Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor

TL;DR

This paper investigates how tunneling between vortices in a 2D p+ip superconductor causes Majorana zero modes to split, analyzing the effects of vortex interactions and superconducting fluctuations on energy degeneracy.

Contribution

It provides a detailed calculation of Majorana mode splitting due to intervortex tunneling using the Bogoliubov-de Gennes framework, including fluctuation effects.

Findings

Intervortex tunneling lifts Majorana zero mode degeneracy.

Superconducting fluctuations influence energy splitting.

Quantitative analysis of Majorana mode splitting in vortex systems.

Abstract

We consider a two-dimensional px+i py superconductor in the presence of multiple vortices, which support zero-energy Majorana fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.