Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays

Abstract

We study the flux noise $S_Φ(ω)$ and finite frequency conductivity $σ_1(ω)$ 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 $S_Φ(ω)\propto ω^{-3/2}$ at high frequencies $ω$ and flattens at low $ω$, indicative of vortex diffusion, while $σ_1 \propto ω^{-2}$ at sufficiently high $ω$. 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 $S_Φ$, but not its frequency dependence, is in agreement with recent experiments on Josephson junction arrays.