Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays

TL;DR

This paper investigates flux noise and conductivity in 2D unfrustrated Josephson junction arrays, revealing frequency-dependent behaviors and critical phenomena near the Kosterlitz-Thouless transition through numerical simulations.

Contribution

It provides the first detailed numerical analysis of flux noise and conductivity in unfrustrated Josephson junction arrays, highlighting their critical dynamics near the KTB transition.

Findings

Flux noise scales as ω^{-3/2} at high frequencies

Conductivity scales as ω^{-2} at high frequencies

Evidence of critical slowing down near the KTB transition

Abstract

We study the flux noise $S_{\Phi}(\omega)$ and finite frequency conductivity $\sigma_1(\omega)$ in two dimensional unfrustrated Josephson junction arrays (JJA's), by numerically solving the equations of the coupled overdamped resistively-shunted-junction model with Langevin noise. We find that $S_{\Phi}(\omega)\propto \omega^{-3/2}$ at high frequencies $\omega$ and flattens at low $\omega$, indicative of vortex diffusion, while $\sigma_1 \propto \omega^{-2}$ at sufficiently high $\omega$. Both quantities show clear evidence of critical slowing down and possibly scaling behavior near the Kosterlitz-Thouless-Berezinskii (KTB) transition. The critical slowing down of $S_{\Phi}$, but not its frequency dependence, is in agreement with recent experiments on Josephson junction arrays.