A number conserving theory for topologically protected degeneracy in one-dimensional fermions

TL;DR

This paper develops a number-conserving theoretical framework for understanding topologically protected degeneracies in one-dimensional fermionic systems, emphasizing the role of local interactions and multiple channels in stabilizing Majorana modes.

Contribution

It introduces a bosonization-based model showing how local attractive interactions induce topological degeneracies in number-conserving quasi-1D superfluids, highlighting the importance of multiple channels.

Findings

Topological degeneracy is generated by local attractive interactions in multi-channel wires.

Quantum phase slips cause splitting of degeneracy, which decreases rapidly with the number of channels.

A large number of channels in the superconductor is essential for robust topological degeneracy.

Abstract

Semiconducting nanowires in proximity to superconductors are among promising candidates to search for Majorana fermions and topologically protected degeneracies which may ultimately be used as building blocks for topological quantum computers. The prediction of neutral Majorana fermions in the proximity-induced superconducting systems ignores number-conservation and thus leaves open the conceptual question of how a topological degeneracy that is robust to all local perturbations arises in a number-conserving system. In this work, we study how local attractive interactions generate a topological ground-state near-degeneracy in a quasi one-dimensional superfluid using bosonization of the fermions. The local attractive interactions opens a topological quasiparticle gap in the odd channel wires (with more than one channel) with end Majorana modes associated with a topological near-degeneracy. We explicitly study the robustness of the topological degeneracy to local perturbations and find that such local perturbations result in quantum phase slips which split of the topological degeneracy by an amount that does not decrease exponentially with the length of the wire, but still decreases rapidly if the number of channels is large. Therefore a bulk superconductor with a large number of channels is crucial for true topological degeneracy.