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# Dichroic spin–valley photocurrent in monolayer molybdenum disulphide

## Abstract

The aim of valleytronics is to exploit confinement of charge carriers in local valleys of the energy bands of semiconductors as an additional degree of freedom in optoelectronic devices. Thanks to strong direct excitonic transitions in spin-coupled K valleys, monolayer molybdenum disulphide is a rapidly emerging valleytronic material, with high valley polarization in photoluminescence. Here we elucidate the excitonic physics of this material by light helicity-dependent photocurrent studies of phototransistors. We demonstrate that large photocurrent dichroism (up to 60%) can also be achieved in high-quality molybdenum disulphide monolayers grown by chemical vapour deposition, due to the circular photogalvanic effect on resonant excitations. This opens up new opportunities for valleytonic applications in which selective control of spin–valley-coupled photocurrents can be used to implement polarization-sensitive light-detection schemes or integrated spintronic devices, as well as biochemical sensors operating at visible frequencies.

## Introduction

Research on two-dimensional (2D) materials synthesis and characterization has accelerated since the discovery of graphene1, for the purpose of utilizing these multifunctional materials in highly efficient nano- and biotechnological platforms2. Among 2D materials, particularly transition metal dichalcogenide (TMD) monolayers3,4 have shown various interesting properties such as charge density waves5, unusual strain6 and thermal energy dependence7, tunable light emission by chemical control8 and fast photoresponse9, which can be used in interdisciplinary device applications. Today’s nanodevices mostly use charge and spin degree of freedom; however, it is also possible to exploit the valley degree of freedom, which is simply the confinement of charge carriers in momentum space of 2D materials. For instance, in molybdenum disulphide (MoS2)—a 2D semiconductor TMD and a non-centrosymmertic crystal—inherent broken inversion symmetry in monolayers leads to a large spin–orbit interaction (SOI) that splits the valence band (VB) by 150 meV10 and gives rise to strong excitonic transitions due to the direct band gap at low energy K and −K valleys. The upper (lower) VB is associated with the A (B) excitons. The same broken inversion symmetry together with time reversal symmetry is responsible for spin–valley coupling in monolayer MoS2 and similar TMDs (WS2, WSe2 and MoSe2); that is, the sign of the hole spin in the upper (or lower) VB will oppose in different valleys. The descriptive Hamiltonian10 can be simply expressed as where a is the lattice constant, t the effective hopping integral, τ (±1) the valley index, the Pauli matrices, Δ the energy gap, 2λ the spin splitting at the VB, and the Pauli matrix for spin; kx, ky, kz are the momentum components in x, y, z coordinates, respectively. The first term is related to the valley related hopping, the second term is purely spin dependent and the last term describes the spin-dependent phenomena as a result of SOI in each valleys. The spin–valley coupling in the last term, which leads to the valley polarization, was demonstrated experimentally by light helicity-dependent photoluminescence measurements corresponding to the A and B excitons in monolayer MoS211,12. Recently, in suspended monolayer MoS2 samples, photocurrent (PC) due to the A and B excitons was also revealed13. A useful framework to study light–matter interactions in 2D materials is based on PC experiments performed by circularly polarized excitation14. However, helicity-dependent PCs due to excitons with on-resonance and off-resonance excitations in monolayer TMDs are still to be uncovered.

There have been extensive studies on growth techniques of TMDs to synthesize high-quality, single-crystal and large-area samples. Among these efforts, high-quality single layer but small area (<10 μm) samples that are mechanically cleaved, have shown strong photoluminescence, fluorescence15,16, high-mobility–low-power switching17, and large photoresponse18. Alternatively, samples grown by chemical vapour deposition (CVD) methods19,20,21,22 also yield quite intense light emission23, particularly monolayers of tungsten disulphide (WS2) have shown stronger photoluminescence than mechanically cleaved monolayers24. In terms of electrical transport, both mechanically cleaved and CVD grown WS2 and MoS2 have n-type behaviour. In addition, since CVD method allows also growing multiple 2D materials to form hetero- and hybrid structures4, it offers to tailor functional physical systems and, particularly for optoelectronics and spin-dependent valleytronics. The possibility of synthesizing high-quality samples with much larger size (>500 μm) than mechanically cleaved samples gives CVD growth techniques a major advantage in the development of future technologies based on TMDs.

