Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes

Jackiw-Rebbi zero modes were first proposed in 1976 as topologically protected zero-energy states localized at domain walls in one-dimensional Dirac systems. They have attracted widespread attention in the field of topological quantum computing, as they serve as non-superconducting analogs of Majorana zero modes and support non-Abelian statistics in topological insulator systems. %In the braiding process of the Jackiw-Rebbi zero modes, their braiding properties are closely related to the strength of disorder. However, compared to their Majorana cousins, the braiding properties of Jackiw-Rebbi zero modes are vulnerable to the on-site energy deviation between the modes involved in the experiment. In this work, we propose to estimate the braiding properties of Jackiw-Rebbi zero-modes through measurements of transport signatures, which are readily measurable in current experiments. We find that the fidelity of braiding operation reaches unity when the current noise is fully suppressed, while this braiding fidelity monotonously decreases with the increasing of the current noise. Based on these transport signatures, we further discuss the correspondence between Majorana and Jackiw-Rebbi zero modes, highlighting their similarity in supporting non-Abelian statistics.