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

## TL;DR

This paper investigates negative electronic compressibility and nanoscale inhomogeneity in ionic-liquid gated two-dimensional superconductors, proposing a model of superconducting puddles within a metallic matrix to explain experimental observations.

## Contribution

It introduces a model of inhomogeneity with superconducting puddles embedded in a metallic background, explaining resistance behavior and metallic states in 2D superconductors.

## Key findings

- Negative electronic compressibility indicates phase separation tendencies.
- Inhomogeneous superconducting puddles explain resistance curves.
- Metallic states are due to non-percolating superconducting clusters.

## Abstract

When the electron density of highly crystalline thin films is tuned by chemical doping or ionic liq- uid gating, interesting effects appear including unconventional superconductivity, sizeable 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 inhomo- geneity. 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 behaviour of the metal-to-superconductor transition. Modelling the system with super- conducting 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 non-percolating superconducting clusters. An intrinsically inhomogeneous character naturally raises the question of the formation mechanism(s). We propose a mechanism based on the interplay be- tween electrons and the charges of the gating ionic liquid.