Long Range Coulomb Interaction and the Majorana Fermions

TL;DR

This paper studies how long-range Coulomb interactions influence topological superconductivity in a semiconductor wire, revealing that interactions can both shrink and enlarge the bulk gap depending on the magnetic field, aiding experimental observation.

Contribution

It provides a detailed analysis of Coulomb effects on topological phases in semiconductor wires, highlighting conditions where interactions enhance the bulk gap.

Findings

Coulomb interactions enlarge the topological phase region.

Interactions decrease the bulk gap near the phase transition.

Moderate magnetic fields see an enhanced bulk gap due to interactions.

Abstract

We have investigated the effects of long-range Coulomb interaction on the topological superconducting phase in a quasi-one dimensional semiconductor wire, proximity coupled to a s-wave using the exact diagonalization approach. We find that in accordance with previous studies the addition of Coulomb interaction results in an enlargement of the region of parameter values where topological superconductivity can be observed. However, we also find that although the interaction decreases the bulk gap for values of the magnetic field close to the phase transition point, for moderate magnetic fields away from the transition point, the interaction actually enhances the bulk gap which can be important for observation of topological superconductivity in this system.