Optical Control of Spin Polarization in Monolayer Transition Metal

Optical Control of Spin Polarization in Monolayer Transition Metal Dichalcogenides Xi Chen, Tengfei Yan, Bairen Zhu, Siyuan Yang, and Xiaodong Cui* Physics Department, University of Hong Kong, Pokfulam, Hong Kong, China S Supporting Information *

ABSTRACT: Optical excitation could generate electrons’ spin polarization in some semiconductors with the control of the field polarization. In this article, we report a series of spin-resolved photocurrent experiments on monolayer tungsten disulfide. The experiments demonstrate that the optical excitations with the same helicity could generate opposite spin polarization around the Fermi level by tuning the excitation energy. The mechanism lies in the valley-dependent optical selection rules, the giant spin−orbit coupling, and spin-valley locking in monolayer transition metal dichalcogenides (TMDs). These exotic features make monolayer TMDs promising candidates for conceptual semiconductor-based spintronics. KEYWORDS: transition metal dichalcogenide, monolayer WS2, spin polarization, optical control, spintronics

M

K and K′ valley must be circularly polarized but with contrasting helicity.18−24 As the bands at K and K′ valleys are mainly constructed by d-orbitals of transition metal atoms, the inherited strong SOC reshapes the bands with a Zeeman-like spin-splitting, particularly at valence bands. In the case of monolayer tungsten disulfide (WS2), the spin-splitting is above 0.4 eV at the valence band and tens of meV at the conduction band.16,19,25−29 Owing to the time reversal symmetry, the spinsplitting has an opposite sign at K and K′ valleys. Namely, if the spin is up at band edge of the K valley, the spin must be down at the K′ valley. The coupling between spin and valley degrees of freedom, so-called spin-valley locking, stimulates alternative protocols to manipulate the spin and valley.16,19 It is experimentally demonstrated that the spin polarization could be generated by optical pumping via valley-dependent optical selection rules and spin-valley locking.11,12 As the optical selection rules directly correspond to valley instead of spin, it is possible to generate contrasting spin polarization with the same optical field polarization as sketched in Figure 1a. Besides, the

anipulating spin degrees of freedom with light− matter interactions has been a focused topic in nonmagnetic semiconductor-based spintronics and quantum computing.1−4 Paradigms have been successfully demonstrated in a wide range of conventional semiconductors in the form of bulk crystals (three-dimensional),5 quantum wells (quasi-two-dimensional),6,7 and quantum dots (zerodimensional).8 The general idea utilizes the angular momentum transfer where the angular momentum of photons is transferred to the spin momentum of electrons under “spin-dependent” optical selection rules via spin−orbit coupling (SOC).3,9,10 One could also generate the electrons’ spin polarization in transition metal dichalcogenides (TMDs) with the control of light polarization.11,12 In this article, we demonstrate that the optical excitation with the same helicity could generate opposite spin polarization in monolayer TMDs depending on the energy of photons. The newly discovered monolayer TMDs as a family of atomic two-dimensional (2D) crystals with honeycomb lattice features degenerate but inequivalent valleys K and K′ (or −K) where the direct band gap is located.13−17 The intrinsic spatial inversion symmetry breaking leads to distinct optical selection rules at inequivalent valleys. The interband optical transitions at © 2017 American Chemical Society

Received: October 19, 2016 Accepted: January 6, 2017 Published: January 6, 2017 1581

