, while its polarity depends on which side of the electrode is optically excited. A similar conclusion is obtained for different electrode pair configurations at different temperatures [see Figs. 2(a) and 2(b)], and Supplement 1, Figs. S3 and S4).

 figure: Fig. 2.

Fig. 2. Circular photocurrent map and characterization against source-drain voltage at 140 K. (a) Circular photocurrent map with source: electrode 3, and drain: electrode 2, and (b) with source: electrode 6, and drain: electrode 5; (c) photocurrent versus the QWP fast axis angle at various source-drain voltages; (d) circular photocurrent versus source-drain voltage. Equation (1) is used to fit the data in Fig. 2(c). A 720 nm 100 µW optical excitation is used.

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 figure: Fig. 3.

Fig. 3. Circular photocurrent characterization versus gate voltage at 295 K. (a) Circular photocurrent versus gate voltage; a liquid crystal modulator and a 720 nm 115 µW optical excitation are used. (b) Photocurrent versus QWP fast axis angle at various back-gate voltages; (c) circular, linear, and polarization-independent current versus the source-drain voltage. Equation (1) is used to fit the data in Fig. 3(b). Here, ${I_{{\rm LPGE}}} = \sqrt {{I_1}^2 + {I_2}^2} \approx {I_1}$.

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These experimental data show that this geometric photocurrent depends on parameters that are significant only near the electrode edges. One candidate for such parameters is the built-in in-plane electric field, which is caused by the band bending near the electrode–sample interface. We then study how the in-plane electric field affects the circular photocurrent. This is done by modulating the source-drain voltage, which mainly affects the in-plane electric field (see Supplement 1, Fig. S6 (c, d)). The QWP is used to modulate the optical excitation polarization. In Fig. 2(c), the photocurrent at various source-drain voltages is plotted as a function of a QWP fast axis angle with respect to the polarizer axis. The data are fitted using the fitting function

$${I_{{\rm SD}}} = {I_0} + {I_1}\sin (4\theta) + {I_2}\cos (4\theta) + {I_{{\rm CPGE}}}\sin (2\theta).$$
Here, ${I_0}$ is the polarization-independent photocurrent while ${I_1}$ and ${I_2}$ are related to the linear photocurrent (i.e., the photocurrent caused by a linearly polarized optical excitation). In Fig. 2(d), ${I_{{\rm CPGE}}}$ obtained from the fitting is plotted as a function of the source-drain voltage. From this figure, it can be concluded that the in-plane electric field modulates both the magnitude and the polarity of the circular photocurrent.
 figure: Fig. 4.

Fig. 4. Microscopic model and the simulation result. (a) The in-plane electric field shifts the valence band at K and ${\rm Kn}$ valley in two opposite directions. Resonant optical excitation creates an electron and hole in the ${{\rm WSe}_2}$ layer. Electrons then transfer to the ${{\rm MoS}_2}$ layer. The difference in the carrier relaxation time of the electron (${\tau _M}$) and hole (${\tau _W}$) results in a nonzero valley-dependent photocurrent with opposite directions in the K and ${{\rm K}^\prime}$ valleys. Combined with the valley optical selection rule, this results in an electrically tunable circular photocurrent density. (b)–(c) COMSOL simulation of ${I_{{\rm CPGE}}}$ for (source, drain): (electrode 3, 2) and (electrode 6, 5), respectively. The unit for ${I_{{\rm CPGE}}}$ is the same in both figures. The simulation results agree well with the experimental result.

