Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions

TL;DR

This paper explores universal transport behaviors of Majorana fermions in superconductor-Luttinger liquid junctions, revealing how interactions influence conductance signatures and phase diagrams, with implications for detecting Majorana modes.

Contribution

It provides a comprehensive analysis of transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions, highlighting the effects of interactions on conductance and local density of states.

Findings

Universal low-energy transport governed by fixed points of reflection types

Strong repulsion removes Majorana conductance anomalies

Strong attraction can generate effective Majorana modes in trivial superconductors

Abstract

One of the most promising proposals for engineering topological superconductivity and Majorana fermions employs a spin-orbit coupled nanowire subjected to a magnetic field and proximate to an s-wave superconductor. When only part of the wire's length contacts to the superconductor, the remaining conducting portion serves as a natural lead that can be used to probe these Majorana modes via tunneling. The enhanced role of interactions in one dimension dictates that this configuration should be viewed as a superconductor-Luttinger liquid junction. We investigate such junctions between both helical and spinful Luttinger liquids, and topological as well as non-topological superconductors. We determine the phase diagram for each case and show that universal low-energy transport in these systems is governed by fixed points describing either perfect normal reflection or perfect Andreev reflection. In addition to capturing (in some instances) the familiar Majorana-mediated `zero-bias anomaly' in a new framework, we show that interactions yield dramatic consequences in certain regimes. Indeed, we establish that strong repulsion removes this conductance anomaly altogether while strong attraction produces dynamically generated effective Majorana modes even in a junction with a trivial superconductor. Interactions further lead to striking signatures in the local density of states and the line-shape of the conductance peak at finite voltage, and also are essential for establishing smoking-gun transport signatures of Majorana fermions in spinful Luttinger liquid junctions.