Topologically Induced Fermion Parity Flips in Superconductor Vortices

TL;DR

This paper explores how vortices in two-dimensional topological superconductors induce fermion parity flips in Majorana bound states, revealing a topological mechanism with potential implications for quantum computing.

Contribution

It demonstrates that vortex motion causes fermion parity changes in Majorana states across various topological systems, extending the understanding of parity pumps.

Findings

Fermion parity flips occur during vortex orbiting in topological superconductors.

Level crossings indicate parity changes in multiple topological systems.

The work links vortex-induced parity flips to higher-dimensional topological effects.

Abstract

A highlighting feature of Majorana bound states in two-dimensional topological superconductors is that they gain a phase factor of $\pi$ upon being orbited by a vortex. This work focuses on the vortex degree of freedom itself and demonstrates that the change in the Majorana state is accompanied by a fermion parity change within the vortex. Such a parity flip is interpreted as a higher dimensional analog of the fermion parity pump mechanism in superconducting wires as well as through general topological arguments. It is demonstrated in terms of level crossings in three different situations - in i) spin-triplet paired superconductors, and in proximity-induced superconducting systems involving ii) quantum spin Hall-ferromagnet hybrids and iii) Chern insulators.