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Next, we study the back-gate voltage dependence of the photocurrent. We first use the liquid crystal modulator to modulate the optical polarization. Additionally, we also study the polarization-independent part, which is defined as $\overline {{I_{{\rm SD}}}} = 0.5\{{{I_{{\rm SD}}}({\sigma _ +}) + {I_{{\rm SD}}}({\sigma _ -})} \}$ (i.e., it includes the dark current) using this setup. The plot of ${I_{{\rm CPGE}}}$ and $\overline {{I_{{\rm SD}}}}$ as a function of the back-gate voltage ${V_G}$ are shown in the upper and lower panels of Fig. 3(a), respectively. We can see that both ${I_{{\rm CPGE}}}$ and $\overline {{I_{{\rm SD}}}}$ approach zero as the back-gate voltage goes to a more negative value. We then replace the liquid crystal modulator with a QWP. Figure 3(b) shows the photocurrent as a function of the QWP fast axis angle at various back-gate voltages. The plots of all three types of photocurrent [extracted using Eq. (1)] as functions of the back-gate voltage are given in Fig. 3(c). As can be seen from this figure, all photocurrents approach zero as the back-gate voltage is reduced.

Based on the experiments above, we can conclude that: (1) the in-plane electric field affects both the circular photocurrent magnitude and polarity; (2) the back gating does not change the circular photocurrent polarity; and (3) the back-gate voltage affects the circular photocurrent magnitude the same way as it affects the magnitude of other types of current. These indicate that the circular photocurrent generation mechanism depends on the in-plane electric field, while the back gating affects the overall conductivity.

3. THEORETICAL INTERPRETATION

We start by analyzing the effect of the in-plane electric field on the circular photocurrent. Under the influence of the in-plane electric field, the electron wave packet velocity will have two components: (1) a component proportional to the slope of the energy band, and (2) the anomalous velocity perpendicular to the in-plane electric field [2931]. Since the observed circular photocurrent has a direction parallel to the electric field, it cannot be attributed to the anomalous velocity. Hence, the observed geometric circular photocurrent must be attributed to the modification of the energy band due to the in-plane electric field. Near the electrode–sample boundary, the nonzero in-plane electric field causes the valence band at the K and ${{\rm K}^\prime}$ valley to shift in two opposite directions. Given this band shift, we can then explain the geometric circular photocurrent mechanism.

The proposed mechanism is illustrated in Fig. 4(a) for the resonant excitation case (i.e., the excitation is resonant with the ${{\rm WSe}_2}$ exciton energy). The optical excitation creates the nonequilibrium electron and hole populations, with their velocity proportional to the conduction and valence band slope, respectively. Due to the valley optical selection rule in ${{\rm WSe}_2}$, the light with ${\sigma _ +}$ (${\sigma _ -}$) polarization can only generate a carrier around the K (${{\rm K}^\prime}$) valley. In one valley, there are two transitions with the same energy. One of the transitions generates a nonzero electron current, while the other generates a nonzero hole current, both in the same direction. Due to the opposite charge between the electron and the hole, the two contributions tend to eliminate each other. However, in the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure, the electron will undergo ultrafast charge transfer to the ${{\rm MoS}_2}$ layer [32]. Because of this charge transfer, and considering that both the electron relaxation time and the conduction band curvature of the ${{\rm MoS}_2}$ are different from those in the ${{\rm WSe}_2}$, the current generated by the electrons and holes will not cancel each other. As a result, a nonzero photocurrent is generated in the ${\rm K}/{{\rm K}^\prime}$ valley. Due to the opposite shift between the valence band in the K and ${{\rm K}^\prime}$ valley, the photocurrent will have an opposite direction for these two valleys, which results in a nonzero circular photocurrent. Furthermore, since the shift is linearly proportional to the in-plane electric field, the circular photocurrent will also be linearly proportional to this field.

