Robustness of Majorana Fermion induced Fractional Josephson Effect

TL;DR

This paper investigates the robustness of the fractional Josephson effect induced by Majorana fermions in realistic conditions with multiple fermionic states, showing it remains stable against coupling but is thermally suppressed.

Contribution

It demonstrates that the fractional Josephson effect persists despite strong coupling to other fermionic states, and analyzes its temperature dependence.

Findings

Absence of avoided energy crossing is robust against fermion coupling.

Fractional Josephson current is suppressed by thermal excitations.

Robustness holds even with arbitrary coupling strengths.

Abstract

It is shown in previous works that the coupling between two Majorana end states in superconducting quantum wires leads to fractional Josephson effect. However, in realistic experimental conditions, multiple bands of the wires are occupied and the Majorana end states are accompanied by other fermionic end states. This raises the question concerning the robustness of fractional Josephson effect in these situations. In this work, we show that the absence of the avoided energy crossing which gives rise to the fractional Josephson effect is robust, even when the Majorana fermions are coupled with arbitrary strengths to other fermions. Moreover, we calculate the temperature dependence of the fractional Josephson current and show that it is suppressed by thermal excitations to the other fermion bound states.