Nonequilibrium thermoelectric transport through vibrating molecular quantum dots

We employ the functional renormalization group to study the effects of phonon-assisted tunneling on the nonequilibrium steady-state transport through a single level molecular quantum dot coupled to electronic leads. Within the framework of the spinless Anderson-Holstein model we focus on small to intermediate electron-phonon couplings and we explore the evolution from the adiabatic to the antiadiabatic limit and also from the low-temperature nonperturbative regime to the high-temperature perturbative one. We identify the phononic signatures in the bias-voltage dependence of the electrical current and the differential conductance. Considering a temperature gradient between the electronic leads we further investigate the interplay between the transport of charge and heat. Within the linear response regime we compare the temperature dependence of various thermoelectric coefficients to our earlier results obtained within the numerical renormalization group [Phys. Rev. B 96, 195156 (2017)]. Beyond the linear response regime in the context of thermoelectric generators we discuss the influence of molecular vibrations on the output power and the efficiency. We find that in the antiadiabatic limit the thermoelectric efficiency can be significantly enhanced