We study inelastic electron tunneling through a molecular junction using the nonequilibrium Green’s function formalism. The effect of the mutual influence between the phonon and the electron subsystems on the electron tunneling process is considered within a general self-consistent scheme. Results of this calculation are compared to those obtained from the simpler Born approximation and the simplest perturbation theory approaches, and some shortcomings of the latter are pointed out. The self-consistent calculation allows also for evaluating other related quantities such as the power loss during electron conduction. Regarding the inelastic spectrum, two types of inelastic contributions are discussed. Features associated with real and virtual energy transfer to phonons are usually observed in the second derivative of the current I with respect to the voltage Φ when plotted against Φ. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative dI/dΦ and may show phonon sidebands. The dependence of the observed vibrationally induced lineshapes on the junction characteristics, and the linewidth associated with these features are also discussed.

Much current experimental research on transport in molecular junctions focuses on finite voltages, where substantial polarization-induced nonlinearities may result in technologically relevant device-type responses. Because molecules have strong polarization responses to changing charge state or external field, molecules isolated between electrodes can show strongly nonlinear current-voltage responses. For small applied voltages (up to ∼0.3 volt), weak interaction between transporting electrons and molecular vibrations provides the basis for inelastic electron tunneling spectroscopy. At higher voltages and for certain time scale regimes, strong coupling effects occur, including Coulomb blockade, negative differential resistance, dynamical switching and switching noise, current hysteresis, heating, and chemical reactions. We discuss a general picture for such phenomena that arise from charging, strong correlation, and polarization (electronic and vibrational) effects in the molecule and at the interface.

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 et al., Phys. Rev. B 69, 245302 (2004)].

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green’s functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.