Mean-field theory of first-order quantum superconductor-insulator transition

TL;DR

This paper develops a mean-field theory explaining the first-order quantum phase transition between superconducting and insulating states in disordered films, highlighting the competition between distinct ground states and predicting a discontinuous transition.

Contribution

It introduces a theoretical framework based on competing ground states with different order parameters, explaining the first-order transition observed in disordered superconductors.

Findings

Discontinuous jump in superfluid stiffness at the transition

Existence of an upper bound for kinetic inductance

Phase diagram illustrating transition conditions

Abstract

Recent experimental studies on strongly disordered indium oxide films have revealed an unusual first-order quantum phase transition between the superconducting and insulating states (SIT). This transition is characterized by a discontinuous jump from non-zero to zero values of superfluid stiffness at the critical point, contradicting the conventional "scaling scenario" typically associated with SIT. In this paper, we present a theoretical framework for understanding this first-order transition. Our approach is based on the concept of competition between two fundamentally distinct ground states that arise from electron pairs initially localized by strong disorder: the superconducting state and the Coulomb glass insulator. These ground states are distinguished by two crucially different order parameters, suggesting a natural expectation of a discontinuous transition between them at $T=0$. This transition occurs when the magnitudes of the superconducting gap $\Delta$ and the Coulomb gap $E_C$ become comparable. Additionally, we extend our analysis to low non-zero temperatures and provide a mean-field "phase diagram" in the plane of $(T/\Delta,E_C/\Delta)$. Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.