In this work, we demonstrate spin-coupled valley-dependent dichroic PC of a CVD grown single-layer MoS2 phototransistor excited by on-resonance and off-resonance photon energies (1.96 and 2.33 eV, respectively). A PC due to the circular photogalvanic effect (CPGE) arises as a result of circularly polarized light incident on monolayer MoS2 with an oblique angle. The spin–valley coupling, the valley selection rules and the excitation frequencies determine the magnitude of PC for left and right circularly polarized states. For excitations that are on-resonance with the excitons, there should be a difference between the CPGE PCs due to left and right circularly polarized excitations; while for excitations, which are off-resonance with the excitons, there should be no difference between these CPGE PCs. Our PC measurements evidence this variation and reveal a high-CPGE PC polarization. We remark on further possibilities of making use of this unique opto-valleytronic control for interdisciplinary applications.

## Results

### Spin–valley coupling and circular photogalvanic effect

The phenomenological expression of light helicity-dependent PC is strictly determined by the crystal symmetry, the angle of incidence, θ, (with respect to the normal to the sample plane), the azimuthal angle, φ, (light propagation with respect to the x-direction in the xy plane) of the excitation beam and the angle of photon polarization, ϕ, (with respect to the electric field vector direction)14. In transverse geometry (as shown in the experimental configuration) in which light is directed in the xz plane and the PC is measured in the y-direction, φ is fixed. If not otherwise specified, in this work, we used φ=90° and θ=45°, so that by rotating a quarter-wave plate (QWP), polarization of a linearly polarized laser can be varied from 0° linear (↔) to 45° left circular (σ−), back to 90° linear (↔) to 135° right circular (σ+) and then back to 180° linear (↔) polarization, and so on.

Monolayer MoS2 has crystal symmetry10,11,12. When a Mo atom is in an inversion centre, there is no coinciding atom when a S atom is projected to the 2D plane. When such a symmetry system is subjected to a circularly polarized light field with an oblique angle θ, (θ≠0°) a PC with sin 2ϕ dependence—current due to the CPGE, jCPGE will be the major PC. The angle of incidence θ dependence of jCPGE is sin θ. At the same time, a PC with cos 4ϕ dependence, which is due to the transfer of light momentum to electrons, is also present—the so-called linear photon drag effect (LPDE), jLPDE14. In addition, a PC similar to jCPGE in origin, but related to the linear polarization of light as jLPDE—linear photogalvanic effect (LPGE), jLPGE14 is also possible, although it should ideally vanish at σ+ and σ− excitations. On the basis of these three contributions, the total PC can be generally expressed by the phenomenological formula J=C1 sin 2ϕ+L1 sin 4ϕ+L2 cos 4ϕ+D. Here C1 is the coefficient for the CPGE current (jCPGE=C1 sin 2ϕ); L1 for the LPGE current (jLPGE=L1 sin 4ϕ); L2 for the LPDE current (jLPDE=L2 cos 4ϕ); and D is polarization-independent term.

