Statistics of the vortex pinning potential in superconducting films

TL;DR

This paper analyzes the statistical properties of vortex pinning potentials in superconducting films, revealing Gaussian behavior under weak disorder and non-Gaussian corrections when vortex core relaxation is considered, with implications for vortex distribution.

Contribution

It introduces a model for vortex pinning potential statistics considering both weak disorder and core relaxation effects, providing new analytical insights into the pinning landscape.

Findings

In the weak disorder regime, the energy landscape is Gaussian with minima density ~ (6ξ)^{-2}.

Allowing vortex core relaxation leads to non-Gaussian statistics and reduces the density of minima.

The correction due to core deformation scales as (T_c - T)^{-1/2}.

Abstract

We investigate the statistical properties of the vortex pinning potential in a thin superconducting film. Modeling intrinsic inhomogeneities by a random-temperature Ginzburg-Landau functional with short-range Gaussian disorder, we derive the pinning landscape $E(\mathbf{R})$ by determining how the vortex core adapts to randomness. Within the hard-core approximation, applicable for weak disorder, the energy landscape exhibits Gaussian statistics. In this regime, the mean areal density of its minima is given by $n_\text{min}\approx(6\xi)^{-2}$, indicating that the typical spacing between neighboring minima is significantly larger than the vortex core size $\xi$. Going beyond the hard-core approximation, we allow the vortex order parameter to relax in response to the inhomogeneities. As a result, the pinning potential statistics become non-Gaussian. We calculate the leading correction due to the core deformation, which reduces the density of minima with a relative magnitude scaling as $(T_c-T)^{-1/2}$.