Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Negative electronic compressibility and tunable spin splitting in WSe2

Abstract

Tunable bandgaps1, extraordinarily large exciton-binding energies2,3, strong light–matter coupling4 and a locking of the electron spin with layer and valley pseudospins5,6,7,8 have established transition-metal dichalcogenides (TMDs) as a unique class of two-dimensional (2D) semiconductors with wide-ranging practical applications9,10. Using angle-resolved photoemission (ARPES), we show here that doping electrons at the surface of the prototypical strong spin–orbit TMD WSe2, akin to applying a gate voltage in a transistor-type device, induces a counterintuitive lowering of the surface chemical potential concomitant with the formation of a multivalley 2D electron gas (2DEG). These measurements provide a direct spectroscopic signature of negative electronic compressibility (NEC), a result of electron–electron interactions, which we find persists to carrier densities approximately three orders of magnitude higher than in typical semiconductor 2DEGs that exhibit this effect11,12. An accompanying tunable spin splitting of the valence bands further reveals a complex interplay between single-particle band-structure evolution and many-body interactions in electrostatically doped TMDs. Understanding and exploiting this will open up new opportunities for advanced electronic and quantum-logic devices.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Electronic-structure evolution of chemically gated WSe2.
Figure 2: Tunable valley spin splitting.
Figure 3: Spectroscopic signatures of NEC.
Figure 4: Interplay of band bending and negative compressibility.

References

  1. 1

    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).

    Article  Google Scholar 

  2. 2

    Ugeda, M. M. et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nature Mater. 13, 1091–1095 (2014).

    CAS  Article  Google Scholar 

  3. 3

    Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    CAS  Article  Google Scholar 

  4. 4

    Liu, X. et al. Strong light-matter coupling in two-dimensional atomic crystals. Nature Photon. 9, 30–34 (2015).

    CAS  Article  Google Scholar 

  5. 5

    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. 108, 196802 (2012).

    Article  Google Scholar 

  6. 6

    Gong, Z. et al. Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nature Commun. 4, 2053 (2013).

    Article  Google Scholar 

  7. 7

    Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nature Phys. 10, 343–350 (2014).

    CAS  Article  Google Scholar 

  8. 8

    Riley, J. M. et al. Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor. Nature Phys. 10, 835–839 (2014).

    CAS  Article  Google Scholar 

  9. 9

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nature Nanotech. 7, 699–712 (2012).

    CAS  Article  Google Scholar 

  10. 10

    Zhang, Y., Ye, J., Matsuhashi, Y. & Iwasa, Y. Ambipolar MoS2 thin flake transistors. Nano Lett. 12, 1136–1140 (2012).

    CAS  Article  Google Scholar 

  11. 11

    Eisenstein, J., Pfeiffer, L. & West, K. Negative compressibility of interacting two-dimensional electron and quasiparticle gases. Phys. Rev. Lett. 68, 674–677 (1992).

    CAS  Article  Google Scholar 

  12. 12

    Eisenstein, J., Pfeiffer, L. & West, K. Compressibility of the two-dimensional electron gas: measurements of the zero-field exchange energy and fractional quantum Hall gap. Phys. Rev. B 50, 1760–1778 (1994).

    CAS  Article  Google Scholar 

  13. 13

    Ilani, S., Donev, L. A. K., Kindermann, M. & McEuen, P. L. Measurement of the quantum capacitance of interacting electrons in carbon nanotubes. Nature Phys. 2, 687–691 (2006).

    CAS  Article  Google Scholar 

  14. 14

    Li, L. et al. Very large capacitance enhancement in a two-dimensional electron system. Science 332, 825–828 (2011).

    CAS  Article  Google Scholar 

  15. 15

    Yu, G. L. et al. Interaction phenomena in graphene seen through quantum capacitance. Proc. Natl Acad. Sci. USA 110, 3282–3286 (2013).

    CAS  Article  Google Scholar 

  16. 16

    Zhang, Y. J., Oka, T., Suzuki, R., Ye, J. T. & Iwasa, Y. Electrically switchable chiral light-emitting transistor. Science 344, 725–728 (2014).

    CAS  Article  Google Scholar 

  17. 17

    Yuan, H. et al. Zeeman-type spin splitting controlled by an electric field. Nature Phys. 9, 563–569 (2013).

    CAS  Article  Google Scholar 

  18. 18

    Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).

    CAS  Article  Google Scholar 

  19. 19

    Finteis, T. et al. Occupied and unoccupied electronic band structure of WSe2 . Phys. Rev. B 55, 10400–10411 (1997).