DOI: 10.1021/acsnano.6b07061 ACS Nano 2017, 11, 1581−1587

Article

www.acsnano.org

Article

ACS Nano

RESULTS AND DISCUSSION Figure 2 is the scanning photocurrent measurements at a source−drain bias VDS = 5 V under circularly polarized optical excitations at 2.12 eV, which is nearly resonant with A-exciton (ground-state band-edge exciton). Photocurrents arise when the laser scans near the electrodes, where the electric field is presumably large as a result of the Schottky barrier between monolayer WS2 and electrodes (Figure 2b). The photocurrent spatial distribution is also strongly dependent on the source− drain bias VDS, which modifies the potential profiles around the contacts (Supporting Information Figure S7). The variation of the photocurrent spatial distribution shows that the exciton dissociation is dominated by the local electric field, a joint force of the external bias, and the band alignment between the electrodes and monolayer WS2. It is a natural result of the giant binding energy of excitons in monolayer TMDs. Only a strong local electric field could convert excitons to free carriers and consequently contribute to photocurrents. Thermal excitation in the experiment range is not enough to dissociate excitons to free electron−hole pairs. Asymmetric photocurrent distributions under VDS are attributed to asymmetric Schottky contacts formed at the two opposite sides throughout the multiple-step fabrication process, which frequently occurs in nanodevices. For the photocurrent difference Iσ+ − Iσ− between σ+ and σ− excitations, the sign will be opposite when the direction of the magnetization is reversed, as shown in Figure 2c,d. According to the valley-dependent optical selection rules, the optical excitation with contrasting polarization generates excitons in opposite valleys. If the ferromagnetic electrodes are upwardly magnetized, the photocurrent difference between two opposite helicities Iσ+ − Iσ− shows positive values (Iσ+ − Iσ− > 0) in the region of the sample near the drain side of the electrode contacts (Figure 2c). If the magnetization of the electrodes is reversed, the photocurrent difference signal keeps the same spatial distribution but turns into a negative value (Iσ+ − Iσ− < 0) (Figure 2d). The sign reversal in the photocurrent difference at opposite magnetizations of ferromagnetic electrodes coincides with what has been reported in previous research.11 This phenomenon is fully expected by the spin-valley locking and the spin filtering of the spin-valve device. Valley-dependent selection rules and spin-valley locking generate the valley and spin-polarized photocarriers. Those holes and electrons will be separated spatially with local electric fields and accelerated toward opposite electrodes by the source−drain bias. Spin-up carriers polarized by σ+ excitation exhibit spin orientation parallel to that of the positively magnetized electrodes, making their effective resistance smaller than that of spin-down ones polarized by σ− excitation. Therefore, photocurrent under σ+ excitation is larger than that under σ− excitation, leading to the positive photocurrent difference Iσ+ − Iσ− in the case of positive magnetization of electrodes (M↑). By contrast, the sign of photocurrent difference Iσ+ − Iσ− will be reversed when the electrodes are negatively magnetized (M↓) because carriers polarized by σ− excitation rather than the one by σ+ excitation have smaller effective resistance because of sharing the same spin orientation with the electrodes. This manifests the spinvalley coupling in monolayer TMDs. The strength of the photocurrent difference also depends on the source−drain bias VDS. It monotonically increases with the increased source−drain bias VDS (Supporting Information Figure S6). The reason is two-fold. First, the higher the VDS, the larger the chance of exciton dissociation and the more

Figure 1. Monolayer WS2-based spin-valve-like device for spinpolarized photocurrent measurements. (a) Schematics of valleydependent optical selection rules and spin-valley locking at K/K′ valleys in the momentum space of monolayer TMDs, with the proposed mechanism of the spin-resolved photocurrent measurement. Solid green (orange) curves denote bands with spin-up (spindown) along the out-of-plane direction. The splitting in the conduction band is exaggerated for clarity. ωA and ωB are transition frequencies from the two split valence band tops to the conduction band bottoms, respectively. (b) Schematic of the monolayer WS2based spin-valve-like device for spin-polarized photocurrent measurements under σ+ optical excitation with different frequencies (resonant to A-exciton and B-exciton). The electrons and holes in valley K are denoted by white “−” and “+” symbols. σ+ polarized light with frequency ωA (ωB) can generate spin-up (spin-down) electrons and spin-down (spin-up) holes in the K valley, denoted by green (orange) circles and arrows.

spin-valley locking dramatically suppresses the spin and valley relaxation and theoretically makes robust spin/valley polarization possible.16,19,30 Although the contrasting spin polarization under the same optical polarization is theoretically sound, it is questionable if the contrasting spin polarization of excitons could survive with the carriers around the Fermi level. In this article, we conducted spin-sensitive photocurrent experiments and time-resolved Kerr rotation spectroscopy on monolayer WS2. The electron (hole) spin polarization was generated by circularly polarized optical excitation, and the spin polarization of free carriers at Fermi level was electrically detected by a spin-valve-like structure (as sketched in Figure 1b). It is experimentally demonstrated that the contrasting spin polarization could be generated in monolayer WS2 by the same optical polarization at different excitation energy. Besides, the contrasting spin polarization survives through energetic relaxation and remains around the Fermi level. This shows that monolayer TMDs can be good candidates for building blocks in conceptual nonmagnetic spintronics. 1582


