Numerical Investigation of the Dynamics of a Thin Film Type II Superconductor with and without Disorder

TL;DR

This study numerically explores the equilibrium dynamics of thin film type II superconductors with and without disorder, revealing no phase transition or Bragg glass phase, and characterizing vortex relaxation mechanisms.

Contribution

It provides a detailed numerical analysis of vortex dynamics and correlations in thin film superconductors, including effects of disorder and temperature.

Findings

Correlation length increases as temperature decreases

Disorder reduces the correlation length and prevents Bragg glass formation

Vortex relaxation is activated with a barrier growing linearly with correlation length

Abstract

The equilibrium dynamics of a thin film type II superconductor with spherical geometry are investigated numerically in a simulation based on the lowest Landau level approximation to the time-dependent Ginzburg-Landau equation. Both the static and time-dependent density-density correlation functions of the superconducting order parameter have been investigated. As the temperature is lowered the correlation length, the length-scale over which the vortices have short-range crystalline order, increases but the introduction of quenched random disorder reduces this correlation length. We see no signs of a phase transition in either the pure or the disordered case. For the disordered system there is no evidence for the existence of a Bragg glass phase with quasi long-range correlations. The dynamics in both the pure and disordered systems is activated, and the barrier of the relaxation mechanism grows linearly with the correlation length. The self-diffusion time scale of the vortices was also measured and has the same temperature dependence as that of the longest time scales found in the time dependent density-density correlation function. The dominant relaxation mechanism observed is a change in orientation of a correlated region of size of the correlation length. A scaling argument is given to explain the value of the barrier exponent.