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 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> . This transition occurs when the magnitudes of the superconducting gap \Delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi></mml:math> and the Coulomb gap E_C <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>E</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math> 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) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="true" form="prefix">(</mml:mo><mml:mi>T</mml:mi><mml:mi>/</mml:mi><mml:mi>Δ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>C</mml:mi></mml:msub><mml:mi>/</mml:mi><mml:mi>Δ</mml:mi><mml:mo stretchy="true" form="postfix">)</mml:mo></mml:mrow></mml:math> . Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.