Simulating time-dependent thermoelectric transport in quantum systems

TL;DR

This paper introduces a gauge-invariant theoretical framework and computational tools for simulating time-dependent thermoelectric transport in quantum systems, enabling analysis of heat and charge currents under dynamic conditions.

Contribution

It develops a novel gauge-invariant approach and extends existing wave-function methods to compute time-resolved heat currents in non-interacting quantum devices.

Findings

Validated the method with the Resonant Level Model results.

Demonstrated the simulation of thermal transport in a Quantum Point Contact.

Extended the t-Kwant library to include heat current calculations.

Abstract

We put forward a gauge-invariant theoretical framework for studying time-resolved thermoelectric transport in an arbitrary multiterminal electronic quantum system described by a non-interacting tight-binding model. The system is driven out of equilibrium by an external time-dependent electromagnetic field (switched on at time $t_0$) and possibly by static temperature or electrochemical potential biases applied (from the remote past) between the electronic reservoirs. Numerical simulations are conducted by extending to energy transport the wave-function approach developed by Gaury et al. and implemented in the t-Kwant library. We provide a module that allows us to compute the time-resolved heat currents and powers in addition to the (already implemented) charge currents, and thus to simulate dynamical thermoelectric transport through realistic devices, when electron-electron and electron-phonon interactions can be neglected. We apply our method to the non-interacting Resonant Level Model and verify that we recover the results reported in the literature for the time-resolved heat currents in the expected limits. Finally, we showcase the versatility of the library by simulating dynamical thermal transport in a Quantum Point Contact subjected to voltage pulses.