Valley-dependent spin polarization in bulk MoS2 with broken inversion symmetry

Journal name:
Nature Nanotechnology
Year published:
Published online


The valley degree of freedom of electrons is attracting growing interest as a carrier of information in various materials, including graphene, diamond and monolayer transition-metal dichalcogenides. The monolayer transition-metal dichalcogenides are semiconducting and are unique due to the coupling between the spin and valley degrees of freedom originating from the relativistic spin–orbit interaction. Here, we report the direct observation of valley-dependent out-of-plane spin polarization in an archetypal transition-metal dichalcogenide—MoS2—using spin- and angle-resolved photoemission spectroscopy. The result is in fair agreement with a first-principles theoretical prediction. This was made possible by choosing a 3R polytype crystal, which has a non-centrosymmetric structure, rather than the conventional centrosymmetric 2H form. We also confirm robust valley polarization in the 3R form by means of circularly polarized photoluminescence spectroscopy. Non-centrosymmetric transition-metal dichalcogenide crystals may provide a firm basis for the development of magnetic and electric manipulation of spin/valley degrees of freedom.

At a glance


  1. Crystal structure and Brillouin zones of monolayer, 2H and 3R forms of MoS2.
    Figure 1: Crystal structure and Brillouin zones of monolayer, 2H and 3R forms of MoS2.

    a, Stick-and-ball crystal structure of MoS2 monolayer (top view). b, Side views of three forms of MoS2 (left to right): monolayer, 2H crystal and 3R crystal. Blue and red spheres correspond to molybdenum and sulphur atoms, respectively. Black dashed lines indicate unit cells. Orange arrows indicate lattice vectors. Green vectors indicate the orthogonal axis of the real space. c, First Brillouin zones of 2H- and 3R-MoS2. Solid blue lines and pink shaded areas represent the conventional and primitive Brillouin zones, respectively. The hexagonal plane with Γ_, , and represents the corresponding two-dimensional projected Brillouin zone.

  2. Structural and optical characterizations of 2H and 3R single crystals of MoS2.
    Figure 2: Structural and optical characterizations of 2H and 3R single crystals of MoS2.

    a, Optical micrograph image of the surface of MoS2 crystals showing contrasting screw dislocations reflecting the crystal symmetry. Scale bars, 10 µm. b, Convergent-beam electron diffraction patterns for MoS2. The 2H and 3R crystals show mirror symmetries, indicated by yellow, white and red lines, at the positions of the six-fold and three-fold symmetry, respectively. c, Optical reflectivity spectra for 2H and 3R crystals. The two-peak structures are assigned as exciton transitions. The energy splittings were 0.18 eV and 0.14 eV for the 2H and 3R crystals, respectively, consistent with earlier literature28, 36.

  3. Valence bandstructures of 3R- and 2H-MoS2.
    Figure 3: Valence bandstructures of 3R- and 2H-MoS2.

    a, Valence bandstructures of 3R-MoS2 recorded along (shown as the red line in i) by ARPES with  = 40.8 eV (left) and 21.2 eV (right). b, Bulk bandstructures of 3R-MoS2 along ky obtained by first-principles calculations. The band dispersions for various kz, indicated by the inset colour-scale, are overlapped. c,d, Bandstructures of 2H-MoS2 obtained by ARPES and calculation as in a,b. e,f, ARPES image and corresponding calculation focusing near the valence band top at the point for 3R-MoS2. g,h, ARPES image and calculation for 2H-MoS2. The measurement regions for e and g correspond to the green rectangles in a and c, respectively. i, Momentum cut of the measurement region in a (red line), overlaid on the projected two-dimensional first Brillouin zone of 3R-MoS2.

  4. Detection of the spin polarization near the valence band top at the  and  points.
    Figure 4: Detection of the spin polarization near the valence band top at the and points.

    a, Intensity mapping at 0.3 eV relative to the top of the valence band at the point obtained by ARPES ( = 21.2 eV) and the calculated equi-energy surfaces at kz = π/c overlaid on the two-dimensional first Brillouin zone. Hereafter, red and blue indicate spin-up and spin-down components, respectively. b,c, Spin-resolved energy distribution curves (EDCs, b) at the point and the corresponding spin polarization with statistical errors of photoelectron counting (c) for 3R-MoS2, obtained by SARPES. Here, the quantization axes of spin are along the x, y and z crystal axes defined in Fig. 1a (see Supplementary Section 2, Fig. 1 for a detailed analysis). d, Spin-resolved EDCs for spin along the z axis, recorded at the inequivalent valleys of the and points. e, Spin-resolved EDCs at the point from the centrosymmetric materials 2H-MoS2 and 2H-WSe2 (see Supplementary Section 3 for a detailed analysis). f, Image obtained by subtraction of the SARPES intensities for z-oriented spin-up and spin-down (ΔI) recorded along ky. g, Calculated spin polarizations Pz of the valence bands along (0, ky, 0) for 3R-MoS2. h, Calculated total spin polarization of the valence bands along (0, ky, 0) for centrosymmetric 2H-MoS2.

