Unitary symmetry-protected non-Abelian statistics of Majorana modes

Hong, Jian-Song1,2; Poon, Ting-Fung Jeffrey1,2; Zhang, Long1,2; Liu, Xiong-Jun1,2,3,4,5

2022-01-05

10.1103/PhysRevB.105.024503

PHYSICAL REVIEW B   影响因子和分区

2469-9950

2469-9969

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 statistics of MZMs and propose the experimental realization. We show that braiding two vortices with each hosting N MZMs protected by commutative or noncommutative unitary symmetries generically reduces to N independent sectors, with each sector braiding two different Majorana modes. This renders the unitary symmetry-protected non-Abelian statistics. 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, and an experimental scheme of observation being proposed. This work suggests that there are a much broader range of symmetry-protected topological superconductors which host non-Abelian Majorana modes.

SCI ; EI

英语

通讯

National Key R&D Pro-gram of China[2021YFA1400900] ; National Nat-ural Science Foundation of China[11825401,11921005] ; Strategic Priority Research Program of Chinese Academy of Science[XDB28000000]

Materials Science ; Physics

Materials Science, Multidisciplinary ; Physics, Applied ; Physics, Condensed Matter

WOS:000742361000002

AMER PHYSICAL SOC

20220211445007

Statistics ; Superconducting materials ; Topology

Fluid Flow, General:631.1 ; Superconducting Materials:708.3 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4 ; Mathematical Statistics:922.2

PHYSICS

Web of Science

1.Peking Univ, Int Ctr Quantum Mat & Sch Phys, Beijing 100871, Peoples R China
2.Collaborat Innovat Ctr Quantum Matter, Beijing 100871, Peoples R China
3.Univ Chinese Acad Sci, CAS Ctr Excellence Topol Quantum Computat, Beijing 100190, Peoples R China
4.Southern Univ Sci & Technol, Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China

Hong, Jian-Song,Poon, Ting-Fung Jeffrey,Zhang, Long,et al. Unitary symmetry-protected non-Abelian statistics of Majorana modes[J]. PHYSICAL REVIEW B,2022,105(2).

Hong, Jian-Song,Poon, Ting-Fung Jeffrey,Zhang, Long,&Liu, Xiong-Jun.(2022).Unitary symmetry-protected non-Abelian statistics of Majorana modes.PHYSICAL REVIEW B,105(2).

Hong, Jian-Song,et al."Unitary symmetry-protected non-Abelian statistics of Majorana modes".PHYSICAL REVIEW B 105.2(2022).