Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor

TL;DR

This paper applies the index theorem to analyze Majorana zero modes along non-Abelian vortices in color superconductors, revealing conditions for their existence and stability at high densities.

Contribution

It demonstrates the use of the index theorem to identify and confirm Majorana zero modes in the CFL phase with non-Abelian vortices, including effects of finite chemical potential.

Findings

Triplet, doublet, and singlet sectors have specific zero modes at zero chemical potential.

Number and chirality of zero modes match the index theorem predictions.

Zero modes persist if the index is odd, even at finite chemical potential.

Abstract

Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high density limit.