Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes

• URL: http://arxiv.org/abs/2010.07844v2
• Date: Thu, 29 Oct 2020 16:28:34 GMT
• Title: Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Authors: Jian-Song Hong, Ting-Fung Jeffrey Poon, Long Zhang, Xiong-Jun Liu
• Abstract summary: We show that braiding two vortices with each hosting $N$ unitary symmetry-protected MZMs generically reduces to $N$ independent sectors. This renders the unitary symmetry-protected non-Abelian statistics. Our work opens a new route for Majorana-based topological quantum computation.
• Score: 2.0502751783060003
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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