Unpaired Majorana fermions in a layered topological superconductor

TL;DR

This paper investigates the conditions under which unpaired Majorana fermions can exist in layered topological superconductors, extending known criteria and considering effects of supercurrents and spin-orbit coupling.

Contribution

It extends Kitaev's Majorana chain model by adding conditions for supercurrent flow and analyzes the emergence of Majorana modes in layered superconductors.

Findings

Unpaired Majorana modes can exist in vortex lines with specific spin-orbit coupling.

A nonzero supercurrent is necessary for Majorana modes in certain configurations.

The paper discusses implications for vortex exchange statistics and experimental detection.

Abstract

We study the conditions for the existence of unpaired Majorana modes at the ends of vortex lines or the side edges of a layered topological superconductor. We show that the problem is mapped to that of a general Majorana chain and extend Kitaev's condition for the existence of its nontrivial phase by providing an additional condition when a supercurrent flows in the chain. Unpaired Majorana bound states may exist in a vortex line that threads the layers if the spin-orbit coupling has certain in-layer components but, interestingly, only if a nonzero supercurrent is maintained along the vortex. We discuss the exchange statistics of vortices in the presence of unpaired Majorana modes and comment on their experimental detection.