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 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.