In a recent work on multilayer WSe2, the jCPGE was observed due to absorption at Λ valleys—intraband transitions within the conduction band (CB)25. In the case of monolayer MoS2, spin–valley coupling will be at K valleys and the jCPGE should be due to interband transitions from the VB to the CB, for circularly polarized radiation with energies closer to the exciton energies. When spin couples to valley10, sign of the spin states of A (or B) excitons in one valley oppose to that in the other valley. By a simple approach, when excited by σ+ (σ−) excitations with energy slightly higher than the formation/dissociation energy of A exciton, an electron in VB makes an interband transition in K (−K) valley, with hole spin up ↑ (spin down ↓). Similarly, when excited by σ+ (σ−) excitations with energy slightly higher than the formation/dissociation energy of B exciton, an electron in VB makes an interband transition in K (−K) valley, with hole ↓ (↑) (Fig. 1). This coupling can be understood by the PC generated when circularly polarized light-field irradiated on the sample is perpendicular to the electrodes (as shown in the experimental setup). In such a case, the velocities υv of the carriers in the VB, which absorb this light field, will have a contribution additional to the one due to the band dispersion δɛ(k)/δk for energy ɛ(k) in k space. That contribution is the anomalous velocity which appears as the second term in υv(k)=(1)(δɛ(k)/δk)—((e/ħ) E × Ω)26, where ħ is the Planck constant, E the electric field vector, and Ω the Berry curvature that has the same magnitude but different sign in K and −K valleys, . Then, for excitation that is on-resonance with the A excitons, we can write the magnitude of υv(k) at K(−K), which actually depends on the light helicity, as υv(i) (↓)=|(e/ħ)E × Ω K(–K)|; and for excitation which is on-resonance with the B excitons, as υv(ii)↓()=|(e/ħ)E × ΩK(−K)|. In this case, the PC due to the υv(i) (υv(ii)), at σ+ excitation will be larger than the PC due to the υv(i) (υv(ii) ) at σ− excitation. As an example, for the A excitons, the CPGE current jCPGE (ħω), (ω is the excitation frequency) is given by jCPGE(ω)σ+ (σ−) or jCPGE(ω)K(−K)=(8/ħ) [∑v(i)→c (υcτ(ɛc)—((δɛv(i)k)—υv(i)(↓)τ(ɛv(i)))] |Mv(i)→c| |f(ɛc)–f(ɛv(i))| δ (ɛc–ɛv(i)ħω), and (υcτ(ɛc))>((δɛv(i)k)υv(i) (↓)τ(ɛv(i))); where v(i) is the initial VB state on-resonance with the A excitons and c is final CB states, Mvc is the transition matrix from the upper VB states to CB states, υc is the electron velocity in the CB states, τ(ɛv) and τ(ɛc) are the momentum relaxation times in the VB and CB, respectively. The Fermi–Dirac functions f(ɛc) and f(ɛv) are dependent on the gate voltage and to study purely interband transitions, the Fermi level must be lowered by negative gate voltage (off state). Here we remark at the condition (υcτ(ɛc))>((δɛvk)—υv (↓)τ(ɛv)), which determines the sign of jCPGE(ω)K(−K). We can consider the jCPGE(ω)K(−K) with three components: (1) υcτ(ɛc); (2) ɛvk); and (3) υv(i)(↓)τ(ɛv(i)). The third part (anomalous part) is the one that differs for on-resonance excitations. Anomalous parts of the electron velocities in the upper VB states for K and −K valleys for excitations on-resonance with the A excitons are υv(i) and υv(i)↓, respectively, which are equal in magnitude but opposite in sign. For excitations on-resonance with the B excitons, anomalous parts of the electron velocities in the lower VB states for K and −K valleys are υv(ii) and υv(ii)↓, respectively. On the basis of valley selection rules, the sign of υv(i)(↓) opposes with the sign of υv(ii)(↓), leading to a PC with opposite sign. However, the overall PC jCPGE(ω)K and jCPGE(ω)K should be in the same direction as shown in upper panel of Fig. 1, because (υcτ(ɛc))>((δɛvk)—υv (↓)τ(ɛv)). Hence on σ+ (σ−) excitations on-resonance with these excitons, the PC jCPGE(ω)σ+ (σ−) will be determined by the contributions due to υv(i)(↓) and υv(ii)(↓). This will make the main difference between jCPGE(ω)K and jCPGE(ω)K. Therefore, spin-coupled valley-dependent currents are expected due to excitons formed after light helicity-selective transitions of electrons from the VB to the CB. For off-resonance excitations, the PC expression due to the CPGE is more complicated; jCPGE(ω)σ+(σ−) can be jCPGE(ω)K or −K(−K or K)=(8/ħ) [∑vc (υcτ(ɛc))—((δɛvk)—υv(or↓)τ(ɛv))] |Mvc| |f(ɛc)–f(ɛv)| δ (ɛc–ɛvħω), in which v can be v(i) (upper VB) or v(ii) (lower VB). However, we can simply expect that for off-resonance excitation, jCPGE(ω)σ+ and jCPGE(ω)σ− will yield similar current values, since the off-resonance excitation simultaneously populates both K and −K valleys11. In the off-resonance excitation, we cannot take advantage of the valley selection rules and spin–valley coupling, which is reflected in the variance between jCPGE(ω)σ+ and jCPGE(ω)σ− in on-resonance excitations. This underlines the importance of strong excitonic character that can be obtained in high-quality samples to observe a pronounced difference between jCPGE(ω)σ+ and jCPGE(ω)σ−.

