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

Abstract

It is well known that quantized topological charge pumping takes place in the half-filled Rice-Mele chainperforming a closed cycle in parameter space. We extend previous studies to the case of charge and heat transportat arbitrary filling and temperature using the corresponding continuity equation with focus on the noninteractingcase. The amount of charge or heat transported for any adiabatic time dependence of the parameters is givenby 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 nontrivial charge transport at zerotemperature, the heat transported in the cycle vanishes. For other pumping circuits, there is a heat transportamong even and odd sites of the chain and the environment. As the temperature is increased, the transportedcharge and heat decrease and vanish at infinite temperature.