Correlations between Majorana fermions through a superconductor

TL;DR

This paper investigates how Majorana fermions in a topological superconductor wire can hybridize through virtual quasiparticle states in the superconductor, leading to additional energy splitting beyond direct overlap effects.

Contribution

It introduces a new mechanism of Majorana fermion hybridization via elastic correlated tunneling through the superconductor, expanding understanding of Majorana state interactions.

Findings

Majorana fermions can hybridize via virtual quasiparticle states in the superconductor.

This hybridization causes an additional energy splitting between Majorana states.

The effect occurs both within the same wire and between different wires.

Abstract

We consider a model of ballistic quasi-one dimensional semiconducting wire with intrinsic spin-orbit interaction placed on the surface of a bulk s-wave superconductor (SC), in the presence of an external magnetic field. This setup has been shown to give rise to a topological superconducting state in the wire, characterized by a pair of Majorana-fermion (MF) bound states formed at the two ends of the wire. Here we demonstrate that, besides the well-known direct overlap-induced energy splitting, the two MF bound states may hybridize via elastic correlated tunneling processes through virtual quasiparticles states in the SC, giving rise to an additional energy splitting between MF states from the same as well as from different wires.