Fermion zero modes on vortices in chiral superconductors

TL;DR

This paper analyzes fermion bound states in vortices of chiral superconductors, revealing distinct energy spectra for two classes and examining impurity effects, with implications for understanding vortex core states.

Contribution

It distinguishes the energy spectra of fermion bound states in two classes of chiral superconductors and studies impurity effects on these spectra.

Findings

Class I vortices have spectrum E=(n+1/2)ω₀, similar to s-wave superconductors.

Class II vortices have spectrum E=nω₀, including zero-energy states.

Impurities do not affect the spectrum in class II superconductors.

Abstract

The energy levels of the fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the superconducting state of class I the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in s-wave superconductor: E=(n+1/2)\omega_0 with integral n. In the class II the corresponding spectrum is E=n\omega_0 and thus contains the state with exactly zero energy. The effect of a single impurity on the spectrum of bound state is also considered. For the class I the spectrum acquires the double period \Delta E=2\omega_0 and consists of two equidistant sets of levels in accordance with A.I. Larkin and Yu.N. Ovchinnikov, Phys. Rev. B57 (1998) 5457. The spectrum is not influenced by a single impurity if the same approximation is applied for vortices in the class II superconducting states.