Article

ACS Nano

Figure 2. Representative mappings of photocurrent and photocurrent difference. (a) Laser scanning reflection image of the device as a position reference. Areas outlined with the black dashed line are FM electrodes. Inset: Optical micrograph of the device with black scale bar of 5 μm. The white thick horizontal bars label the ferromagnetic Co/Pd electrodes. (b) Photocurrent map with excitation energy resonant to the A-exciton at bias voltage VDS (white arrow denotes the direction of electric field corresponding to the bias voltages). Mappings of photocurrent difference Iσ+ − Iσ− between σ+ and σ− excitations at bias voltage VDS = 5 V with excitation energy resonant to energy of the Aexciton at positive magnetization M↑ (c) and at negative magnetization M↓ (d).

photocurrent. Second, the high VDS leads to high drift velocity of carriers, and consequently, the spin and valley could propagate longer distances until reaching the FM electrodes. The photocurrent difference always peaks around the contacts where the holes flow from monolayer TMDs to the FM electrodes (namely, electrons flow from electrodes to TMDs to fill in the vacancies generated by optical excitations). This is partially due to the relatively robust holes’ valley and spin polarization protected by the giant SOC in valence bands. A more efficient spin filtering for hole transport also potentially contributes as the device behaves as n-type, though it has to be confirmed by the band alignment and spin filter engineering in the future. If the excitation energy is tuned to 2.54 eV, nearly resonant with B-excitons (corresponding to interband transition from the lower sub-band of spin-splitting in the valence band to the band edge of the conduction band), the photocurrent difference Iσ+ − Iσ− switches the sign under the same circular polarization and the magnetization of electrodes, as shown in Figure 3.

To further investigate the results, both the photocurrent and the photocurrent difference were measured and plotted as a function of photon energy of the excitation light under the same magnetization, as shown in Figure 4. It turns out that the photocurrent spectrum (Figure 4a) shares similar peak features with the linear absorption spectrum (Figure 4b) of monolayer WS2, with two apparent peaks at 2.11 and 2.52 eV, respectively, in the spectral range of 1.9−2.6 eV. Positions of these two peaks are consistent with those of exciton peaks A and B in the linear absorption spectrum. The energy separation of 0.41 eV between peak A and peak B in the photocurrent spectrum also indicates that these two peaks result from the spin−orbit splitting in the same valley. This agreement on the spectral peak positions between the photocurrent spectrum and the absorption spectrum has also been observed in monolayer MoS2.14,31 Remarkably, a prominent sign change of the signal from region A to region B is presented in the photocurrent difference spectrum (Figure 4c). The reversed sign of the photocurrent difference Iσ+ − Iσ− under excitations with different photon energy can be explained by the change of spin polarization 1583


Article

ACS Nano

Figure 3. Comparison of photocurrent and photocurrent difference mappings under different excitation laser energy (top row at 2.12 eV and bottom row at 2.54 eV). (a,c) Photocurrent map; (b,d) photocurrent difference map under excitation laser energy nearly resonant to Aexciton and under excitation laser energy nearly resonant to B-exciton, respectively. The measurements were done under bias voltage of VDS = 5 V and temperature at 10 K.

rotation measurements, where valley polarization at band edges and excited states (spin-split lower band) is initiated by a circularly polarized pump beam, and the valley polarization at the band edge is probed by the Kerr rotation angle of the reflected linearly polarized probe beam (resonant with Aexciton). The Kerr rotation angle, which reflects the polarization change of the probe beam, monitors the valley polarization.30,32−35 The Kerr rotation at 77 K shows opposite sign between the same helicity polarized pumps at 2.18 eV (nearly resonant with A-excitons) and 2.34 eV, with valley lifetime of 2.2 and 2.3 ps, respectively (Figure 5). The sign of the Kerr signal is reversed below the expected photon energy of B-exciton reflected by linear absorption spectrum (2.52 eV as from Figure 4b). It is speculated that the actual peak energy of the B-exciton during the pump-and-probe measurement is shifted toward the lower energy part, which is probably due to the band gap renormalization at high transit carrier density as demonstrated in monolayer TMDs.36 Therefore, we surmise that the laser energy at 2.34 eV is nearly resonant to the actual peak energy of the B-exciton of monolayer WS2. The opposite sign shows that the intervalley spin-conserved scatterings dominate the hot carrier (B-excitons) relaxation process, as sketched in Figure 1a, fully consistent with our photocurrent

