Abstract
Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager's results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems -- deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems -- provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.
Highlights
To get a better grip on this nonequilibrium regime, the implications of time-reversal symmetry—often exploited in thermoelectrics—have been expressed in fluctuation-relations using the powerful tools of counting statistics [14,15,16,17,18]
By discussing a simple, yet relevant model of a nanoscale system, this paper aims to illustrate how the understanding of the role of Coulomb interaction in thermoelectric transport is advanced by the fermion-parity duality
We have shown that besides time-reversal symmetry, our duality involving fermion-parity superselection is a crucial general principle for understanding both the linear and nonlinear thermoelectric transport through strongly interacting electronic nanoscale systems
Summary
A thorough understanding of the thermoelectric operation of basic circuit elements such as quantum dots is important for future energy- and information-technologies, see, for example, the review articles [1,2] and references therein. Entropy 2017, 19, 668 since in strongly confined devices the coupled nonlinear transport of charge and heat is rich and correspondingly difficult to compute The reason for this is the energy-dependent transmission caused by the system itself, having discrete quantum states and strong Coulomb interaction, rather than by its coupling. Some of us have shown [29] that for any fermionic open system in the wide-band limit, a quite general duality exists between the modes and amplitudes of the time-evolution kernel This holds even when the reduced density operator of the open system obeys. Exploiting the new duality relation, the present paper revisits the thermoelectric response of a weakly coupled, but strongly interacting single-level quantum dot subject to both electrical and thermal biases, both in the linear and nonlinear regime. The manuscript contains an appendix which is substantial, not because the new derivations are complicated, but because the steps are nonstandard and deserve to be outlined
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