### Device characterization and photocurrent

Figure 2 shows the microphotoluminescence of the device prepared by CVD as shown in the inset. The microphotoluminescence measurement was performed by 532-nm laser excitation at room temperature. The strong excitonic peak of A (B) exciton corresponds to pair of an electron in the CB and a hole in the upper (lower) band of the split VB at K valleys. The PL peak for A (B) excitons in these samples is around 1.84 eV (2 eV) and the A excitons are much stronger in intensity. The quality of the flakes was demonstrated by Raman microspectroscopy and contrast-enhanced fluorescence optical microscope image in Supplementary Figs 1 and 2, respectively. Initial electrical measurements of monolayer MoS2 field-effect transistors were performed in dark. Drain current versus drain voltage (Vd) characteristics, at zero gate voltage (Vg), are shown in Supplementary Fig. 3. For 10 V applied Vd, the field-effect transistors characteristics mark an on-state at −30 V (Fig. 3a). By a linear fit between 30 and 40 V, we can estimate the mobility of these devices from μ=(L/W) (dI/dV) (1/CVd). Here L is the device length, W the device width and C is the back gate capacitance. The mobility is 0.5 cm2 V−1 s−1, as shown in Supplementary Fig. 4, which is in agreement with the reported values18. Subsequent drain current measurements on illumination by 2.33 eV laser with 20 mW cm−2 power density, and comparison with the dark measurements, are illustrated as a function of Vd in Supplementary Fig. 5. The drain current as a function of Vg, on illumination (IIllumination) and in dark (IDark) are compared in Fig. 3a. The ratio of IIllumination/IDark is 104 in the off state (Vg=−35 V).

Laser power density dependence of drain current at −40 V Vg and 10 V Vd was measured. Figure 3 shows PC (IIlluminationIDark) versus laser power density. Photoresponsivity (R) at the minimum power for the device shown in the inset to Fig. 2 is about 3.5 A W−1, which is about two orders of magnitude lower than the reported one18. The power dependence of the measured drain current (Id) can be fitted according to Id (Laser Power)α, where α is about 0.7 for our samples and the reported MoS218. At higher power densities, R drops either due to the trap states in MoS2 or the interface of MoS2 and the substrate27. Therefore, to elucidate the photoinduced transport effects of monolayer MoS2, further PC measurements at both high and low laser power densities were performed using conventional amplitude modulation and lock-in detection.

In Fig. 4b, gate dependence of PC signal for different Vd and laser power density with 2.33-eV excitation is presented for ϕ=0° and θ=45° configuration as described in the experimental setup of Fig. 4a. Both PC signal amplitude and phase were measured. Phase is around 0° while the Vg, Vd and laser power were varied; no sign change of PC was observed as shown in Supplementary Fig. 6. At high Vd of 10 V, both high-power-density data (9.78 W cm−2) and low-power-density data (60 mW cm−2) are being affected by bolometric effects as in the AB-stacked bilayer graphene28, which are due to the high channel doping. The PC amplitude increases almost linearly from 100 to 200 nA from −40 V to 40 V for high power density; from 3 to 20 nA for low power density. At low Vd of 0.7 V and low power density (60 mW cm−2), the measured PC is dominated by photogalvanic effect, photon drag effect and low channel doping. The PC amplitude increases logarithmically from 0.1 to 8 nA, in accordance with the gate dependence of drain current data in Fig. 4b. Low Vd also prevents from artificial PC such as photogating effects29 and photothermal effects30. Therefore, intrinsic photogalvanic effects are expected to appear at low Vd and low illumination intensity. Here we focus on this regime to address subtle effects of light helicity on spin–valley PCs, which has been a subject of fundamental opto-spintronic applications31,32,33.

