Topological Majorana and Dirac zero modes in superconducting vortex cores

TL;DR

This paper uses a flux insertion argument to identify conditions under which topologically non-trivial superconductors host protected zero modes in vortex cores, applicable even in disordered systems.

Contribution

It introduces a flux insertion-based approach to determine the existence of zero modes in vortex cores of various topological superconductors, including disordered cases.

Findings

Protected zero modes exist in certain topological superconductors

Conditions for zero mode protection depend on topological invariants

Method applies to disordered and symmetry-broken systems

Abstract

We provide an argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem and applies to disordered systems as well. It also provides a new way of understanding the zero modes in the vortex cores of a spinless $p_{x} + i p_{y}$ superconductor. Applying this approach to superconductors with and without time reversal and spin rotational symmetry, we predict the necessary and sufficient conditions for protected zero modes to exist in their vortices.