Double-frequency Aharonov-Bohm effect and non-Abelian braiding property 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 fractional quantization, topologically protected zero-energy and possible non-Abelian statistics. We numerically investigate the Jackiw-Rebbi zero-mode in a quantum spin Hall insulator heterostructure and show that its zero-energy nature leads to a double-frequency Aharonov-Bohm effect in electronic transport. Such observation suggests that Majorana zero-mode could be viewed as a special case of Jackiw-Rebbi zero-mode. Moreover, similar to the Majorana zero-modes, Jackiw-Rebbi zero-modes also show non-Abelian braiding properties in a cross-shaped junction. However, such non-Abelian property can be destroyed by infinitesimal disorder breaking charge-conjugation symmetry, implying the presence of charge-conjugation symmetry is of equal importance as the topological gap in the topological quantum computation.