Finite Size Effects in Vortex Localization

TL;DR

This paper investigates how finite sample sizes influence vortex localization in disordered superconductors, revealing size-dependent critical fields and behaviors akin to directed polymers in random media.

Contribution

It introduces a novel analysis linking vortex pinning properties to finite size effects and the density of states near the band edge, expanding understanding of vortex behavior in disordered systems.

Findings

H_{c1} inversely proportional to log of sample size

Screening length decreases with temperature

Extended vortex states exhibit wandering behavior with directed polymer exponents

Abstract

The equilibrium properties of flux lines pinned by columnar disorder are studied, using the analogy with the time evolution of a diffusing scalar density in a randomly amplifying medium. Near H_{c1}, the physical features of the vortices in the localized phase are shown to be determined by the density of states near the band edge. As a result, H_{c1} is inversely proportional to the logarithm of the sample size, and the screening length of the perpendicular magnetic field decreases with temperature. For large tilt the extended ground state turns out to wander in the plane perpendicular to the defects with exponents corresponding to a directed polymer in a random medium, and the energy difference between two competing metastable states in this case is extensive. The divergence of the effective potential associated with strong pinning centers as the tilt approaches its critical value is discussed as well.