Relaxation and Coarsening Dynamics in Superconducting Arrays

TL;DR

This paper studies the nonequilibrium coarsening dynamics in two-dimensional superconducting arrays, revealing different growth behaviors of vortex and domain structures depending on dissipation mechanisms and frustration levels.

Contribution

It provides a detailed analysis of how dissipation and frustration influence coarsening dynamics and domain growth in superconducting arrays through numerical simulations.

Findings

Vortex length scale grows as t^{1/2} in unfrustrated arrays.

Number of vortices decays as 1/t in unfrustrated arrays.

Domain growth in frustrated arrays follows a power law with a temperature-dependent exponent.

Abstract

We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance. The nonequilibrium relaxation of the unfrustrated array and also of the fully frustrated array, quenched to low temperature ordered states or quasi-ordered ones, is dominated by characteristic features of coarsening processes via decay of point and line defects, respectively. In the case of unfrustrated arrays, it is argued that due to finiteness of the friction constant for a vortex (in the limit of large spatial extent of the vortex), the typical length scale grows as $\ell_s \sim t^{1/2}$ accompanied by the number of point vortices decaying as $N_v \sim 1/t $. This is in contrast with the case that dominant dissipation occurs between each island and the substrate, where the friction constant diverges logarithmically and the length scale exhibits diffusive growth with a logarithmic correction term. We perform extensive numerical simulations, to obtain results in reasonable agreement. In the case of fully frustrated arrays, the domain growth of Ising-like chiral order exhibits the low-temperature behavior $\ell_q \sim t^{1/z_q}$, with the growth exponent $1/z_q$ apparently showing a strong temperature dependence in the low-temperature limit.