# Superconductor-Insulator Transition in disordered Josephson junction chains

## TL;DR

This paper investigates the superconductor-insulator transition in disordered Josephson junction chains, deriving a field theory, analyzing disorder effects, and mapping the phase diagram with RG methods, revealing complex non-monotonic behaviors.

## Contribution

It introduces a detailed field theory for disordered Josephson chains and analyzes the phase transition considering short-range and long-range couplings with renormalization-group techniques.

## Key findings

- Phase diagram mapped using RG analysis.
- Temperature-dependent conductivity shows non-monotonic behavior.
- Resistance exhibits complex size and temperature dependence near transition.

## Abstract

We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground ($C_0$) as well as between the islands ($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppress the coherence of phase slips, thus favoring superconducting correlations. Using the renormalization-group approach, we determine the phase diagram and evaluate the temperature dependence of the dc conductivity and system-size dependence of the resistance around the superconductor-insulator transition. These dependences have in general strongly non-monotonic character, with several distinct regimes reflecting an intricate interplay of superconductivity and disorder.