Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion

TL;DR

This paper investigates electrical noise in fractional quantum Hall edges, revealing how it encodes the interplay between topological conductance and heat diffusion, especially in the ν=2/3 state.

Contribution

It introduces a model linking electrical noise to heat and charge transport in structured quantum Hall edges, highlighting measurable signatures of topological and thermal interplay.

Findings

Noise reflects the competition between ballistic charge and diffusive heat transport.

Distinct noise signatures can reveal upstream heat propagation.

Proposed setups enable experimental verification of the theoretical predictions.

Abstract

Electrical and thermal conductances of a quantum Hall bar reflect the topological structure of the incompressible bulk phase. Here we show that noise of electrical current carried through the edge evidences the interplay between these two topological observables. Transport through a structured edge is modeled by a voltage-biased line junction made up of two counter-propagating modes associated with respective filling factors. Specifically, we focus on the edge of a $\nu=2/3$ fractional quantum Hall state. Noise is generated at a point distinctly separated from the hot spot (where most of the Ohmic dissipation takes place) and reflects the competition between ballistically carried downstream current and diffusively carried heat (which can propagate also upstream). We propose specific setups where our predictions can be measured.