Chiral heat transport in driven quantum Hall and quantum spin Hall edge states

TL;DR

This paper investigates chiral heat transport along edge states in quantum Hall and quantum spin Hall systems under ac driving, revealing how heat propagates and thermalizes in these topological electronic systems.

Contribution

It introduces a model for heat transport in driven quantum Hall and quantum spin Hall edge states, analyzing the effects of ac voltage and reservoir coupling on local temperature and voltage profiles.

Findings

Heat propagates chirally along the edge in both regimes.

Electrons thermalize with the upstream reservoir.

Similar behavior occurs with stationary thermal reservoirs.

Abstract

We consider a model for an edge state of electronic systems in the quantum Hall regime with filling $\nu=1$ and in the quantum spin Hall regime. In both cases the system is in contact with two reservoirs by tunneling at point contacts. Both systems are locally driven by applying an ac voltage in one of the contacts. By weakly coupling them to a third reservoir, the transport of the generated heat is studied in two different ways: i) when the third reservoir acts as a thermometer the local temperature is sensed, and ii) when the third reservoir acts as a voltage probe the time-dependent local voltage is sensed. Our results indicate a chiral propagation of the heat along the edge in the quantum Hall case and in the quantum spin Hall case (if the injected electrons are spin polarized). We also show that a similar picture is obtained if instead of heating by ac driving the system is put in contact to a stationary reservoir at a higher temperature. In both cases the temperature profile shows that the electrons along the edge thermalize with the closest "upstream" reservoir.