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

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.

Superconductors without Symmetry Breaking

“…The point is that vortices are not Noether charges but are topological ones, and, as such, at very low temperatures, they can freely tunnel between different topological sectors. Let us consider, in particular, a quantum event in which all phases on a line ending in a particular island simultaneously flip by 2π, with alternating signs [43]. No phase degrees of freedom, neither small fluctuations (like spin waves) nor vortices, are involved in such an event, except at the endpoint, where it corresponds to the tunneling of one vortex from one plaquette to the neighboring one.…”