Gauge Theories of Josephson Junction Arrays: Why Disorder Is Irrelevant for the Electric Response of Disordered Superconducting Films

TL;DR

This paper reviews the topological gauge theory of Josephson junction arrays and thin film superconductors, highlighting the irrelevance of disorder in their quantum phases and explaining the mechanisms behind superinsulation and topological states.

Contribution

It introduces a comprehensive gauge theory framework that explains quantum phase transitions and the irrelevance of disorder in disordered superconducting films.

Findings

Disorder does not affect electric response in quantum phases due to symmetry protection or neutrality.

Quantum phase transitions are driven by increasing electric interactions, preventing Bose condensation.

Electric flux tubes induce confinement, leading to superinsulation.

Abstract

We review the topological gauge theory of Josephson junction arrays and thin film superconductors, stressing the role of the usually forgotten quantum phase slips, and we derive their quantum phase structure. A quantum phase transition from a superconducting to the dual, superinsulating phase with infinite resistance (even at finite temperatures) is either direct or goes through an intermediate bosonic topological insulator phase, which is typically also called Bose metal. We show how, contrary to a widely held opinion, disorder is not relevant for the electric response in these quantum phases because excitations in the spectrum are either symmetry-protected or neutral due to confinement. The quantum phase transitions are driven only by the electric interaction growing ever stronger. First, this prevents Bose condensation, upon which out-of-condensate charges and vortices form a topological quantum state owing to mutual statistics interactions. Then, at even stronger couplings, an electric flux tube dual to Abrikosov vortices induces a linearly confining potential between charges, giving rise to superinsulation.