### Helicity-dependent PC by 2.33 and 1.96 eV excitations

Figure 5 shows our light helicity-dependent PC results by varying the angle of photon polarization (ϕ) for off-resonance (2.33 eV photon energy, 0.7 V drain voltage and 60 mW cm−2 illumination intensity) and for on-resonance excitation (1.96 eV photon energy, 2 V drain voltage and 100 mW cm−2 illumination intensity) at Vg=−40 V. As expected, for off-resonance excitation, (Fig. 5a) the PC exhibits no clear dependence on angle of photon polarization (that is, σ+ and σ− excitation). Indeed, there is no preferential optical transition (due to electron–photon interaction and scattering events) from the upper or lower VBs to the CB, in terms of valleys, on absorption of photon energies off-resonance with the excitonic transition. The data are fitted to the phenomenological formula J=C1 sin 2ϕ+L1 sin 4ϕ+L2 cos 4ϕ+D and the fitting parameters are tabulated in Table 1. The component of PC response related to circularly polarized light is the jCPGE. But for this excitation, jLPDE is the dominant contribution. Thus, by subtracting jLPDE and polarization-independent term from the measured PC, PC (σ±), one can obtain jCPGE (σ±)=PC (σ±)—(−L2+D). Then PC polarization can be defined as P=[|jCPGE (σ+)|−|jCPGE (σ−)|]/[|jCPGE (σ+)|+|jCPGE (σ−)|]. By using the parameters in Table 1, P is 0.8±0.4 %. On the basis of microscopic description of the CPGE valley current, υv(i)- and υv(ii)-dependent terms cancel each other and eventually results in a negligible PC polarization.

The picture changes markedly in the case of PC observed for excitation with photon energy=1.96 eV, which is on-resonance with the excitonic transitions. This photon energy is on-resonance mainly with A excitons, as explained in Supplementary Note 1. The angle of photon polarization dependence of PC exhibits a clear difference between σ+ and σ− excitations in Fig. 5b, as expected for spin-coupled valley currents with resonant excitation. As shown in Table 1, the parameter C1 is much larger compared with the 2.33-eV excitation, although L1 still small and L2 gets relatively smaller. The coefficients C1 and L2 stand as the most prominent ones in determining polarization-dependent PC(σ±). The parameter C1 becomes negligible for the on-resonance excitation once the angle of incidence θ=0°, as shown in Supplementary Fig. 7 and Supplementary Table 1. The figure of merit for PC polarization can be taken as the ratio of |C1|/|L2|, which is 0.06 for off-resonance (2.33 eV) excitation and 1.94 for on-resonance (1.96 eV) excitation. In terms of microscopic origin, the PC polarization for the excitation on resonance with the A excitons can be qualitatively given as |υv(i)τ(ɛv)|/|υcτ(ɛc)| based on the jCPGE defined earlier in Fig. 1. In other words, jCPGE dominates and the concomitant P has high values of 60±30% when excited by 1.96 eV. This value is larger when compared with PL polarization at zero Vg presented in Supplementary Fig. 8. This could be due to loss of polarization during the process of circularly polarized excitation and collection in PL measurements. Also, in PC measurements we are able to identify purely the CPGE-dependent valley current and additional effects in PL are suppressed. The large error in P is due to the fluctuations in the data as explained in Supplementary Note 2. It is possible to obtain a better signal by further improvement of device fabrication. As a control experiment, we used the same experimental setup at θ=45° with on-resonance laser, only by replacing circularly polarized light by linearly polarized light (we used half-wave plate instead of QWP); the data at 45°, 135°, 225° and 315° yield similar values, unlike circularly polarized excitation. We also give a comparison of our results of the CVD grown monolayer MoS2 sample with the results of a mechanically cleaved monolayer MoS2 sample in Supplementary Figs 9 and 10, by electrical measurements in Supplementary Figs 3, 4 and 11, photoresponse in Supplementary Fig. 12, circularly polarized PL in Supplementary Fig. 13 and light helicity-dependent spin–valley current in Supplementary Fig. 14 and in Supplementary Table 2. In mechanically cleaved sample, the PC polarization that reflects the spin–valley coupling is relatively smaller than the CVD sample as explained in Supplementary Note 2, which makes CVD grown MoS2 devices promising for spin-dependent opto-valleytronic applications.

