Interference Effect of Majorana Fermions in a Spin-orbit Coupled Superconducting Wire

TL;DR

This paper investigates the interference effects of Majorana fermions in a spin-orbit coupled superconducting wire, revealing distinctive oscillation patterns in the density of states that can distinguish Majorana states from trivial states.

Contribution

It demonstrates that the density of states exhibits a parity-correlated $4\pi$ period oscillation for Majorana fermions, providing a practical method for their identification in experiments.

Findings

Density of states shows $4\pi$ oscillation for Majorana fermions.

Trivial states cause $2\pi$ oscillation in density of states.

The phenomena can be observed in short wires with gate control.

Abstract

Two majorana Fermions (MFs) localized at the two ends of the topological superconducting wire can interfere with each other and form the well known $4\pi$ Josephson current. We reveal that the density of states (Dos) for the electron part and the hole part also follow a parity correlated $4\pi$ period oscillation, while the Dos displays a $2\pi$ period oscillation when two trivial states interfere with each other. Thus, the period of Dos oscillation can be used to distinguish the MFs from the trivial localized states. Interestingly, such phenomena can be directly observed in a short superconducting wire controlled by the gate voltage. This largely simplifies the experimental setup. We suggest that the interference effects can be detected through two STM leads or two norm leads.