Localization of quasiparticles in a disordered vortex

TL;DR

This paper investigates how low-energy quasiparticles move and localize within vortex cores in disordered superconductors, revealing universal spectral correlations and energy-dependent localization effects that impact heat transport.

Contribution

It introduces a supersymmetric nonlinear sigma model for quasiparticles in vortex cores and analyzes localization phenomena and spectral correlations in this context.

Findings

Spectral correlations match random matrix theory predictions for class C.

Weak localization correction observed in quasiparticle transmittance at zero energy.

Localization length decreases significantly as quasiparticle energy approaches zero.

Abstract

We study the diffusive motion of low-energy normal quasiparticles along the core of a single vortex in a dirty, type-II, s-wave superconductor. The physics of this system is argued to be described by a one-dimensional supersymmetric nonlinear sigma model, which differs from the sigma models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy, we recover the spectral correlations that are predicted by random matrix theory for the universality class C. We then consider the transport problem of transmission of quasiparticles through a vortex connected to particle reservoirs at both ends. The transmittance at zero energy exhibits a weak localization correction reminiscent of quasi-one-dimensional metallic systems with symmetry index beta = 1. Weak localization disappears with increasing energy over a scale set by the Thouless energy. This crossover should be observable in measurements of the longitudinal heat conductivity of an ensemble of vortices under mesoscopic conditions. In the regime of strong localization, the localization length is shown to decrease by a factor of 8 as the quasiparticle energy goes to zero.