Resonant inelastic tunneling in molecular junctions

Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the second order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion (EOM) method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of many-particle operators present in the Hamiltonian. To zero order it is similar in particular cases (empty or filled bridge level) to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations (partially filled bridge level) is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current versus gate voltage plot when the source-drain voltage is small [Mitra, Phys. Rev. B 69, 245302 (2004)].