Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions

TL;DR

This paper studies how repulsive interactions affect topological superconducting phases in one-dimensional wires with spin-orbit coupling, revealing that interactions can expand the topological phase's parameter range and potentially enable Majorana fermions without magnetic fields.

Contribution

It demonstrates that repulsive interactions in topological superconducting wires can broaden the parameter space for Majorana fermions and may eliminate the need for magnetic fields.

Findings

Interactions reduce the bulk gap but expand the topological phase range.

The topological phase becomes more robust against disorder due to interactions.

Strong interactions may enable Majorana fermions without magnetic fields.

Abstract

Among the broad spectrum of systems predicted to exhibit topological superconductivity and Majorana fermions, one-dimensional wires with strong spin-orbit coupling provide one of the most promising experimental candidates. Here we investigate the fate of the topological superconducting phase in such wires when repulsive interactions are present. Using a combination of Density Matrix Renormalization Group, bosonization, and Hartree-Fock techniques, we demonstrate that while interactions degrade the bulk gap -consistent with recent results of Gangadharaiah et al.- they also greatly expand the parameter range over which the topological phase arises. In particular, we show that with interactions this phase can be accessed over a broader chemical potential window, thereby leading to greater immunity against disorder-induced chemical potential fluctuations in the wire. We also suggest that in certain wires strong interactions may allow Majorana fermions to be generated without requiring a magnetic field.