Theoretical approaches for nanoscale thermoelectric phenomena

TL;DR

This chapter reviews theoretical methods for analyzing nanoscale thermoelectric phenomena, focusing on quantum coherence, many-body interactions, and vibrational effects to understand and optimize thermoelectric performance.

Contribution

It provides a comprehensive overview of theoretical approaches for nanoscale thermoelectric analysis, including quantum, many-body, and vibrational effects, highlighting recent advancements.

Findings

Quantum coherence can enhance thermoelectric efficiency.

Many-body interactions can significantly alter thermoelectric properties.

Vibrational effects often reduce thermoelectric performance at room temperature.

Abstract

Focus of the chapter is on the theoretical approaches aimed to analyze thermoelectric properties at the nanoscale. We discuss several relevant theoretical approaches for different set-ups of nano-devices providing estimations of the thermoelectric parameters in the linear and non-linear regime, in particular the thermoelectric figure of merit and the power-efficiency trade-off. Moreover, we analyze the role of not only electronic, but also of vibrational degrees of freedom. First, nanoscale thermoelectric phenomena are considered in the quantum coherent regime using the Landauer-B\"uttiker method and focusing on effects of energy filtering. Then, we analyze the effects of many-body couplings between nano-structure degrees of freedom, such as electron-electron and electron-vibration interactions, which can strongly affect the thermoelectric conversion. In particular, we discuss the enhancement of the thermoelectric figure of merit in the Coulomb blockade regime for a quantum dot model starting from the master equation for charge state probabilities and the tunneling rates through the electrodes. Finally, within the non-equilibrium Green function formalism, we quantify the reduction of the thermoelectric performance in simple models of molecular junctions due to the effects of the electron-vibration coupling and phonon transport at room temperature.