We focus 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-BÂĺuttiker method and focusing on effects of energy filtering. Then, we analyze the effects of many-body couplings between nanostructure 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.
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