Vortex pinning by a columnar defect in planar superconductors with point disorder

TL;DR

This paper investigates how a single columnar defect influences vortex pinning in planar superconductors with point disorder, revealing that the defect's effectiveness varies with temperature and disorder, and is irrelevant at large scales.

Contribution

It demonstrates that the columnar pin is irrelevant at long scales in disordered systems, contrasting with the disorder-free case, and analyzes the crossover between pure and disordered regimes using renormalization group methods.

Findings

Maximum vortex pinning occurs at the vortex glass transition temperature.

Columnar pin is irrelevant at large scales both above and below the transition.

Density oscillations around the pin are computed and analyzed.

Abstract

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.