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

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 insulator. 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 breaking particle-hole symmetry. Such relation is strengthened since Jackiw-Rebbi zero-modes also exhibit non-Abelian braiding properties in the absence of superconductivity, and the symmetry-protected degeneracy of both Jackiw-Rebbi and Majorana zero-modes is proved to be equally important as the topological gap for their non-Abelian statistics.