Majorana fermions in strongly interacting helical liquids

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 a helical liquid offers a mechanism that protects the very existence of Majorana edge states: whereas moderate interactions close the proximity gap that supports the edge states, in helical liquids the gap reopens 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.