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.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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).
Ugeda, M. M. et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nature Mater. 13, 1091–1095 (2014).
Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).
Liu, X. et al. Strong light-matter coupling in two-dimensional atomic crystals. Nature Photon. 9, 30–34 (2015).
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).
Gong, Z. et al. Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nature Commun. 4, 2053 (2013).
Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nature Phys. 10, 343–350 (2014).
Riley, J. M. et al. Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor. Nature Phys. 10, 835–839 (2014).
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).
Zhang, Y., Ye, J., Matsuhashi, Y. & Iwasa, Y. Ambipolar MoS2 thin flake transistors. Nano Lett. 12, 1136–1140 (2012).
Eisenstein, J., Pfeiffer, L. & West, K. Negative compressibility of interacting two-dimensional electron and quasiparticle gases. Phys. Rev. Lett. 68, 674–677 (1992).
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).
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).
Li, L. et al. Very large capacitance enhancement in a two-dimensional electron system. Science 332, 825–828 (2011).
Yu, G. L. et al. Interaction phenomena in graphene seen through quantum capacitance. Proc. Natl Acad. Sci. USA 110, 3282–3286 (2013).
Zhang, Y. J., Oka, T., Suzuki, R., Ye, J. T. & Iwasa, Y. Electrically switchable chiral light-emitting transistor. Science 344, 725–728 (2014).
Yuan, H. et al. Zeeman-type spin splitting controlled by an electric field. Nature Phys. 9, 563–569 (2013).
Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).
Finteis, T. et al. Occupied and unoccupied electronic band structure of WSe2 . Phys. Rev. B 55, 10400–10411 (1997).
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).
Bahramy, M. et al. Emergent quantum confinement at topological insulator surfaces. Nature Commun. 3, 1159 (2012).
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).
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).
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).
Das Sarma, S., Jalabert, R. & Yang, S.-R. E. Band-gap renormalization in semiconductor quantum wells. Phys. Rev. B 41, 8288–8294 (1990).
Larentis, S. et al. Band offset and negative compressibility in graphene–MoS2 heterostructures. Nano. Lett. 14, 2039–2045 (2014).
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).
Liang, Y. & Yang, L. Carrier plasmon induced nonlinear band gap renormalization in two-dimensional semiconductors. Phys. Rev. Lett. 114, 063001 (2014).
Mak, K. F. et al. Tightly bound trions in monolayer MoS2 . Nature Mater. 12, 207–211 (2013).
Vinter, B. Many-body effects in n-type Si inversion layers. I. Effects in the lowest subband. Phys. Rev. B 13, 4447–4456 (1976).
Blaha, P. et al. WIEN2K package, Version 10.1 (Vienna University of Technology, 2010).
Souza, I. et al. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).
King, P. D. C. et al. Quasiparticle dynamics and spin-orbital texture of the SrTiO3 two-dimensional electron gas. Nature Commun. 5, 3414 (2014).
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.
The authors declare no competing financial interests.
About this article
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
Physical Review B (2020)
The Journal of Physical Chemistry C (2020)
npj 2D Materials and Applications (2020)
AIP Advances (2020)
Physica Scripta (2020)