Phenomenological theory of heat transport in the fractional quantum Hall effect

TL;DR

This paper develops a phenomenological model for heat transport in fractional quantum Hall states, accounting for edge-bulk dissipation and predicting how thermal conductance varies with environmental coupling, aiding experimental interpretation.

Contribution

It introduces rate equations incorporating dissipation and edge-bulk interactions, providing a new framework to analyze thermal conductance in FQH states.

Findings

Thermal conductance depends on coupling strength to the thermal bath.

Strong coupling can lead to non-universal thermal conductance values.

Proposes an experimental setup to determine the sign of the thermal Hall conductance.

Abstract

The thermal Hall conductance is a universal and topological property which characterizes the fractional quantum Hall (FQH) state. The quantized value of the thermal Hall conductance has only recently been measured experimentally in integer quantum Hall (IQH) and FQH regimes, however, the existing setup is not able to detect if the thermal current is counter-propagating or co-propagating with the charge current. Furthermore, although there is experimental evidence for heat transfer between the edge modes and the bulk, the current theories do not take this dissipation effect in consideration. In this work we construct phenomenological rate equations for the heat currents which include equilibration processes between the edge modes and energy dissipation to an external thermal bath. Solving these equations in the limit where temperature bias is small, we compute the temperature profiles of the edge modes in a FQH state, from which we infer the two terminal thermal conductance of the state as a function of the coupling to the external bath. We show that the two terminal thermal conductance depends on the coupling strength, and can be non-universal when this coupling is very strong. Furthermore, we propose an experimental setup to examine this theory, which may also allow the determination of the sign of the thermal Hall conductance.