  5. Circular dichroic photoluminescence of bilayer 2H- and 3R-MoS2.
    Figure 5: Circular dichroic photoluminescence of bilayer 2H- and 3R-MoS2.

    a, Circularly polarized photoluminescence spectra at 4 K for mono-, bi-, tri- and quadrilayers of 2H- (left column) and 3R- (right column) MoS2, pumped by a left circularly polarized (σ) He–Ne laser with a 633-nm wavelength. Sharp structures are Raman peaks from the MoS2 and Si substrate. b, Layer number (N) dependence of polarization ρ for 2H- and 3R-stackings with error bars of experimental standard deviation for several samples. c, Inverse layer number (1/N) dependence of polarization ρ for 2H- and 3R-stackings with error bars of experimental standard deviation for several samples. Dashed lines in b and c are the least-square fit by the model described in the text. d, Schematics of crystal and bandstructures of 2H- and 3R-bilayer MoS2. Valence bands in red and blue correspond to the spin-up and spin-down states, respectively. Green conduction bands are not spin-polarized. The character of the valence bands is exchanged between K and points in the 2H-stacking, but preserved in the 3R-stacking. White and black spheres indicate holes and electrons forming excitons at the K point following illumination with circularly polarized light. Intralayer relaxation, shown by yellow arrows, is the intervalley scattering from the K to point. In 2H-stacking, the interlayer scattering indicated by a blue arrow is also an effective relaxation mechanism for multilayer 2H-stacking. In 3R-stacking, on the other hand, the interlayer scattering indicated by a blue dotted line is much suppressed, and does not reduce ρ.


