Topological Superconductor-Luttinger Liquid Junctions

TL;DR

This paper investigates the complex interactions at a T-junction between a topological superconductor and multiple Luttinger liquid channels, revealing a critical point that separates different scattering phases.

Contribution

It introduces a theoretical analysis of multi-channel Luttinger liquids coupled to Majorana modes, highlighting the emergence of a critical point with phase transition behavior.

Findings

Coupling multi-channel Luttinger liquids to Majorana modes causes frustration.

A critical point separates phases with different scattering behaviors.

The study advances understanding of topological superconductor junctions.

Abstract

Experimental evidence was recently obtained for topological superconductivity in spin-orbit coupled nano wires in a magnetic field, proximate to an s-wave superconductor. When only part of the wire contacts the superconductor, a localized Majorana mode exists at the junction between superconducting and normal parts of the nanowire. We consider here the case of a T-junction between the superconductor and two normal nanowires and also the case of a single wire with two (or more) partially filled bands in the normal part. We find that coupling this 2-channel Luttinger liquid to the single Majorana mode at the junction produces frustration, leading to a critical point separating phases with perfect Andreev scattering in one channel and perfect normal scattering in the other.