Quantum bounds for power production, efficiency and thermal currents in thermoelectric nanostructures

Abstract

The wave-like nature of electrons leads to the existence of upper bounds on the thermoelectric response of nanostructured devices [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014); Phys. Rev. B 91, 115425 (2015)]. This fundamental result, not present in classical thermodynamics, was demonstrated exploiting a two-terminal device modelled by non-linear scattering theory. In the present paper, we consider non-linear quantum transport through the same type of device working both as thermal machine and as refrigerator. For both operations, starting from charge and heat current expressions, we provide analytic quantum bounds for power exchanged, thermal currents and device efficiencies. For this purpose, we adopt a thermoelectric system with a transmission function that corresponds to the quantum bound conditions, and show that we can recover the result with an alternative simple and transparent procedure.