Identify the topological superconducting order in a multi-band quantum wire

How to distinguish the zero-bias peak (ZBP) caused by the Majorana fermions from that by the other effects remains a challenge in detecting the topological order of a quantum wire. In this paper we propose to distinguish the topological superconducting phase from the topologically trivial phase by making a Josephson junction of the quantum wire attached to a side lead and then measuring the tunneling conductance through it as the phase difference across the junction $ϕ$ varies. Even if the ZBPs exist in both phases, we can identify the topological superconducting phase by a conductance peak at $ϕ=π$ and a nearby butterfly pattern.

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