Relaxation dynamics and interrupted coarsening in irrationally frustrated superconducting arrays

TL;DR

This study investigates the relaxation dynamics of irrationally frustrated superconducting arrays, revealing complex multi-stage relaxation behaviors linked to vortex coarsening and domain wall fluctuations, with implications for low-temperature resistivity.

Contribution

It provides a detailed numerical analysis of non-equilibrium relaxation in irrationally frustrated arrays, highlighting the role of vortex dynamics and coarsening in relaxation processes.

Findings

Three-stage relaxation of chirality autocorrelations observed.

Intermediate power-law relaxation linked to vortex coarsening.

Long-time stretched exponential decay due to domain wall fluctuations.

Abstract

Equilibrium and non-equilibrium relaxation behaviors of two-dimensional superconducting arrays are investigated via numerical simulations at low temperatures in the presence of incommensurate transverse magnetic fields, with frustration parameter f= (3-\sqrt{5})/2. We find that the non-equilibrium relaxation, beginning with random initial states quenched to low temperatures, exhibits a three-stage relaxation of chirality autocorrelations. At the early stage, the relaxation is found to be described by the von Schweidler form. Then it exhibits power-law behavior in the intermediate time scale and faster decay in the long-time limit, which together can be fitted to the Ogielski form; for longer waiting times, this crosses over to a stretched exponential form. We argue that the power-law behavior in the intermediate time scale may be understood as a consequence of the coarsening behavior, leading to the local vortex order corresponding to f=2/5 ground-state configurations. High mobility of the vortices in the domain boundaries, generating slow wandering motion of the domain walls, may provide mechanism of dynamic heterogeneity and account for the long-time stretched exponential relaxation behavior. It is expected that such meandering fluctuations of the low-temperature structure give rise to finite resistivity at those low temperatures; this appears consistent with the zero-temperature resistive transition in the limit of irrational frustration.