direction of the photoexcited carriers in the sample. According to valley-dependent optical selection rules, the circularly polarized light couples to the valley degrees of freedom. If the optical excitation is resonant with the B-exciton, the interband transitions pump electrons from the spin-split lower band, due to opposite spin at the band edge (spin-split upper band), to the band edge of conduction band in the same valley, as sketched in Figure 1a. So the same optical polarization could raise different spin states depending on the interband transition energy. Nevertheless, it is not necessary that the spin polarization in excited states survives when it relaxes to the Fermi level/band edges. As the electric measurements sense the electrons (holes) around the Fermi level, the band edges of conduction, and valence bands, the sign switch of the photocurrent difference Iσ+ − Iσ− between the interband transitions corresponding to A- and B-excitons unambiguously demonstrates that the spin polarization of the excited state of holes (related to B-excitons) survives throughout the energetic relaxation. It implies that the spin-conserved intervalley scattering instead of spin-flipped intravalley scattering dominates the holes’ relaxation process. Independent evidence of the spin/valley relaxation process through intervalley scattering is given by the time-resolved Kerr 1584


Article

ACS Nano

Figure 5. Kerr rotation dynamics with pump energy resonant to that of A-excitons (red curve) and B-excitons (blue curve) of the same helicity circularly polarized light (intensity of the signal normalized for simplicity). The valley polarization of the A-excitons (band-edge excitons) is monitored by the Kerr rotation of the probe beam resonant with A-excitons in both cases at 77 K. Inset: Schematics of the optical selection rules of the excitons in K and K′ valleys and the spin-conserved intervalley scattering when pumping B-excitons in the time-resolved Kerr rotation measurements.

valley and the corresponding electrons to the higher spin-split conduction band via Coulomb interactions, forming A-excitons at the K′ valley. The Kerr rotation probed by a probe beam resonant with A-excitons reflects the valley depolarization of Aexcitons at the K′ valley. In contrast, the Kerr rotation of the probed and the pump beams both nearly resonant with Aexcitons and with the same helicity reflects the valley depolarization of the A-excitons at the K valley. The valley lifetime of these A-excitons shows similar time scale or similar exchange interaction strength as a result of time reversal symmetry (inset of Figure 5). The pronounced spin/valley lifetime difference between the time-resolved Kerr rotation measurements and the estimation from the spin-resolved photocurrent experiments lies in the Kerr rotation probes the valley lifetime of excitons, while the photocurrent measurement probes that of free carriers.11 The excitons experience a strong spin-exchange interaction which serves as the major valley depolarization channel.38−41 Nevertheless, the spin-exchange interaction is suppressed for free carriers due to the spatial separation. Therefore, the valley/spin lifetime of free carriers is orders of magnitude longer than that of excitons.

Figure 4. Comparison of the photocurrent, linear absorption, and photocurrent difference spectrum in the spectral range of 1.9 to 2.6 eV at 10 K. (a) Photocurrent spectrum, (b) linear absorption spectrum, and (c) photocurrent difference spectrum as a function of photon energy, showing two characteristic features marked as A region and B region. Positions of these two regions in the photocurrent and photocurrent difference spectrum are consistent with those of exciton peaks A and B in the linear absorption spectrum. In the photocurrent and photocurrent difference spectrum, square symbols represent the average values of several repeated measurements. Error bars are the differences between individual measurements and the average value.

CONCLUSION In summary, our spin-valve-like device enables distinction of two states with opposite spin polarization generated in monolayer TMDs. The average spin of an ensemble of electrons around the Fermi level could be manipulated by optical technique, combining the controls of the polarization of optical fields and of the excitation energy. The interplay of spin and valley degrees of freedom makes monolayer TMDs promising for nonmagnetic semiconductor-based spintronics and valleytronics.

measurements. Spin/valley relaxation processes of the Bexciton and the A-exciton could be quite different.37 As demonstrated in Figure 5, when B-excitons are generated at the K valley by the σ+ polarized pump beam nearly resonant with B-excitons, holes associated with B-excitons in the K valley could be scattered to the top of the valence band of the K′

METHODS Device Preparation and Characterization. A typical field-effect transistor device with a back gate was fabricated with optical lithography. Source and drain electrodes were built with a ferromagnetic structure with perpendicular magnetic anisotropy to 1585


