Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces

TL;DR

This paper proposes a novel method using a $$-shaped geometry to distinguish topologically distinct quantum Hall phases, especially non-Abelian states, by analyzing charge conductance and neutral modes.

Contribution

It introduces a coherent charge conductance technique in a $$-shaped geometry to identify neutral modes and differentiate between various quantum Hall phases, including non-Abelian states.

Findings

Neutral sector can be determined via charge conductance in a $$-shaped geometry.

Non-Abelian paired states and anti-Read-Rezayi states can be identified.

Charge behavior mimics Majorana modes in certain interfaces.

Abstract

Multiple topologically distinct quantum Hall phases can occur at the same Landau level filling factor. It is a major challenge to distinguish between these phases as they only differ by the neutral modes, which do not affect the charge conductance in conventional geometries. We show that the neutral sector can be determined with coherent charge conductance in a $\pi$-shaped geometry that interfaces three different filling factors. Specifically, non-Abelian paired states at a half-filled Landau level and the anti-Read-Rezayi state can be identified. Interestingly, for interfaces between paired states and Jain states, the electric current in the $\pi$ geometry behaves as if pairs of neutral Majoranas edge modes were charge modes of Jain states.