Following this model, the circular photocurrent density, $\overrightarrow {{J_{{\rm CPGE}}}}$, can be expressed as

$$\overrightarrow {{J_{{\rm CPGE}}}} \propto A\!\left({\hat x{C_1}\sin \alpha + \hat y{C_2}\cos \alpha} \right),$$
where $A$ is the in-plane electric field amplitude at the excitation location, ${C_{1(2)}}$ is a constant independent of the in-plane electric field, and $\alpha$ is the angle between the in-plane electric field direction and the zigzag direction ($x$ axis; see Supplement 1, Fig. S7), i.e., the electric field can be written as $\overrightarrow E = A({\hat x\cos \alpha + \hat y\sin \alpha})$. The value of ${I_{{\rm CPGE}}}$ can then be obtained by taking the scalar product between $\overrightarrow {{J_{{\rm CPGE}}}}$ and a virtual electric field going from the (+) electrode to the (−) electrode and integrating it over the sample [33]. By repeating this procedure for all excitation locations, we can obtain the circular photocurrent map.

To give a qualitative picture of the circular photocurrent map, we first neglect the effect of the floating (i.e., noncurrent collecting) electrodes. Near the current-collecting electrode, ${I_{{\rm CPGE}}}$ can be expressed as

$${I_{{\rm CPGE}}} \propto \beta A\sin \left({2\alpha} \right),$$
where $\beta = 1$ for the (+) electrode and $\beta = - 1$ for the (−) electrode. Since the built-in in-plane electric field is only significant near the electrode edge, ${I_{{\rm CPGE}}}$ is reduced significantly for the optical excitation far away from the edge. Moreover, at the two sides of the same electrode, $\alpha$ differs by 180°, which results in the same sign for the circular photocurrent, while between the two perpendicular sides of the electrode, $\alpha$ differs by 90°, which results in the opposite sign for the circular photocurrent. This is in line with the conclusions obtained from the experimental results. The circular photocurrent simulation results, including the effect of both current-collecting and floating electrodes, are shown in Figs. 4(b) and 4(c). They show a good agreement with the experimental results.

We now discuss the effect of the back-gate voltage, which mainly affects the carrier doping and the out-of-plane electric field. The carrier doping due to the back-gate voltage will change the Fermi level. There are two effects of changing the Fermi level. The first one is that it will change the built-in in-plane electric field, since it affects the band bending between the ${{\rm MoS}_2}$ (${{\rm WSe}_2}$) and the Cr/Au electrode. This will affect ${I_{{\rm CPGE}}}$ in the same way as the in-plane electric field does. The second effect is that it can change the conduction band electron mobility. When the Fermi level is higher than some defect states’ energy, the defects will be fully occupied and cannot act as scattering centers [22]. This results in higher mobility of the conduction band electron. Unlike the first mechanism, the second one will affect all types of current. The interplay between these two mechanisms depends on the energy level of the traps. However, based on the fact that all types of currents show similar behavior as the gate voltage is changed, we conclude that the second mechanism is more dominant in our case. This is supported by further theoretical analysis (see Supplement 1, Note 5), which also shows that the effect of the out-of-plane electric field inside the heterostructure due to the back gating can be omitted.

4. SUMMARY

We have demonstrated the circular photocurrent under normal incidence optical excitation near an ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure-electrode interface. The circular photocurrent has a geometric dependence and can be controlled by the source-drain bias and the back gating. The source-drain dependence can be explained by the field-induced valence band shift and the valley-specific optical selection rules. The simulation results of the circular photocurrent maps fit well with the experimental results. The back-gate dependence is attributed to the back-gate modulation of the carrier mobility. Combined with the long carrier and spin polarization lifetime in the 2D heterostructure [34], this finding may be utilized to realize practical valleytronics and spintronics semiconductor devices.

Funding

China Scholarship Council (No. 201709345003); National Natural Science Foundation of China (No. 61974075, No. 61704121); Agency for Science, Technology and Research (QTE); National Research Foundation Singapore (QEP, NRF-CRP21-2018-0007); Ministry of Education - Singapore (MOE2016-T2-1-163, MOE2016-T2-2-077, MOE2016-T3-1-006 (S)).