Article

ACS Nano Notes

work as a spin valve. Ferromagnetic electrodes consisting of 20 periods of alternating cobalt (5 Å) and palladium (15 Å) layers were deposited in a metal molecular beam epitaxy system, following the deposition of an ultrathin aluminum oxide to improve the efficiency of spin filtering. The ferromagnetic electrodes were magnetized by an external magnetic field of 0.1 T perpendicular to the plane. The ferromagnetic magnetization in the perpendicular direction was checked by Kerr rotation. The electric transport characteristic measurement of source− drain current IDS as a function of gate voltage VG (Supporting Information Figure S1b) reflects its n-type behavior, consistent with previous studies.42 Representative transport measurements with/ without laser excitation show that the source−drain current is significantly higher under laser exposure, particularly on the “off state”, where the IDS is 2−3 orders of magnitude higher (Supporting Information Figure S4), indicating that the photocarriers dominate the thermal and tunneling current. To maximize the spin polarization, back-gating of −20 V was applied to set the device to the “off state”, minimizing the dark free carriers. Photocurrent Measurements. A light beam filtered from a supercontinuum fiber source was focused through a 50× longworking-distance objective to a spot with a diameter of around 2 μm on the sample. The beam spectra width is around 10 nm, and the power is kept lower than 90 μW at all wavelengths. The photoexcited holes and electrons are separated by local electric fields (from defects, surface charge trap, source−drain bias, etc.) and the source−drain bias, and the free carriers are driven by the external bias. A photoelastic modulator and lock-in technique were exploited to increase the sensitivity. The whole photocurrent Iσ+ − Iσ− and its difference Iσ+ − Iσ− (Iσ+/Iσ− means the photocurrent under σ+/σ− circularly polarized excitation) between two helicities were measured at the same time by two lock-in amplifiers. The light spot scanned across the whole device and the reflectance signal of the sample were collected to do real-time monitoring for the photocurrent scanning. The whole experiments were conducted at 10 K with the sample in a vacuum cryostat. Time-Resolved Kerr Rotation Measurements. Monolayer WS2 sample was pumped and probed at 77 K with two-color beams filtered from a supercontinuum optical fiber pumped by a mode-locked Ti:sapphire laser with 80 MHz repetition frequency. A Kerr rotation spectroscopic setup with a photoelastic modulator and optical bridge technique was applied.

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The work is financially supported by Area of Excellency (AoE/ P-04/08), GRF (17300415), and CRF(HKU9/CRF/13G) of Hong Kong Research Grant Council and SRT on New Materials of The University of Hong Kong. REFERENCES (1) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; Von Molnar, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 1488−1495. (2) Awschalom, D. D.; Flatté, M. E. Challenges for Semiconductor Spintronics. Nat. Phys. 2007, 3, 153−159. (3) Ž utić, I.; Fabian, J.; Das Sarma, S. Spintronics: Fundamentals and Applications. Rev. Mod. Phys. 2004, 76, 323−410. (4) Meier, F., Zakharchenya, B. P., Eds. Optical Orientation; Elsevier: Amsterdam, 1984. (5) Lampel, G. Nuclear Dynamic Polarization by Optical Electronic Saturation and Optical Pumping in Semiconductors. Phys. Rev. Lett. 1968, 20, 491−493. (6) Ganichev, S. D.; Prettl, W. Spin Photocurrents in Quantum Wells. J. Phys.: Condens. Matter 2003, 15, R935. (7) Pfalz, S.; Winkler, R.; Nowitzki, T.; Reuter, D.; Wieck, A. D.; Hägele, D.; Oestreich, M. Optical Orientation of Electron Spins in GaAs Quantum Wells. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 165305. (8) Hanson, R.; Kouwenhoven, L. P.; Petta, J. R.; Tarucha, S.; Vandersypen, L. M. K. Spins in Few-Electron Quantum Dots. Rev. Mod. Phys. 2007, 79, 1217−1265. (9) McIver, J. W.; Hsieh, D.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. Control over Topological Insulator Photocurrents with Light Polarization. Nat. Nanotechnol. 2012, 7, 96−100. (10) Bychkov, Y. A.; Rashba, E. I. Properties of a 2D Electron Gas with Lifted Spectral Degeneracy. JETP Lett. 1984, 39, 78. (11) Xie, L.; Cui, X. Manipulating Spin-Polarized Photocurrents in 2D Transition Metal Dichalcogenides. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 3746−3750. (12) Eginligil, M.; Cao, B.; Wang, Z.; Shen, X.; Cong, C.; Shang, J.; Soci, C.; Yu, T. Dichroic Spin-Valley Photocurrent in Monolayer Molybdenum Disulphide. Nat. Commun. 2015, 6, 7636. (13) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (14) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (15) Zhang, Y.; Chang, T. R.; Zhou, B.; Cui, Y. T.; Yan, H.; Liu, Z.; Schmitt, F.; Lee, J.; Moore, R.; Chen, Y.; Lin, H.; Jeng, H.; Mo, S.-K.; Hussain, Z.; Bansil, A.; Shen, Z. Direct Observation of the Transition from Indirect to Direct Bandgap in Atomically Thin Epitaxial MoSe2. Nat. Nanotechnol. 2013, 9, 111−115. (16) Xu, X.; Yao, W.; Xiao, D.; Heinz, T. F. Spin and Pseudospins in Layered Transition Metal Dichalcogenides. Nat. Phys. 2014, 10, 343− 350. (17) Jin, W.; Yeh, P.-C.; Zaki, N.; Zhang, D.; Sadowski, J. T.; AlMahboob, A.; van der Zande, A. M.; Chenet, D. A.; Dadap, J. I.; Herman, I. P.; Sutter, P.; Hone, J.; Osgood, R. M., Jr. Direct Measurement of the Thickness-Dependent Electronic Band Structure of MoS2 Using Angle-Resolved Photoemission Spectroscopy. Phys. Rev. Lett. 2013, 111, 106801. (18) Yao, W.; Xiao, D.; Niu, Q. Valley-Dependent Optoelectronics from Inversion Symmetry Breaking. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 235406.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b07061. Basic characterizations of the device; comparison between dark and bright electrical response; comparison of the mappings between out-of-plane and in-plane magnetized spin detectors; relation between photocurrent difference and source−drain bias voltage; comparison of the mappings under excitation laser energy between nearly resonant and A-exciton and Bexciton (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Xiaodong Cui: 0000-0002-2013-8336 Author Contributions

