Charge and heat pumping in the Rice-Mele chain at finite temperature

TL;DR

This paper investigates charge and heat transport in the Rice-Mele chain at finite temperature, revealing that quantized topological pumping diminishes with temperature and is generally non-quantized at finite temperatures.

Contribution

It extends the analysis of topological charge pumping in the Rice-Mele model to finite temperatures and arbitrary fillings, providing analytical expressions for transported charge and heat.

Findings

Quantized charge pumping is lost at finite temperature.

Heat transport vanishes at zero temperature for certain circuits.

Transport decreases and vanishes as temperature approaches infinity.

Abstract

It is well known that quantized topological charge pumping takes place in the half filled Rice-Mele chain performing a closed cycle in parameter space. We extend previous studies to the case of charge and heat transport at arbitrary filling and temperature using the corresponding continuity equation with focus in the non-interacting case. The amount of charge and heat transported for any adiabatic time dependence of the parameters is given by a double integral of an analytical function. We find that quantized transport is lost except in trivial cases. In particular, for popular pumping circuits used which lead to quantized non-trivial charge transport at zero temperature, the heat transported in the cycle vanishes. For other pumping circuits, there is a heat transport among even and odd sites of the chain and the environment. As the temperature is increased, the transported charge and heat decrease and vanish at infinite temperature.