Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires

TL;DR

This paper explores fractional helical liquids in quantum wires with spin-orbit coupling, revealing fractional conductance and potential fractional Majorana states, advancing understanding of topological phases in 1D systems.

Contribution

It introduces the concept of fractional helical liquids in quantum wires with strong interactions, predicting fractional conductance and fractional Majorana states in proximity to superconductors.

Findings

Fractional quantized conductance plateaus predicted at low electron density.

Fractional Majorana bound states may be stabilized in proximity-coupled wires.

Disorder destabilizes the fractional phases.

Abstract

We study one dimensional wires with spin-orbit coupling. We show that in the presence of Zeeman field and strong electron-electron interaction a clean wire may form fractional helical liquid states with phenomenology similar to fractional quantum Hall liquids. Most notably, the wire's two terminal conductance is predicted to show fractional quantized conductance plateaus at low electron density. When the system is proximity-coupled to a superconductor, fractional Majorana bound states may be stabilized. We discuss how disorder destabilizes these fractional phases. Possible experimental realizations of similar states in double wire systems are discussed.