Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes

TL;DR

This paper theoretically uncovers a new form of non-Abelian statistics for Majorana zero modes protected by unitary symmetry, demonstrating potential for topological quantum computation and proposing experimental realization in optical lattices.

Contribution

It introduces the concept of unitary symmetry-protected non-Abelian statistics of Majorana modes and proposes an experimental setup to observe this phenomenon.

Findings

Braiding two vortices with N MZMs reduces to N independent sectors.

Demonstration of non-Abelian statistics in a spin-triplet topological superconductor.

Proposal for experimental realization in optical Raman lattices.

Abstract

Symmetry-protected topological superconductors (TSCs) can host multiple Majorana zero modes (MZMs) at their edges or vortex cores, while whether the Majorana braiding in such systems is non-Abelian in general remains an open question. Here we uncover in theory the unitary symmetry-protected non-Abelian statisitcs of MZMs and propose the experimental realization. We show that braiding two vortices with each hosting $N$ unitary symmetry-protected MZMs generically reduces to $N$ independent sectors, with each sector braiding two different Majorana modes. This renders the unitary symmetry-protected non-Abelian statistics. As a concrete example, we demonstrate the proposed non-Abelian statistics in a spin-triplet TSC which hosts two MZMs at each vortex and, interestingly, can be precisely mapped to a quantum anomalous Hall insulator. Thus the unitary symmetry-protected non-Abelian statistics can be verified in the latter insulating phase, with the application to realizing various topological quantum gates being studied. Finally, we propose a novel experimental scheme to realize the present study in an optical Raman lattice. Our work opens a new route for Majorana-based topological quantum computation.