Majorana Fermions in Strongly Interacting Helical Liquids

TL;DR

This paper explores how strong interactions in helical liquids can protect Majorana edge states by reopening the gap closed by moderate interactions, though gapless excitations near interfaces may affect their coherence.

Contribution

It demonstrates that in strongly interacting helical liquids, two-particle processes can restore the topological gap supporting Majorana states, a novel mechanism for their stability.

Findings

Moderate interactions close the topological gap supporting Majorana states.

Strong interactions induce a re-opening of the gap via two-particle processes.

Gapless fermionic excitations near interfaces may threaten Majorana coherence.

Abstract

Majorana fermions were proposed to occur at edges and interfaces of gapped one-dimensional systems where phases with different topological character meet due to an interplay of spin-orbit coupling, proximity-induced superconductivity and external magnetic fields. Here we investigate the effect of strong particle interactions, and show that the helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap which supports the edge states, in helical liquids the gap re-opens due to two-particle processes. However, gapless fermionic excitations occur at spatial proximity to the Majorana states at interfaces and may jeopardize their long term Majorana coherence.