## Discussion

Our results of exciton-related spin-coupled valley-dependent PC are consistent with helicity-dependent PL measurements11 and recent observation of the valley Hall effect in monolayer MoS234. These results may have a number of applications in nanoeletronics and photonics, such as such as polarization-sensitive light-detection schemes or integrated spintronic devices. Furthermore, more examples can be developed based on magnetoelectric effects of bilayer TMDs35 and spin–orbit interaction in graphene/TMD hybrid systems36, since CVD grown TMD devices are promising in terms of electrical transport37. Thanks to room-temperature operation, the control over spin-dependent valley PC is more application oriented than the recently discovered helicity-dependent PC of topological insulators38. Moreover, special attention should be paid to biological environments, which are sensitive to light handedness and colour. Examples can be given in the area of light-harvesting chlorophyll (LHC) research39 and biomolecule–nanoparticle interaction40. For instance, light helicitiy dependence has been demonstrated for the chiral LHC, which functions around red colour (633 nm—1.96 eV) wavelength but insensitive to green colour41. This realizes the possibility of integrating chiral LHC with ultrasensitive spin–valley-coupled MoS2 phototransistors. Also, the biophysical community has been investigating the protein binding to nanomaterials for vision-related nanomedical purposes42. On the basis of our observations, we believe it is viable to utilize the unique optoelectronic features of MoS2 in the exploration of light sensitive bio–nano systems.

We emphasize that high-quality monolayer MoS2, which is a spin–valley coupling system grown by chemical vapour deposition fabricated as phototransistor exhibits helicity-dependent PC behaviour, based on its unique symmetry conditions. Spin-dependent valley currents can be generated by circularly polarized laser, and can be manipulated by laser excitation and electrical gating. We were able to demonstrate that in K or −K valleys with given spin (up or down, respectively) exciton-related electron conduction can take place, and PC polarization as high as 60% was obtained by choosing a suitable visible laser with a known circular polarization (σ+ or σ−). The observed PC polarization degree is even higher than the PL polarization since we are able to resolve purely the CPGE-dependent valley current. The findings in this work-shed light into the intrinsic photogalvanic effects and helicity-selective transitions in monolayer transition metal dichalcogenides. Besides their fundamental importance, we believe these results may pave the way for application of opto-valleytronic device concepts in interdisciplinary research spanning from nanoelectronics and photonics to biotechnologies.

## Methods

### Sample growth and device processing

Monolayer MoS2 flake with size 5 μm is grown by a CVD method (as explained in detail elsewhere24) onto Si substrate with 300-nm SiO2. The triangular flake was picked among homogeneous, high crystalline quality flakes then processed into a device, by e-beam lithography with Ti (5 nm)/Au (75 nm) contacts for electrical and PC measurements.

### PC measurements

By using lock-in technique with a low noise current preamplifier, PC amplitude and phase have been measured for monolayer MoS2 phototransistors at room temperature. The linearly polarized laser beam is centred on the sample with an oblique angle θ after being chopped to a frequency of 137 Hz, which is the frequency of the measured current at the same time. As shown in Fig. 4, the PC setup has the option to circularly polarize the linearly polarized light field by using a QWP. The angle of photon polarization, ϕ, can be varied by rotating the QWP.

How to cite this article: Eginligil, M. et al. Dichroic spin–valley photocurrent in monolayer molybdenum disulphide. Nat. Commun. 6:7636 doi: 10.1038/ncomms8636 (2015).

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## Acknowledgements

This work is supported in part by the Singapore Ministry of Education under MOE2013–T1–2–235, MOE2012-T2–2–049, the Singapore National Research Foundation under NRF RF Award No. NRFRF2010–07 and the Agency for Science, Technology and Research, SERC PSF grant 1321202101. C.S. acknowledges the support from the Singapore Ministry of Education MOE2011-T3-1-005 and MOE2013-T2-1-044, and Nanyang Technological University (NAP-SUG M4080511).

## Author information

Authors

### Contributions

T.Y. supervised the project. M.E. and T.Y. designed the experiments. C.S. coordinated the photocurrent experiments. J.S., C.C. and T.Y. synthesized the flakes. X.S. did the device fabrication. M.E., Z.W. and B.C. carried out the electrical measurements and photocurrent experiments. M.E., J.S., C.C. and B.C. analysed the data. M.E., Z.W., C.S., and T.Y. wrote the manuscript. All authors discussed the results and commented on the manuscript.

### Corresponding author

Correspondence to Ting Yu.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Figures 1-14, Supplementary Tables 1-2, Supplementary Notes 1-2 and Supplementary References. (PDF 560 kb)

## Rights and permissions

Reprints and Permissions

Eginligil, M., Cao, B., Wang, Z. et al. Dichroic spin–valley photocurrent in monolayer molybdenum disulphide. Nat Commun 6, 7636 (2015). https://doi.org/10.1038/ncomms8636

• Accepted:

• Published:

• DOI: https://doi.org/10.1038/ncomms8636

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