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We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on nonequilibrium Green's functions to calculate both equilibrium and nonequilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.

International audienceClassical Hartree effects contribute substantially to the success of time-dependent density functional theory, especially in finite systems. Moreover, exchange-correlation contributions have an asymptotic Coulomb tail similar to the Hartree term, and turn out to be crucial in describing response properties of solids. In this work, we analyze in detail the role of the long-range part of the Coulomb potential in the dielectric response of finite and infinite systems, and elucidate its importance in distinguishing between optical and electron energy loss spectra (in the long wavelength limit q 0). We illustrate numerically and analytically how the imaginary part of the dielectric function and the loss function coincide for finite systems, and how they start to show differences as the distance between objects in an infinite array is decreased (which simulates the formation of a solid). We discuss calculations for the model case of a set of interacting and noninteracting beryllium atoms, as well as for various realistic systems, ranging from molecules to solids, and for complex systems, such as superlattices, nanotubes, nanowires, and nanoclusters

Using non-equilibrium Green's functions (NEGF), we calculate the current through an interacting region connected to non-interacting leads. The problem is reformulated in such a way that a Landauer-like term appears in the current as well as extra terms corresponding to non-equilibrium many-body effects. The interaction in the central region renormalizes not only the Green's functions but also the coupling at the contacts between the central region and the leads, allowing the total current to be further expressed as a generalized Landauer-like current formula. The general expression for the dynamical functional that renormalizes the contacts is provided. We analyze in detail under what circumstances Landauer-like approaches to the current, i.e. without contact renormalization, are valid for interacting electron-electron and/or electron-phonon systems. Numerical NEGF calculations are then performed for a model electron-phonon coupled system in order to validate our analytical approach. We show that the conductance for the off-resonant transport regime is adequately described by Landauer-like approach in the small-bias limit, while for the resonant regime the Landauer-like approach results depart from the exact results even at small finite bias. The validity of applying a Landauer-like approach to inelastic electron tunneling spectroscopy is also studied in detail.

Using non-equilibrium Green's functions, we derive a formula for the electron current through a lead-molecule-lead nanojunction where the interactions are not restricted to the central region, but are spread throughout the system, including the leads and the lead-molecule interfaces. The current expression consists of two sets of terms. The first set corresponds to a generalized Meir and Wingreen expression where the leads' self-energies are renormalized by the interactions crossing at the molecule-lead contacts. The second set corresponds to inelastic scattering events in the leads arising from any arbitrary interaction, including electron-electron and electron-phonon coupling, treated beyond mean-field approximations. Using different levels of approximation, we are able to recover well-known expressions for the current. We also analyse how practical calculations can be performed with our formalism by using the new concept of generalized embedding potentials.

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We study the effects of self-consistency and vertex corrections on different GW -based approximations for model systems of interacting electrons. For dealing with the most general case, we use the Keldysh time-loop contour formalism to evaluate the single-particle Green's functions. We provide the formal extension of Hedin's GW equations for the Green's function in the Keldysh formalism. We show an application of our formalism to the plasmon model of a core electron within the plasmon-pole approximation. We study in detail the effects of the diagrammatic perturbation expansion of the core-electron/plasmon coupling on the spectral functions in the so-called S model. The S model provides an exact solution at equilibrium for comparison with the diagrammatic expansion of the interaction. We show that self-consistency is essential in GW -based calculations to obtain the full spectral information. The second-order exchange diagram (i.e., a vertex correction) is also crucial to obtain the good spectral description of the plasmon satellites. We corroborate these results by considering conventional equilibrium GW -based calculations for the pure jellium model. We find that with no second-order vertex correction, one cannot obtain the full set of plasmon side-band resonances. We also discuss in detail the formal expression of the Dyson equations obtained for the time-ordered Green's function at zero and finite temperature from the Keldysh formalism and from conventional equilibrium many-body perturbation theory.

We study the effect of electron-vibron interactions on the inelastic transport properties of singlemolecule nanojunctions. We use the non-equilibrium Green's functions technique and a model Hamiltonian to calculate the effects of second-order diagrams (double-exchange DX and dressedphonon DPH diagrams) on the electron-vibration interaction and consider their effects across the full range of parameter space. The DX diagram, corresponding to a vertex correction, introduces an effective dynamical renormalization of the electron-vibron coupling in both the purely inelastic and the inelastic-resonant features of the IETS. The purely inelastic features correspond to an applied bias around the energy of a vibron, while the inelastic-resonant features correspond to peaks (resonance) in the conductance. The DPH diagram affects only the inelastic resonant features. We also discuss the circumstances in which the second-order diagrams may be approximated in the study of more complex model systems.