# Zero-temperature resistive transition in Josephson-junction arrays at irrational frustration

## TL;DR

This study investigates the zero-temperature resistive transition in 2D Josephson-junction arrays at irrational frustration, revealing a phase-coherence transition with a vanishing critical temperature and detailed resistivity behavior.

## Contribution

It provides the first detailed dynamic scaling analysis of resistivity and critical exponents at irrational flux, confirming a zero-temperature transition scenario.

## Key findings

- Linear resistivity is nonzero at finite temperatures.
- Nonlinear behavior appears at a temperature-dependent crossover current.
- Results align with earlier resistively shunted-junction model calculations.

## Abstract

We use a driven Monte Carlo dynamics in the phase representation to determine the linear resistivity and current-voltage scaling of a two-dimensional Josephson-junction array at an irrational flux quantum per plaquette. The results are consistent with a phase-coherence transition scenario where the critical temperature vanishes. The linear resistivity is nonzero at any finite temperatures but nonlinear behavior sets in at a temperature-dependent crossover current determined by the thermal critical exponent. From a dynamic scaling analysis we determine this critical exponent and the thermally activated behavior of the linear resistivity. The results are in agreement with earlier calculations using the resistively shunted-junction model for the dynamics of the array. The linear resistivity behavior is consistent with some experimental results on arrays of superconducting grains but not on wire networks, which we argue have been obtained in a current regime above the crossover current.