Thermoelectric effect in a single molecular junction with a vibrational mode.

We investigate thermoelectric properties of single molecular junctions with electron-phonon interaction (EPI) based on a two-level model, and explore the possibility to obtain a thermoelectric device with high efficiency by engineering the energy level splitting in the molecular junction. We derive analytical expressions for electric conductance, thermopower and electronic thermal conductance in the linear response region within the dressed tunneling approximation of EPI. The effects of EPI and the level splitting in the molecule on thermoelectric properties are discussed. We show large value of thermoelectric figure of merit $Z T$ can be achieved for molecular junctions with strong EPI and relatively small energy level splitting between the bonding and antibonding states of the molecule.