Thermoelectric cooling of a finite reservoir coupled to a quantum dot

TL;DR

This paper explores how a finite electron reservoir coupled to a quantum dot can be cooled thermoelectrically, analyzing transport properties, heat flow, and system dynamics to inform experimental approaches.

Contribution

It introduces a phenomenological model combining rate equations and linear response theory to study thermoelectric cooling in quantum dot systems with finite reservoirs.

Findings

Finite reservoirs significantly affect Coulomb diamond features.

Heat can flow out of the finite reservoir near conductance lines.

Cooling efficiency depends on reservoir coupling and electron-phonon interactions.

Abstract

We investigate non-equilibrium transport of charge and heat through an interacting quantum dot coupled to a finite electron reservoir. Both the quantum dot and the finite reservoir are coupled to conventional electric contacts, i.e., infinite electron reservoirs, between which a bias voltage can be applied. We develop a phenomenological description of the system, combining a rate equation for transport through the quantum dot with standard linear response expressions for transport between the finite and infinite reservoirs. The finite reservoir is assumed to be in a quasi-equilibrium state with time-dependent chemical potential and temperature which we solve for self-consistently. We show that the finite reservoir can have a large impact on the stationary state transport properties, including a shift and broadening of the Coulomb diamond edges. We also demonstrate that there is a region around the conductance lines where a heat current flows out of the finite reservoir. Our results reveal the dependence of the temperature that can be reached by this thermoelectric cooling on the system parameters, in particular the coupling between the finite and infinite reservoirs and additional heat currents induced by electron-phonon couplings, and can thus serve as a guide to experiments on quantum dot-enabled thermoelectric cooling of finite electron reservoirs. Finally, we study the full dynamics of the system, with a particular focus on the timescales involved in the thermoelectric cooling.