X.D.C. conceived and supervised the project; X.C. and B.R.Z. conducted the device fabrication and photocurrent experiments; T.F.Y. conducted the pump−probe Kerr rotation experiments; X.C. and X.D.C. wrote the manuscript. 1586


Article

ACS Nano (19) Xiao, D.; Liu, G. B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides. Phys. Rev. Lett. 2012, 108, 196802. (20) Cao, T.; Wang, G.; Han, W.; Ye, H.; Zhu, C.; Shi, J.; Niu, Q.; Tan, P.; Wang, E.; Liu, B.; Feng, J. Valley-Selective Circular Dichroism of Monolayer Molybdenum Disulphide. Nat. Commun. 2012, 3, 887. (21) Zeng, H.; Dai, J.; Yao, W.; Xiao, D.; Cui, X. Valley Polarization in MoS2 Monolayers by Optical Pumping. Nat. Nanotechnol. 2012, 7, 490−493. (22) Mak, K. F.; He, K.; Shan, J.; Heinz, T. F. Control of Valley Polarization in Monolayer MoS2 by Optical Helicity. Nat. Nanotechnol. 2012, 7, 494−498. (23) Jones, A. M.; Yu, H.; Ghimire, N. J.; Wu, S.; Aivazian, G.; Ross, J. S.; Zhao, B.; Yan, J.; Mandrus, D. G.; Xiao, D.; Yao, W.; Xu, X. Optical Generation of Excitonic Valley Coherence in Monolayer WSe2. Nat. Nanotechnol. 2013, 8, 634−638. (24) Xiao, D.; Yao, W.; Niu, Q. Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport. Phys. Rev. Lett. 2007, 99, 236809. (25) Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlögl, U. Giant SpinOrbit-Induced Spin Splitting in Two-Dimensional Transition-Metal Dichalcogenide Semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 153402. (26) MacNeill, D.; Heikes, C.; Mak, K. F.; Anderson, Z.; Kormányos, A.; Zólyomi, V.; Park, J.; Ralph, D. C. Breaking of Valley Degeneracy by Magnetic Field in Monolayer MoSe2. Phys. Rev. Lett. 2015, 114, 037401. (27) Srivastava, A.; Sidler, M.; Allain, A. V.; Lembke, D. S.; Kis, A.; Imamoğlu, A. Valley Zeeman Effect in Elementary Optical Excitations of Monolayer WSe2. Nat. Phys. 2015, 11, 141−147. (28) Li, Y. Valley Splitting and Polarization by Zeeman Effect in Monolayer MoSe2. Probing the Response of Two-Dimensional Crystals by Optical Spectroscopy; Springer International Publishing: Berlin, 2016; pp 55−64. (29) Aivazian, G.; Gong, Z.; Jones, A. M.; Chu, R.