Ordering dynamics in Type-II superconductors

TL;DR

This paper investigates the vortex ordering dynamics in Type-II superconductors after a quench, revealing different scaling behaviors in three dimensions and thin films, and how external magnetic fields influence vortex confinement and scaling crossover.

Contribution

It provides a combined analytical and numerical analysis of vortex dynamics, introducing a one-parameter scaling law for vortex separation under magnetic fields.

Findings

Vortex spacing scales with time as t^0.414 in 3D without field

In thin superconducting sheets, the scaling exponent is approximately 0.294

External magnetic fields induce a crossover between different scaling regimes

Abstract

We use analytic and numerical methods to analyze the dynamics of vortices following the quench of a Type-II superconductor under the application of an external magnetic field. In three dimensions, in the absence of a field, the spacing between vortices scales with time t with an exponent phi=0.414 +/- 0.01, In a thin sheet of superconductor, the scaling exponent is phi=0.294 +/- 0.01. When an external magnetic field h is applied, the vortices are confined with respect to the length scale of the Abrikosov lattice, leading to a crossover between the power-law scaling length scale and the lattice length scale. From this we suggest a one-parameter scaling of dr/dt with h and r that is consistent with numerical data.