Negative electronic compressibility and nanoscale inhomogeneity in ionic-liquid gated two-dimensional superconductors

When the electron density of highly crystalline thin films is tuned by chemical doping or ionic-liquid gating, interesting effects appear including unconventional superconductivity, sizable spin-orbit coupling, competition with charge-density waves, and a debated low-temperature metallic state that seems to avoid the superconducting or insulating fate of standard two-dimensional electron systems. Some experiments also find a marked tendency to a negative electronic compressibility. We suggest that this indicates an inclination for electronic phase separation resulting in a nanoscopic inhomogeneity. Although the mild modulation of the inhomogeneous landscape is compatible with a high electron mobility in the metallic state, this intrinsically inhomogeneous character is highlighted by the peculiar behavior of the metal-to-superconductor transition. Modeling the system with superconducting puddles embedded in a metallic matrix, we fit the peculiar resistance vs temperature curves of systems like TiSe2, MoS2, and ZrNCl. In this framework also the low-temperature debated metallic state finds a natural explanation in terms of the pristine metallic background embedding nonpercolating superconducting clusters. An intrinsically inhomogeneous character naturally raises the question of the formation mechanism(s). We propose a mechanism based on the interplay between electrons and the charges of the gating ionic liquid.