Thermoelectrics of Interacting Nanosystems -- Exploiting Superselection instead of Time-Reversal Symmetry

TL;DR

This paper introduces a duality relation based on fermion-parity superselection that offers new insights into thermoelectric transport in interacting nanosystems, complementing traditional time-reversal symmetry approaches.

Contribution

It demonstrates how fermion-parity duality provides a novel framework for analyzing thermoelectric effects, especially in strongly interacting quantum dots, extending understanding beyond time-reversal symmetry constraints.

Findings

Fermion-parity duality relates thermoelectric coefficients to dual system properties.

Transport features are dominated by charge fluctuations in a dual attractive interaction system.

Duality simplifies analysis of nonlinear thermoelectric transport by connecting to equilibrium quantities.

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.