Acknowledgment

We thank Wang Yao, Feng Wang, and Justin C.W. Song for the discussions. C. J. thanks the Key Laboratory of Photoelectronic Thin Film Devices and Technology of Tianjin and Engineering Research Center of Thin Film Optoelectronics Technology, Ministry of Education of China for the support.

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

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References

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  1. I. Žutić, J. Fabian, and S. D. Sarma, “Spintronics: fundamentals and applications,” Rev. Mod. Phys. 76, 323 (2004).
    [Crossref]
  2. D. D. Awschalom and M. E. Flatté, “Challenges for semiconductor spintronics,” Nat. Phys. 3, 153–159 (2007).
    [Crossref]
  3. A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
    [Crossref]
  4. K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D materials and van der Waals heterostructures,” Science 353, aac9439 (2016).
    [Crossref]
  5. H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
    [Crossref]
  6. M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
    [Crossref]
  7. K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, and A. Singh, “Evidence for moiré excitons in van der Waals heterostructures,” Nature 567, 71–75 (2019).
    [Crossref]
  8. I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, “Proximitized materials,” Mater. Today 22, 85–107 (2019).
    [Crossref]
  9. Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
    [Crossref]
  10. G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
    [Crossref]
  11. K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
    [Crossref]
  12. T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
    [Crossref]
  13. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
    [Crossref]
  14. H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
    [Crossref]
  15. K. F. Mak, K. L. McGill, J. Park, and P. L. McEuen, “The valley Hall effect in MoS2 transistors,” Science 344, 1489–1492 (2014).
    [Crossref]
  16. N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
    [Crossref]
  17. J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
    [Crossref]
  18. H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
    [Crossref]
  19. S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
    [Crossref]
  20. Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
    [Crossref]
  21. M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
    [Crossref]
  22. L. Liu, E. J. Lenferink, G. Wei, T. K. Stanev, N. Speiser, and N. P. Stern, “Electrical control of circular photogalvanic spin-valley photocurrent in a monolayer semiconductor,” ACS Appl. Mater. Interfaces 11, 3334–3341 (2018).
    [Crossref]
  23. H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
    [Crossref]
  24. C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
    [Crossref]
  25. M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, “Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides,” Phys. Rev. B 89, 201302 (2014).
    [Crossref]
  26. T. Yu and M. Wu, “Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayer MoS2,” Phys. Rev. B 89, 205303 (2014).
    [Crossref]
  27. Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
    [Crossref]
  28. C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
    [Crossref]
  29. M.-C. Chang and Q. Niu, “Berry phase, hyperorbits, and the Hofstadter spectrum,” Phys. Rev. Lett. 75, 1348–1351 (1995).
    [Crossref]
  30. Y. Gao, S. A. Yang, and Q. Niu, “Field induced positional shift of Bloch electrons and its dynamical implications,” Phys. Rev. Lett. 112, 166601 (2014).
    [Crossref]
  31. G. Sundaram and Q. Niu, “Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects,” Phys. Rev. B 59, 14915–14925 (1999).
    [Crossref]
  32. C. Jin, E. Y. Ma, O. Karni, E. C. Regan, F. Wang, and T. F. Heinz, “Ultrafast dynamics in van der Waals heterostructures,” Nat. Nanotechnol. 13, 994–1003 (2018).
    [Crossref]
  33. J. C. Song and L. S. Levitov, “Shockley-Ramo theorem and long-range photocurrent response in gapless materials,” Phys. Rev. B 90, 075415 (2014).
    [Crossref]
  34. J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
    [Crossref]

2020 (1)

Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
[Crossref]

2019 (4)

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
[Crossref]

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, and A. Singh, “Evidence for moiré excitons in van der Waals heterostructures,” Nature 567, 71–75 (2019).
[Crossref]

I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, “Proximitized materials,” Mater. Today 22, 85–107 (2019).
[Crossref]

2018 (5)

J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
[Crossref]

