Performance analysis of an interacting quantum dot thermoelectric setup

Abstract

In the absence of phonon contribution, a weakly coupled single orbital noninteracting quantum dot thermoelectric setup is known to operate reversibly as a Carnot engine. This reversible operation, however, occurs only in the ideal case of vanishing coupling to the contacts, wherein the transmission function is delta shaped, and under open-circuit conditions, where no electrical power is extracted. In this paper, we delve into the thermoelectric performance of quantum dot systems by analyzing the power output and efficiency directly evaluated from the nonequilibrium electric and energy currents across them. In the case of interacting quantum dots, the nonequilibrium currents in the limit of weak coupling to the contacts are evaluated using the Pauli master equation approach. The following fundamental aspects of the thermoelectric operation of a quantum dot setup are discussed in detail: (a) With a finite coupling to the contacts, a thermoelectric setup always operates irreversibly under open-circuit conditions, with a zero efficiency. (b) Operation at a peak efficiency close to the Carnot value is possible under a finite power operation. In the noninteracting single orbital case, the peak efficiency approaches the Carnot value as the coupling to the contacts becomes smaller. In the interacting case, this trend depends nontrivially on the interaction parameter U . (c) The evaluated trends of the maximum efficiency derived from the nonequilibrium currents deviate considerably from the conventional figure of merit zT -based results. Finally, we also analyze the interacting quantum dot setup for thermoelectric operation at maximum power output.

Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

“…Comparing the integrands in Eqs. (13,16), we see that J L contains an extra factor of energy compared to P gen . As a result, the transmission of electrons (µ = 1) with large enhances the heat current much more than it enhances the power output.…”

“…This theory assumes the quantum system to be relaxation-free, although decoherence is allowed as it does not change the structure of Eqs. (13)(14)(15)(16). Relaxation is discussed in Section XV.…”

“…Inspection of the integrand of Eq. (16) shows that it only gives positive contributions to the power output,…”

“…Thus, someone asking for a device with a ZT > 3, actually requires one with an efficiency of more than one third of Carnot efficiency. This is crucial, because the efficiency is a physical quantity in linear and nonlinear situations, while ZT is only meaningful in the linear-response regime [15][16][17][18][19][20] . Linear-response theory rarely fails for bulk semiconductors, even when T L and T R are very different.…”

Thermoelectric energy harvesting with quantum dots

“…[19]. Two-terminal geometries using mesoscopic conductors have been considered, notably using quantum dots [5,20,21,7,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. In the two-terminal geometry, both temperature and voltage bias are applied to the sample and the thermoelectric response is investigated.…”