Vortex charge and impurity effects based on quasiclassical theory

TL;DR

This paper analyzes vortex charge densities in s-wave and chiral p-wave superconductors using quasiclassical theory, revealing qualitative differences, impurity effects, and comparisons with BdG results.

Contribution

It introduces an augmented quasiclassical approach to account for particle-hole asymmetry and compares vortex charge effects between s-wave and chiral p-wave superconductors.

Findings

Chiral p-wave vortices can be charged or uncharged, explained qualitatively by the theory.

Larger vortex charge is induced in chiral p-wave superconductors compared to s-wave.

Impurities suppress vortex charge, especially in chiral p-wave superconductors.

Abstract

We investigate charge densities around the vortex cores of an s-wave and a chiral p-wave superconductor (SC) in two dimension within quasiclassical theory. We consider contributions of particle-hole asymmetry through gradient expansions in first order of a quasiclassical parameter using augmented quasiclassical theory. The chiral p-wave SC has two inequivalent vortices: one is charged and the other is uncharged on the basis of Bogoliubov--de Gennes (BdG) equation. We explain this qualitatively distinct charges also by the augmented quasiclassical theory. In addition, we find that much larger charge is induced for the charged vortex of the chiral p-wave SC compared with the vortex of the s-wave SC in the clean system. We also confirm this enhancement through quantitative comparison with results based on the BdG theory. We also study effects of Born-type impurities using self-energy formalism and find that the larger charge density is rather suppressed in contrast to the s-wave's one. Furthermore we study the local density of states as another equilibrium property of particle-hole asymmetry.