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

L. Liu, E. J. Lenferink, G. Wei, T. K. Stanev, N. Speiser, and N. P. Stern, “Electrical control of circular photogalvanic spin-valley photocurrent in a monolayer semiconductor,” ACS Appl. Mater. Interfaces 11, 3334–3341 (2018).
[Crossref]

C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
[Crossref]

C. Jin, E. Y. Ma, O. Karni, E. C. Regan, F. Wang, and T. F. Heinz, “Ultrafast dynamics in van der Waals heterostructures,” Nat. Nanotechnol. 13, 994–1003 (2018).
[Crossref]

2017 (3)

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
[Crossref]

N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
[Crossref]

H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
[Crossref]

2016 (1)

K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D materials and van der Waals heterostructures,” Science 353, aac9439 (2016).
[Crossref]

2015 (2)

Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
[Crossref]

M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
[Crossref]

2014 (8)

H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
[Crossref]

C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
[Crossref]

M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, “Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides,” Phys. Rev. B 89, 201302 (2014).
[Crossref]

T. Yu and M. Wu, “Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayer MoS2,” Phys. Rev. B 89, 205303 (2014).
[Crossref]

J. C. Song and L. S. Levitov, “Shockley-Ramo theorem and long-range photocurrent response in gapless materials,” Phys. Rev. B 90, 075415 (2014).
[Crossref]

Y. Gao, S. A. Yang, and Q. Niu, “Field induced positional shift of Bloch electrons and its dynamical implications,” Phys. Rev. Lett. 112, 166601 (2014).
[Crossref]

K. F. Mak, K. L. McGill, J. Park, and P. L. McEuen, “The valley Hall effect in MoS2 transistors,” Science 344, 1489–1492 (2014).
[Crossref]

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

2013 (1)

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

2012 (5)

G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
[Crossref]

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
[Crossref]

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
[Crossref]

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

2007 (1)

D. D. Awschalom and M. E. Flatté, “Challenges for semiconductor spintronics,” Nat. Phys. 3, 153–159 (2007).
[Crossref]

2004 (1)

I. Žutić, J. Fabian, and S. D. Sarma, “Spintronics: fundamentals and applications,” Rev. Mod. Phys. 76, 323 (2004).
[Crossref]

1999 (1)

G. Sundaram and Q. Niu, “Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects,” Phys. Rev. B 59, 14915–14925 (1999).
[Crossref]

1995 (1)

M.-C. Chang and Q. Niu, “Berry phase, hyperorbits, and the Hofstadter spectrum,” Phys. Rev. Lett. 75, 1348–1351 (1995).
[Crossref]

Addison, Z.

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
[Crossref]

Agarwal, R.

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
[Crossref]

Amand, T.

C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
[Crossref]

M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, “Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides,” Phys. Rev. B 89, 201302 (2014).
[Crossref]

G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
[Crossref]

Awschalom, D. D.

D. D. Awschalom and M. E. Flatté, “Challenges for semiconductor spintronics,” Nat. Phys. 3, 153–159 (2007).
[Crossref]

Belashchenko, K.

I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, “Proximitized materials,” Mater. Today 22, 85–107 (2019).
[Crossref]

Berger, H.

N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
[Crossref]

Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
[Crossref]

Bouet, L.

M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, “Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides,” Phys. Rev. B 89, 201302 (2014).
[Crossref]

G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
[Crossref]

Cai, H.

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
[Crossref]

Cao, B.

M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
[Crossref]

Cao, T.

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
[Crossref]

Carvalho, A.

K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D materials and van der Waals heterostructures,” Science 353, aac9439 (2016).
[Crossref]

Chan, C.-K.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Chang, G.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Chang, M.-C.

M.-C. Chang and Q. Niu, “Berry phase, hyperorbits, and the Hofstadter spectrum,” Phys. Rev. Lett. 75, 1348–1351 (1995).
[Crossref]

Chang, T.-R.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Chen, B.

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
[Crossref]

Chen, H.

Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
[Crossref]

Chen, S.

