Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode

Yijia Wu; Haiwen Liu; Jie Liu; Hua Jiang; X C Xie

doi:10.1093/nsr/nwz189

Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode

Natl Sci Rev. 2020 Mar;7(3):572-578. doi: 10.1093/nsr/nwz189. Epub 2019 Nov 22.

Authors

Yijia Wu¹, Haiwen Liu², Jie Liu³, Hua Jiang⁴, X C Xie^{1

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Affiliations

¹ International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
² Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China.
³ Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, China.
⁴ School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
⁵ Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
⁶ CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China.

Abstract

Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractionalization, topologically protected zero-energy and possible non-Abelian statistics. We investigate these properties through the Jackiw-Rebbi zero-modes in quantum spin Hall insulators. Though charge fractionalization is not manifested, Jackiw-Rebbi zero-mode's zero-energy nature leads to a double-frequency Aharonov-Bohm effect, implying that it can be viewed as a special case of Majorana zero-mode without particle-hole symmetry. Such relation is strengthened for Jackiw-Rebbi zero-modes also exhibiting non-Abelian properties in the absence of superconductivity. Furthermore, in the condition that the degeneracy of Jackiw-Rebbi zero-modes is lifted, we demonstrate a novel non-Abelian braiding with continuously tunable fusion rule, which is a generalization of Majorana zero-modes' braiding properties.

Keywords: Aharanov-Bohm effect; Jackiw-Rebbi zero-mode; Majorana zero-mode; non-Abelian statistics.