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

Recent experimental studies on strongly disordered indium oxide films have revealed an
unusual first-order quantum phase transition between the superconducting and insulat-
ing 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 dif-
ferent order parameters, suggesting a natural expectation of a discontinuous transition
between them at T = 0. This transition occurs when the magnitudes of the supercon-
ducting gap ∆ 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 /∆, E$_C$ /∆). ... mehrOur results reveal the existence of a natural upper bound for
the kinetic inductance of strongly disordered superconductors.