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

Choi, J.

K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, and A. Singh, “Evidence for moiré excitons in van der Waals heterostructures,” Nature 567, 71–75 (2019).
[Crossref]

Cong, C.

M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
[Crossref]

Costanzo, D.

N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
[Crossref]

Crommie, M. F.

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
[Crossref]

Cui, X.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

Cui, Y.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

Dai, J.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

Dean, C. R.

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

Dery, H.

I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, “Proximitized materials,” Mater. Today 22, 85–107 (2019).
[Crossref]

Dini, K.

Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
[Crossref]

Eginligil, M.

M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
[Crossref]

Fabian, J.

I. Žutić, J. Fabian, and S. D. Sarma, “Spintronics: fundamentals and applications,” Rev. Mod. Phys. 76, 323 (2004).
[Crossref]

Fang, H.

Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
[Crossref]

Fang, X.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

Fatemi, V.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Feng, W.

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
[Crossref]

Flatté, M. E.

D. D. Awschalom and M. E. Flatté, “Challenges for semiconductor spintronics,” Nat. Phys. 3, 153–159 (2007).
[Crossref]

Gao, H.

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
[Crossref]

Gao, W.

Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
[Crossref]

Gao, W.-B.

C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
[Crossref]

Gao, Y.

Y. Gao, S. A. Yang, and Q. Niu, “Field induced positional shift of Bloch electrons and its dynamical implications,” Phys. Rev. Lett. 112, 166601 (2014).
[Crossref]

Geim, A. K.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499, 419–425 (2013).
[Crossref]

Ghiasi, T. S.

J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
[Crossref]

Gibson, Q. D.

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Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
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H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
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Taniguchi, T.

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
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J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
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Tongay, S.

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
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K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, and A. Singh, “Evidence for moiré excitons in van der Waals heterostructures,” Nature 567, 71–75 (2019).
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N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
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M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, “Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides,” Phys. Rev. B 89, 201302 (2014).
[Crossref]

C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
[Crossref]

Valdivia, A. M. M.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
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J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
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van der Wal, C. H.

J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
[Crossref]

van Wees, B. J.

J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
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Wang, E.

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
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C. Jin, E. Y. Ma, O. Karni, E. C. Regan, F. Wang, and T. F. Heinz, “Ultrafast dynamics in van der Waals heterostructures,” Nat. Nanotechnol. 13, 994–1003 (2018).
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J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
[Crossref]

Wang, G.

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
[Crossref]

G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
[Crossref]

Wang, X.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
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Wang, Z.

M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
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Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
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M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
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J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
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L. Liu, E. J. Lenferink, G. Wei, T. K. Stanev, N. Speiser, and N. P. Stern, “Electrical control of circular photogalvanic spin-valley photocurrent in a monolayer semiconductor,” ACS Appl. Mater. Interfaces 11, 3334–3341 (2018).
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Wu, F.

K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, and A. Singh, “Evidence for moiré excitons in van der Waals heterostructures,” Nature 567, 71–75 (2019).
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Wu, M.

T. Yu and M. Wu, “Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayer MoS2,” Phys. Rev. B 89, 205303 (2014).
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Wu, S.

S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Wu, Y.

H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
[Crossref]

Xiao, D.

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
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C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
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Xu, G.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

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S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
[Crossref]

Xu, W.

C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
[Crossref]

Xu, X.

H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
[Crossref]

H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
[Crossref]

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
[Crossref]

Xu, Y.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
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Y. Gao, S. A. Yang, and Q. Niu, “Field induced positional shift of Bloch electrons and its dynamical implications,” Phys. Rev. Lett. 112, 166601 (2014).
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M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

Yao, W.

H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
[Crossref]

H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
[Crossref]

D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, “Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides,” Phys. Rev. Lett. 108, 196802 (2012).
[Crossref]

H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
[Crossref]

Ye, H.

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
[Crossref]

You, J. S.