    CAS  Article  Google Scholar 

  20. 20

    King, P. D. C. et al. Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3 . Phys. Rev. Lett. 107, 096802 (2011).

    CAS  Article  Google Scholar 

  21. 21

    Bahramy, M. et al. Emergent quantum confinement at topological insulator surfaces. Nature Commun. 3, 1159 (2012).

    CAS  Article  Google Scholar 

  22. 22

    Zhang, Y. et al. Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2 . Nature Nanotech. 9, 111–115 (2014).

    CAS  Article  Google Scholar 

  23. 23

    Nitta, J., Akazaki, T., Takayanagi, H. & Enoki, T. Gate control of spin–orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure. Phys. Rev. Lett. 78, 1335–1338 (1997).

    CAS  Article  Google Scholar 

  24. 24

    King, P. D. C., Veal, T. D. & McConville, C. F. Nonparabolic coupled Poisson–Schrödinger solutions for quantized electron accumulation layers: band bending, charge profile, and subbands at InN surfaces. Phys. Rev. B 77, 125305 (2008).

    Article  Google Scholar 

  25. 25

    Das Sarma, S., Jalabert, R. & Yang, S.-R. E. Band-gap renormalization in semiconductor quantum wells. Phys. Rev. B 41, 8288–8294 (1990).

    Article  Google Scholar 

  26. 26

    Larentis, S. et al. Band offset and negative compressibility in graphene–MoS2 heterostructures. Nano. Lett. 14, 2039–2045 (2014).

    CAS  Article  Google Scholar 

  27. 27

    He, J. et al. Spectroscopic evidence for negative electronic compressibility in a quasi-three-dimensional spin-orbit correlated metal. Nature Mater. 14, 577–582 (2014).

    Article  Google Scholar 

  28. 28

    Liang, Y. & Yang, L. Carrier plasmon induced nonlinear band gap renormalization in two-dimensional semiconductors. Phys. Rev. Lett. 114, 063001 (2014).

    Article  Google Scholar 

  29. 29

    Mak, K. F. et al. Tightly bound trions in monolayer MoS2 . Nature Mater. 12, 207–211 (2013).

    CAS  Article  Google Scholar 

  30. 30

    Vinter, B. Many-body effects in n-type Si inversion layers. I. Effects in the lowest subband. Phys. Rev. B 13, 4447–4456 (1976).

    CAS  Article  Google Scholar 

  31. 31

    Blaha, P. et al. WIEN2K package, Version 10.1 (Vienna University of Technology, 2010).

  32. 32

    Souza, I. et al. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).

    Article  Google Scholar 

  33. 33

    King, P. D. C. et al. Quasiparticle dynamics and spin-orbital texture of the SrTiO3 two-dimensional electron gas. Nature Commun. 5, 3414 (2014).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Engineering and Physical Sciences Research Council, UK (Grant Nos EP/I031014/1, EP/M023427/1, EP/L505079/1 and EP/G03673X/1), TRF-SUT Grant RSA5680052 and NANOTEC, Thailand, through the Centres of Excellence Network. P.D.C.K. acknowledges support from the Royal Society through a University Research Fellowship. M.S.B. was supported by a Grant-in-Aid for Scientific Research (S) (No. 24224009) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, US Department of Energy, under Contract No. DE-AC02-05CH11231. We thank the Diamond Light Source for access to beamline I05 (proposal numbers SI9500 and SI11383) that contributed to the results presented here.

Author information

Affiliations

Authors

Contributions

The experimental data were measured by J.M.R., W.M., L.B., T.E. and P.D.C.K., and J.M.R. analysed the data. M.A., T.T., H.T. and T.S. grew and characterized the samples. J.M.R. performed the RPA calculations, and M.S.B. performed the first-principles and supercell calculations. T.K.K., M.H. and S.-K.M. maintained the synchrotron ARPES end stations and provided experimental support. P.D.C.K., J.M.R. and M.S.B. wrote the manuscript, with input and discussions from all the co-authors. P.D.C.K. conceived the study and was responsible for the overall project planning and direction.

Corresponding author

Correspondence to P. D. C. King.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 334 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Riley, J., Meevasana, W., Bawden, L. et al. Negative electronic compressibility and tunable spin splitting in WSe2. Nature Nanotech 10, 1043–1047 (2015). https://doi.org/10.1038/nnano.2015.217

Download citation

Further reading

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research