Dirac returns: non-Abelian statistics of vortices with Dirac fermions

TL;DR

This paper demonstrates that vortices with local Dirac fermions in topological superconductors can exhibit non-Abelian statistics, challenging the previous belief that non-locality is necessary for such behavior.

Contribution

It shows that non-Abelian statistics can arise in vortices with local Dirac fermions, overturning the conventional understanding that non-locality is essential.

Findings

Vortices with local Dirac fermions obey non-Abelian statistics.

Challenges the belief that non-locality is required for non-Abelian anyons.

Expands the understanding of topological states in superconductors.

Abstract

Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising example of non-Abelian anyons. On the other hand, types C and DIII admit zero-energy Dirac fermions inside vortex cores. It has been long believed that an essential condition for the realization of non-Abelian statistics is non-locality of Dirac fermions made of two Majorana fermions trapped inside two well-separated vortices as in the case of type D. Contrary to this conventional wisdom, however, we show that vortices with local Dirac fermions also obey non-Abelian statistics.