Thermoelectric transport through vibrating molecular quantum dots

In this thesis, we study the effect of phonon-assisted tunneling on the thermoelectric transport through molecular devices within the framework of the spinless Anderson-Holstein model (SAHM). Molecularquantum dots can be considered as potential candidates for the inter-conversion of heat and electrical energy, with possible applications to cooling or energy harvesting at the nanoscale. From this perspective, studying the thermoelectric transport through such nanostructures is of crucial importance as it can help us to identify scenarios for which the thermoelectric efficiency can be enhanced. Furthermore, from a physical point of view it is interesting to investigate the interplay between the transport of charge and heat in the presence of inelastic scattering processes induced by vibrational effects. To capture the correlation effects in a satisfactory manner, we need sophisticated many-body methods. For this purpose we use the functional renormalization group (FRG), and the numerical renormalization group (NRG).While NRG provides an accurate non-perturbative description of physical properties in all parameter regimes and over the whole temperature range, the approximate (by truncation) FRG has the advantages of providing analytical insights into correlation physics, and also being applicable to non-equilibrium situations. Thereby we employ these two complementary methods to get a thorough understanding of the underlying physics of the SAHM