Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
| Autor: | Jian-Song Hong, Ting-Fung Jeffrey Poon, Long Zhang, Xiong-Jun Liu |
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| Rok vydání: | 2020 |
| Předmět: |
Superconductivity (cond-mat.supr-con)
Quantum Physics Condensed Matter - Mesoscale and Nanoscale Physics Statistical Mechanics (cond-mat.stat-mech) Condensed Matter - Superconductivity Mesoscale and Nanoscale Physics (cond-mat.mes-hall) FOS: Physical sciences Quantum Physics (quant-ph) Condensed Matter - Statistical Mechanics |
| DOI: | 10.48550/arxiv.2010.07844 |
| Popis: | 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. Comment: Main text (5+pages, 4 figures) and Supplementary Material (5+pages, 2 figures); Discussions and refs are updated |
| Databáze: | OpenAIRE |
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