-L.; Yan, J.; Mandrus, D. G.; Zhang, C.; Cobden, D.; Yao, W.; Xu, X. Magnetic Control of Valley Pseudospin in Monolayer WSe2. Nat. Phys. 2015, 11, 148−152. (30) Ochoa, H.; Roldán, R. Spin-Orbit-Mediated Spin Relaxation in Monolayer MoS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 245421. (31) Klots, A. R.; Newaz, A. K. M.; Wang, B.; Prasai, D.; Krzyzanowska, H.; Lin, J.; Caudel, D.; Ghimire, N. J.; Yan, J.; Ivanov, B. L.; Velizhanin, K. A.; Burger, A.; Mandrus, D. G.; Tolk, N. H.; Pantelides, S. T.; Bolotin, K. I. Probing Excitonic States in Suspended Two-Dimensional Semiconductors by Photocurrent Spectroscopy. Sci. Rep. 2014, 4, 6608. (32) Yang, L.; Sinitsyn, N. A.; Chen, W.; Yuan, J.; Zhang, J.; Lou, J.; Crooker, S. A. Long-Lived Nanosecond Spin Relaxation and Spin Coherence of Electrons in Monolayer MoS2 and WS2. Nat. Phys. 2015, 11, 830−834. (33) Plechinger, G.; Nagler, P.; Korn, T. Time-Resolved Kerr Rotation Spectroscopy of Valley Dynamics in Single-Layer MoS2. arXiv:1404.7674 [cond-mat.mes-hall] 2014; e-Print archive, https:// arxiv.org/abs/1404.7674. (34) Yan, T.; Qiao, X.; Tan, P.; Zhang, X. Exciton Valley Dynamics in Monolayer WSe2 Probed by Ultrafast Kerr Rotation. arXiv:1507.04599 [cond-mat.mes-hall] 2016; e-Print archive, https://arxiv.org/abs/ 1507.04599. (35) Hsu, W.-T.; Chen, Y.-L.; Chen, C.-H.; Liu, P.-S.; Hou, T.-H.; Li, L.-J.; Chang, W.-H. Optically Initialized Robust Valley-Polarized Holes in Monolayer WSe2. Nat. Commun. 2015, 6, 8963. (36) Yan, T.; Yang, S.; Li, D.; Cui, X. Long Valley Lifetime of Free Carriers in Monolayer WSe2. arXiv:1612.01336 [cond-mat.mes-hall] 2016; e-Print archive, https://arxiv.org/abs/1612.01336. (37) Kormányos, A.; Burkard, G.; Gmitra, M.; Fabian, J.; Zólyomi, V.; Drummond, N. D.; Fal’ko, V. K·P Theory for Two-dimensional Transition Metal Dichalcogenide Semiconductors. 2D Mater. 2015, 2, 022001.

(38) Yu, T.; Wu, M. Valley Depolarization Due to Intervalley and Intravalley Electron-Hole Exchange Interactions in Monolayer MoS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 205303. (39) Mai, C.; Semenov, Y. G.; Barrette, A.; Yu, Y.; Jin, Z.; Cao, L.; Kim, K. W.; Gundogdu, K. Exciton Valley Relaxation in a Single Layer of WS2 Measured by Ultrafast Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 041414. (40) Wang, Q.; Ge, S.; Li, X.; Qiu, J.; Ji, Y.; Feng, J.; Sun, D. Valley Carrier Dynamics in Monolayer Molybdenum Disulfide from HelicityResolved Ultrafast Pump−Probe Spectroscopy. ACS Nano 2013, 7, 11087−11093. (41) Yu, H.; Cui, X.; Xu, X.; Yao, W. Valley Excitons in TwoDimensional Semiconductors. Natl. Sci. Rev. 2015, 2, 57−70. (42) Zhu, B.; Chen, X.; Cui, X. Exciton Binding Energy of Monolayer WS2. Sci. Rep. 2015, 5, 9218.

1587


Optical Control of Spin Polarization in Monolayer Transition Metal

Recommend Documents