Vortex noise and fluctuation conductivity in Josephson-junction arrays

Abstract

We study the vortex number noise Sv(ω) and fluctuation conductivity σ1(ω) in two-dimensional Josephson-junction arrays at three different applied magnetic fields, corresponding to zero, one-half, and 124 of a flux quantum per plaquette (f=0, 12 and 124). Sv and σ1 are obtained by numerically solving the equations for the coupled overdamped resistively-shunted-junction model with Langevin noise to simulate the effects of temperature. In all three cases, we find that Sv(ω)∝ω−3/2 at high frequencies ω and flattens out to become frequency independent at low ω, indicative of vortex diffusion, while σ1∼ω−2 at sufficiently high ω and ∼ω0 at low frequencies. Both quantities show clear evidence of critical slowing down and a simplified scaling behavior near the normal-to-superconducting transitions at f=0 and f=12, indicating that the vortex diffusion coefficient is approaching zero and the charge-carrier relaxation time is diverging at these temperatures. At f=124, there is no clear phase transition; instead, the vortex diffusion coefficient diminishes continuously as the temperature is lowered towards zero. The critical slowing down of Sv(ω), but not its frequency dependence, is in agreement with recent experiments on the flux noise SΦ(ω) in Josephson-junction arrays, which show a 1/ω frequency dependence. We speculate about some possible reasons for the absence of a 1/ω frequency regime.

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