J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
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M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

Yu, H.

H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, “Moiré excitons: from programmable quantum emitter arrays to spin-orbit–coupled artificial lattices,” Sci. Adv. 3, e1701696 (2017).
[Crossref]

H. Yu, Y. Wu, G.-B. Liu, X. Xu, and W. Yao, “Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals,” Phys. Rev. Lett. 113, 156603 (2014).
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Yu, P.

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
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M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
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T. Yu and M. Wu, “Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayer MoS2,” Phys. Rev. B 89, 205303 (2014).
[Crossref]

Yuan, H.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

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H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, “Valley polarization in MoS2 monolayers by optical pumping,” Nat. Nanotechnol. 7, 490–493 (2012).
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H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
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Zhang, K.

C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
[Crossref]

Zhang, S.-C.

H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
[Crossref]

Zhang, Y.

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
[Crossref]

Zhao, T.

J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K. Watanabe, T. Taniguchi, S. Tongay, M. F. Crommie, and F. Wang, “Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures,” Sci. Adv. 3, e1700518 (2017).
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C. Zhu, K. Zhang, M. Glazov, B. Urbaszek, T. Amand, Z. Ji, B. Liu, and X. Marie, “Exciton valley dynamics probed by Kerr rotation in WSe2 monolayers,” Phys. Rev. B 90, 161302 (2014).
[Crossref]

T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, and B. Liu, “Valley-selective circular dichroism of monolayer molybdenum disulphide,” Nat. Commun. 3, 887 (2012).
[Crossref]

G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
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ACS Appl. Mater. Interfaces (1)

L. Liu, E. J. Lenferink, G. Wei, T. K. Stanev, N. Speiser, and N. P. Stern, “Electrical control of circular photogalvanic spin-valley photocurrent in a monolayer semiconductor,” ACS Appl. Mater. Interfaces 11, 3334–3341 (2018).
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Mater. Today (1)

I. Žutić, A. Matos-Abiague, B. Scharf, H. Dery, and K. Belashchenko, “Proximitized materials,” Mater. Today 22, 85–107 (2019).
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N. Ubrig, S. Jo, M. Philippi, D. Costanzo, H. Berger, A. B. Kuzmenko, and A. F. Morpurgo, “Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping,” Nano Lett. 17, 5719–5725 (2017).
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Z. Huang, Y. Liu, K. Dini, Q. Tan, Z. Liu, H. Fang, J. Liu, T. Liew, and W. Gao, “Robust room temperature valley Hall effect of interlayer excitons,” Nano Lett. 20, 1345–1351 (2020).
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C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. Li, Q. Xiong, and W.-B. Gao, “Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures,” Nat. Commun. 9, 753 (2018).
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M. Eginligil, B. Cao, Z. Wang, X. Shen, C. Cong, J. Shang, C. Soci, and T. Yu, “Dichroic spin–valley photocurrent in monolayer molybdenum disulphide,” Nat. Commun. 6, 7636 (2015).
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J. Quereda, T. S. Ghiasi, J. S. You, J. van den Brink, B. J. van Wees, and C. H. van der Wal, “Symmetry regimes for circular photocurrents in monolayer MoSe2,” Nat. Commun. 9, 3346 (2018).
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Z. Wang, D. K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, “Strong interface-induced spin–orbit interaction in graphene on WS2,” Nat. Commun. 6, 8339 (2015).
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Nat. Mater. (1)

Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A. M. Rappe, C. L. Kane, E. J. Mele, and R. Agarwal, “Spatially dispersive circular photogalvanic effect in a Weyl semimetal,” Nat. Mater. 18, 955–962 (2019).
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H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H. Y. Hwang, and Y. Cui, “Generation and electric control of spin–valley-coupled circular photogalvanic current in WSe2,” Nat. Nanotechnol. 9, 851–857 (2014).
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S.-Y. Xu, Q. Ma, H. Shen, V. Fatemi, S. Wu, T.-R. Chang, G. Chang, A. M. M. Valdivia, C.-K. Chan, and Q. D. Gibson, “Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2,” Nat. Phys. 14, 900–906 (2018).
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G. Sallen, L. Bouet, X. Marie, G. Wang, C. Zhu, W. Han, Y. Lu, P. Tan, T. Amand, and B. Liu, “Robust optical emission polarization in MoS2 monolayers through selective valley excitation,” Phys. Rev. B 86, 081301 (2012).
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M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363, 1059–1064 (2019).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Device, experimental setup, and room temperature circular photocurrent map. (a) Optical image of the device; the device consists of gold electrodes patterned on top of ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure with ${{\rm SiO}_2}/{\rm Si}$ as the substrate. (b) Molecular structure of the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure; the monolayer ${{\rm WSe}_2}$ is stacked on top of the monolayer ${{\rm MoS}_2}$ . (c) Carrier relaxation in the ${{\rm MoS}_2}/{{\rm WSe}_2}$ heterostructure; the electrons relax quickly to the ${{\rm MoS}_2}$ layer while the holes relax to the ${{\rm WSe}_2}$ . (d) Experimental setup; (e) circular photocurrent map with source: electrode 3 and drain: electrode 2 and (f) with source: electrode 6, and drain: electrode 5. A 720 nm 115 µW optical excitation is used at room temperature (295 K). The (+)/(−) indicates the current-collecting electrode, i.e., the current is positive if it flows from the (+) electrode to the (−) electrode. The source-drain bias is not applied.
Fig. 2.
Fig. 2. Circular photocurrent map and characterization against source-drain voltage at 140 K. (a) Circular photocurrent map with source: electrode 3, and drain: electrode 2, and (b) with source: electrode 6, and drain: electrode 5; (c) photocurrent versus the QWP fast axis angle at various source-drain voltages; (d) circular photocurrent versus source-drain voltage. Equation (1) is used to fit the data in Fig. 2(c). A 720 nm 100 µW optical excitation is used.
Fig. 3.
Fig. 3. Circular photocurrent characterization versus gate voltage at 295 K. (a) Circular photocurrent versus gate voltage; a liquid crystal modulator and a 720 nm 115 µW optical excitation are used. (b) Photocurrent versus QWP fast axis angle at various back-gate voltages; (c) circular, linear, and polarization-independent current versus the source-drain voltage. Equation (1) is used to fit the data in Fig. 3(b). Here, ${I_{{\rm LPGE}}} = \sqrt {{I_1}^2 + {I_2}^2} \approx {I_1}$ .
Fig. 4.
Fig. 4. Microscopic model and the simulation result. (a) The in-plane electric field shifts the valence band at K and ${\rm Kn}$ valley in two opposite directions. Resonant optical excitation creates an electron and hole in the ${{\rm WSe}_2}$ layer. Electrons then transfer to the ${{\rm MoS}_2}$ layer. The difference in the carrier relaxation time of the electron ( ${\tau _M}$ ) and hole ( ${\tau _W}$ ) results in a nonzero valley-dependent photocurrent with opposite directions in the K and ${{\rm K}^\prime}$ valleys. Combined with the valley optical selection rule, this results in an electrically tunable circular photocurrent density. (b)–(c) COMSOL simulation of ${I_{{\rm CPGE}}}$ for (source, drain): (electrode 3, 2) and (electrode 6, 5), respectively. The unit for ${I_{{\rm CPGE}}}$ is the same in both figures. The simulation results agree well with the experimental result.

Equations (3)

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I S D = I 0 + I 1 sin ( 4 θ ) + I 2 cos ( 4 θ ) + I C P G E sin ( 2 θ ) .
J C P G E A ( x ^ C 1 sin α + y ^ C 2 cos α ) ,
I C P G E β A sin ( 2 α ) ,

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