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

Recent experimental studies of strongly disordered Indium Oxide films revealed an unusual first-
order quantum phase transition between superconducting and insulating state (SIT), with the jump
between nonzero and zero values of superfluid stiffness at the transition arXiv:2404.09855 . This finding is in sharp contradiction with a ”scaling scenario” discussed usually in relation to SIT. In the present paper we propose a simple theory of this first-order transition. It is based upon idea of competition between two intrinsically different ground states that can be formed by initially localized (due to strong
disorder) electron pairs: superconducting state and Coulomb glass insulator. These two ground
states are characterized by two crucially different order parameters, thus it is natural to expect
a discontinuous transition between them at T = 0. The transition happens when magnitudes of
superconducting gap ∆ and Coulomb gap EC are comparable. We also extend our analysis to
low nonzero temperatures and provide a mean-field ”phase diagram” in the plane (T /∆, EC /∆).
Our results demonstrate the existence of natural upper bound for kinetic inductance of a strongly
disordered superconductor.