Quantized Thermal Transport in the Fractional Quantum Hall Effect

TL;DR

This paper investigates thermal transport in the fractional quantum Hall effect using a Luttinger liquid model, revealing universal properties of thermal Hall conductance and potential for detecting upstream modes.

Contribution

It introduces a hydrodynamic model incorporating impurity scattering to analyze thermal transport and proposes thermal Hall conductance as a universal FQHE state indicator.

Findings

Thermal Hall conductance $K_H$ characterizes FQHE states universally.

Lorenz ratio violates Wiedemann-Franz law and can be negative.

Thermal transport can detect upstream propagating modes.

Abstract

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.