Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states

TL;DR

This paper proposes a method to detect neutral edge modes in non-abelian quantum Hall states via thermal effects, using a series of two point contacts to infer neutral mode presence indirectly through charge noise measurements.

Contribution

It introduces a novel experimental setup with two point contacts to indirectly detect neutral modes through thermal effects and charge noise analysis in non-abelian quantum Hall states.

Findings

Charge noise at the second contact reveals neutral mode signatures.

Explicit formulas for thermal conductance and Lorentz number derived.

Method enables probing neutral modes without direct charge transport measurements.

Abstract

Non-abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasi-particle excitations obeying non-abelian statistics. In general, it is hard to probe the neutral modes in charge transport measurements and a thermal transport measurement seems to be inevitable. Here we propose a setup which can get around this problem by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a non-trivial signature of the presence of the neutral mode hence leading to its indirect detection. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.