Criticality in the crossed Andreev reflection of a quantum Hall edge

TL;DR

This paper develops a theory for non-local transport in quantum Hall edges coupled via a disordered superconductor, revealing a critical state with unique conductance properties that may mimic topological phases.

Contribution

It introduces a self-tuned critical point model for quantum Hall edge transport coupled to a disordered superconductor, highlighting novel conductance behavior.

Findings

Critical conductance is sample-specific with zero average.

Negative conductance values are stable against density changes.

System can appear topological despite being at a critical point.

Abstract

We develop a theory of the non-local transport of two counter-propagating $\nu = 1$ quantum Hall edges coupled via a narrow disordered superconductor. The system is self-tuned to the critical point between trivial and topological phases by the competition between tunneling processes with or without particle-hole conversion. The critical conductance is a random, sample-specific quantity with a zero average and unusual bias dependence. The negative values of conductance are relatively stable against variations of the carrier density, which may make the critical state to appear as a topological one.