# Disordered BKT transition and superinsulation

## TL;DR

This paper develops a theoretical framework for disordered Josephson junction arrays, revealing that strong disorder leads to Vogel-Fulcher-Tammann criticality and a nonergodic insulating phase, contrasting with the BKT transition observed in weaker disorder.

## Contribution

It introduces a model linking disordered Josephson arrays to a Coulomb gas with correlated disorder, explaining different critical behaviors and phases.

## Key findings

- Strong disorder induces VFT criticality instead of BKT.
- Transition to a nonergodic insulator phase occurs under strong disorder.
- The model explains the nature of superinsulation in disordered films.

## Abstract

Strongly disordered superconducting films have been observed to undergo finite temperature transitions to a superinsulating state, of apparently infinite resistance, mirroring superconductivity. Approaching the transition, some of the films reportedly exhibit Berezinskii-Kosterlitz-Thouless (BKT) criticality implying that superinsulation is associated with an ordered charge BKT phase. An even more singular Vogel-Fulcher-Tammann (VFT) criticality has also been seen, positing the question of the existence of fundamentally different states of finite temperature insulators. Here we develop a theory of the criticality of a disordered lateral Josephson junction array with weak Josephson coupling. We show that it is equivalent to a two-dimensional Coulomb gas with logarithmically correlated disorder. We show that strong disorder results in a regime exhibiting VFT criticality instead of the usual BKT one, and find that it corresponds to transition to a nonergodic insulator phase.