Thermoelectric efficiency of nanoscale devices in the linear regime

TL;DR

This paper analyzes the thermoelectric efficiency of nanoscale devices in the linear regime, providing analytic expressions and guidelines for optimizing energy conversion in quantum transport systems.

Contribution

It introduces analytic formulas for efficiency and thermoelectric parameters in nanoscale devices, focusing on Lorentzian, antiresonance, and Fano transmission functions.

Findings

Analytic expressions for charge and heat currents.

Guidelines for optimal thermoelectric efficiency.

Application to specific transmission functions like Lorentzian and Fano.

Abstract

We study quantum transport through two-terminal nanoscale devices in contact with two particle reservoirs at different temperatures and chemical potentials. We discuss the general expressions controlling the electric charge current, heat currents and the efficiency of energy transmutation in steady conditions in the linear regime. With focus in the parameter domain where the electron system acts as a power-generator, we elaborate workable expressions for optimal efficiency and thermoelectric pameters of nanoscale devices. The general concepts are set at work in the paradigmatic cases of Lorentzian resonances and antiresonances, and the encompassing Fano transmission function: the treatments are fully analytic, in terms of the trigamma functions and Bernoulli numbers. From the general curves here reported describing transport through the above model transmission functions, useful guidelines for optimal efficiency and thermopower can be inferred for engineering nanoscale devices in energy regions where they show similar transmission functions.