Negative electronic compressibility and tunable spin splitting in WSe₂

Tunable bandgaps¹, extraordinarily large exciton-binding energies^{2, 3}, strong light–matter coupling⁴ and a locking of the electron spin with layer and valley pseudospins^{5, 6, 7, 8} have established transition-metal dichalcogenides (TMDs) as a unique class of two-dimensional (2D) semiconductors with wide-ranging practical applications^{9, 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 effect^{11, 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.