Fano-Josephson effect of Majorana bound states

TL;DR

This paper explores how Fano interference influences the Josephson effect in topological superconducting wires hosting Majorana zero modes, revealing phase transitions and conditions for normal Josephson junction behavior.

Contribution

It introduces a detailed analysis of Fano interference effects on Majorana-based Josephson junctions, highlighting conditions for phase transitions and the robustness of the normal Josephson current.

Findings

Fano interference induces Josephson phase transitions.

Appropriate couplings can suppress the fractional Josephson effect.

Majorana bound states lead to a robust 0-phase Josephson current.

Abstract

We investigate the Josephson current in a Fano-Josephson junction formed by the direct coupling between two topological superconducting wires and their indirect coupling via a quantum dot. It is found that when two Majorana zero modes respectively appear in the wires, the Fano interference causes abundant Josephson phase transition processes. What is notable is that in the presence of appropriate direct and indirect inter-wire couplings, the fractional Josephson effect disappears and then such a structure transforms into a $0$-phase normal Josephson junction. On the other hand, if finite coupling occurs between the Majorana bound states at the ends of each wire, the normal Josepshon current is robustly in the $0$ phase, weakly dependent on the Fano effect. We believe that the results in this work are helpful for describing the Fano-modified Josephson effect.