Localization of quasiparticles in a disordered vortex

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 σ model, which differs from the σ models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy E Th , 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 β = 1. Weak localization disappears with increasing energy over a scale set by E Th . 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.

Tail states in disordered superconductors with magnetic impurities: the unitarity limit

“…In the present case, such investigations reveal that mechanisms of quantum interference lead to the delocalisation of the quasi-particle states even in low dimension [11,12,13,14]. This behaviour provides a striking contrast with that of other superconducting (and normal metallic) systems where mechanism of quantum interference have a tendency to bring about localisation of the quasi-particle states.…”

“…In the present case, one must consider simply how to tailor this analysis to the consideration of unitarity scattering limit of the magnetic impurity system. Since the general theoretical framework has been reviewed in a number of publications [16,11] and discussed for the magnetic impurity system in particular [15], we will keep our discussion concise focussing primarily on the idiosyncrasies of the present theory.…”

“…To formulate a field theory of the non-interacting superconducting system, we will follow the standard scheme [16,11] and begin with the generating functional for the single quasi-particle Green function:…”

Optimal Fluctuations and Tail States of Non-Hermitian Operators

“…Motivated by the correspondence outlined above, the analysis will parallel previous investigations of the weakly disordered superconductor [37,38,39]. The starting point is the generating functional for the singleparticle Green function.…”

“…As usual, the contour of integration over the boson-boson field θ bb includes the entire real axis, while for the fermion-fermion field iθ ff runs along the imaginary axis from 0 to iπ. With a smooth deformation of the integration contours, the mean-field saddle-point is accessible to both the anglesθ [37,38]. By contrast, the particular bounce solution and the mean-field solution can be reached simultaneously by a smooth deformation of the integration contour only for the boson-boson field θ bb (see Fig.…”