  1. Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nature Nanotech. 6, 147150 (2011).
  2. Podzorov, V., Gershenson, M. E., Kloc, Ch., Zeis, R. & Bucher, E. High-mobility field-effect transistors based on transition metal dichalcogenides. Appl. Phys. Lett. 84, 3301 (2004).
  3. Zhang, Y. J., Ye, J. T., Matsuhashi, Y. & Iwasa, Y. Ambipolar MoS2 thin flake transistors. Nano Lett. 12, 11361140 (2012).
  4. Braga, D., Lezama, I. G., Berger, H. & Morpurgo, A. F. Quantitative determination of the band gap of WS2 with ambipolar ionic liquid-gated transistors. Nano Lett. 12, 52185223 (2012).
  5. Ye, J. T., Zhang, Y. J., Akashi, R., Bahramy, M. S., Arita, R. & Iwasa, Y. Superconducting dome in a gate-tuned band insulator. Science 338, 11931196 (2012).
  6. Taniguchi, K., Matsumoto, A., Shimotani, H. & Takagi, H. Electric-field-induced superconductivity at 9.4 K in a layered transition metal disulphide MoS2. Appl. Phys. Lett. 101, 042603 (2012).
  7. Yuan, H. T. et al. Zeeman-type spin splitting controlled by an electric field. Nature Phys. 9, 563569 (2013).
  8. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: A new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).
  9. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 12711275 (2010).
  10. Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nature Nanotech. 7, 490493 (2012).
  11. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nature Nanotech. 7, 494498 (2012).
  12. Sallen, G. et al. Robust optical emission polarization in MoS2 monolayers through selective valley excitation. Phys. Rev. B 86, 081301 (2012).
  13. Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nature Commun. 3, 887 (2012).
  14. Takashina, K., Ono, Y., Fujiwara, A., Takahashi, Y. & Hirayama, Y. Valley polarization in Si(100) at zero magnetic field. Phys. Rev. Lett. 96, 236801 (2006).
  15. Isberg, J. et al. Generation, transport and detection of valley-polarized electrons in diamond. Nature Mater. 12, 760764 (2013).
  16. Shkolnikov, Y. P., De Poortere, E. P., Tutuc, E. & Shayegan, M. Valley splitting of AlAs two-dimensional electrons in a perpendicular magnetic field. Phys. Rev. Lett. 89, 226805 (2002).
  17. Gunawan, O. et al. Valley susceptibility of an interacting two-dimensional electron system. Phys. Rev. Lett. 97, 186404 (2006).
  18. Gunawan, O. et al. Spin-valley phase diagram of the two-dimensional metal–insulator transition. Nature Phys. 3, 388391 (2007).
  19. Zhu, Z., Collaudin, A., Fauque, B., Kang, W. & Behnia K. Field-induced polarization of Dirac valleys in bismuth. Nature Phys. 8, 8994 (2012).
  20. Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).
  21. Rycerz, A., Tworzydlo, J. & Beenakker, C. W. J. Valley filter and valley valve in graphene. Nature Phys. 3, 172175 (2007).
  22. Yao, W., Xiao, D. & Niu, Q. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B 77, 235406 (2008).
  23. Gunlycke, D. & White, C. T. Graphene valley filter using a line defect. Phys. Rev.Lett. 106, 136806 (2011).
  24. Xiao, D., Liu, G., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
  25. Zhu, C. R. et al. Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS2. Phys. Rev. B 88, 121301 (2013).
  26. Wu, S. et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nature Phys. 9, 149153 (2013).
  27. Jones, A. M. et al. Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe2. Nature Phys. 10, 130134 (2014).
  28. Wilson, J. A. & Yoffe, A. D. The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Adv. Phys. 18, 193334 (1969).
  29. Wildervanck, J. C. Chalcogenides of Molybdenum, Tungsten, Technetium and Rhenium. PhD thesis, Univ. of Groningen (1970).
  30. Zhu, Z. Y., Cheng, Y. C. & Schwingenschlogl, U. Giant spin–orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B 84, 153402 (2011).
  31. Lee, Y. et al. Synthesis of large-area MoS2 atomic layers with chemical vapor deposition. Adv. Mater. 24, 23202325 (2012).
  32. Wu, S. et al. Vapor–solid growth of high optical quality MoS2 monolayers with near-unity valley polarization. ACS Nano 7, 27682772 (2013).
  33. Liu, K-K. et al. Growth of large-area and highly crystalline MoS2 thin layers on insulating substrates. Nano Lett. 12, 15381544 (2012).
  34. Towle, L. C., Oberbeck, V., Brown, B. E. & Stajdohar, R. E. Molybdenum diselenide: rhombohedral high pressure-high temperature polymorph. Science 154, 895896 (1966).
  35. Al-hilli, A. A. & Evans, B. L. The preparation and properties of transition metal dichalcogenide single crystals. J. Cryst. Growth 15, 93101 (1972).
  36. Beal, A. R., Knights, J. C. & Liang, W. Y. Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination. J. Phys. C 5, 35403551 (1972).
  37. Coehoorn, R. et al. Electronic structure of MoSe2, MoS2, and WSe2. I. Band-structure calculations and photoelectron spectroscopy. Phys. Rev. B 35, 61956202 (1987).
  38. Jin, W. et al. Direct measurement of the thickness-dependent electronic band structure of MoS2 using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 111, 106801 (2013).
  39. Ishizaka, K. et al. Giant Rashba-type spin splitting in bulk BiTeI. Nature Mater. 10, 521526 (2011).
  40. Okuda, T. et al. Efficient spin resolved spectroscopy observation machine at Hiroshima Synchrotron Radiation Center. Rev. Sci. Instrum. 82, 103302 (2011).
  41. Meier, F., Dil, H., Lobo-Checa, J., Patthey, L. & Osterwalder, J. Quantitative vectorial spin analysis in angle-resolved photoemission: Bi/Ag(111) and Pb/Ag(111). Phys. Rev. B 77, 165431 (2008).
  42. Sakamoto, K. et al. Valley spin polarization by using the extraordinary Rashba effect on silicon. Nature Commun. 4, 2073 (2013).
  43. Lee, C. et al. Anomalous lattice vibrations of single- and few-layer MoS2. ACS Nano 4, 26952700 (2010).
  44. Li, H. et al. From bulk to monolayer MoS2: evolution of Raman scattering. Adv. Funct. Mater. 22, 13851390 (2012).
  45. Gong, Z. et al. Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nature Commun. 4, 2053 (2013).

Download references

Author information

  1. These authors contributed equally to this work

    • R. Suzuki &
    • M. Sakano


  1. Quantum-Phase Electronics Centre (QPEC) and Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan

    • R. Suzuki,
    • M. Sakano,
    • Y. J. Zhang,
    • R. Akashi,
    • K. Ishizaka,
    • R. Arita &
    • Y. Iwasa
  2. RIKEN Centre for Emergent Matter Science, Wako 351-0198, Japan

    • D. Morikawa,
    • R. Arita &
    • Y. Iwasa
  3. Institute for Solid State Physics, University of Tokyo, Kashiwa, 277-8581, Japan

    • A. Harasawa &
    • K. Yaji
  4. Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

    • K. Kuroda
  5. Hiroshima Synchrotron Radiation Centre, Hiroshima University, Higashi-Hiroshima 739-0046, Japan

    • K. Miyamoto &
    • T. Okuda


R.S., Y.Z. and Y.I. conceived and designed the research. R.S. grew and characterized all the crystals used in the research and D.M. generated CBED patterns. M.S., K.I., A.H., K.Y., K.K., K.M. and T.O. performed SARPES measurements. M.S. and K.I. analysed (S)ARPES data. First-principles calculations were made by R.Ak. and R.Ar. Y.Z. built a photoluminescence measurement system and R.S. measured the photoluminescence spectra. R.S., M.S., Y.Z., R.Ak., D.M., K.I., R.Ar. and Y.I. wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (1,291 KB)

    Supplementary Information

Additional data