  We consider the steady-state thermoelectric transport through a vibrating
molecular quantum dot that is contacted to macroscopic leads. For moderate
electron-phonon interaction strength and comparable electronic and phononic
timescales, we investigate the impact of the formation of a local polaron on
the thermoelectric properties of the junction. We apply a variational
Lang-Firsov transformation and solve the equations of motion in the
Kadanoff-Baym formalism up to second order in the dot-lead coupling parameter.
We calculate the thermoelectric current and voltage for finite temperature
differences in the resonant and inelastic tunneling regimes. For a near
resonant dot level, the formation of a local polaron can boost the
thermoelectric effect because of the Franck-Condon blockade. The line shape of
the thermoelectric voltage signal becomes asymmetrical due to the varying
polaronic character of the dot state and in the nonlinear transport regime,
vibrational signatures arise.
