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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