Vortex noise and fluctuation conductivity in Josephson-junction arrays

We study the vortex number noise S-upsilon(omega) and fluctuation conductivity sigma(1)(omega) in two-dimensional Josephson-junction arrays at three different applied magnetic fields, corresponding to zero, one-half, and 1/24 of a flux quantum per plaquette (f = 0, 1/2 and 1/24). S-upsilon and sigma(1) 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 S-upsilon(omega)proportional to omega(-3/2) at high frequencies omega and flattens out to become frequency independent at low omega, indicative of vortex diffusion, while sigma(1) similar to omega(-2) at sufficiently high omega and similar to omega(0) 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 = 1/2, indicating that the vortex diffusion coefficient is approaching zero and the charge-carrier relaxation time is diverging at these temperatures. At f = 1/24, 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 S-upsilon(omega), but not its frequency dependence, is in agreement with recent experiments on the flux noise S-Phi(omega) in Josephson-junction arrays, which show a 1/omega frequency dependence. We speculate about some possible reasons for the absence of a 1/omega frequency regime.