Nonequilibrium transport with self-consistent renormalized contacts for a single-molecule nanodevice with electron-vibron interaction

Abstract

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions [Phys. Rev. B 84, 235428 (2011)]. We consider a model singlemolecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of electron density matrix, one interaction is diagonal in the central region and the second is offdiagonal in between the central region and the left electrode. We use a non-equilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and at the Hartree level for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasi-resonant regime, and for a wide range of parameters. They show that a non-equilibrium (i.e. bias dependent) static (i.e. energy independent) renormalisation is obtained for the nominal hopping matrix element between the left electrode and the central region. Such a renormalisation is highly non-linear and non-monotonic with the applied bias, however it always lead to a reduction of the current, and also affects the resonances in the conductance. Furthermore, we show that the relationship between the non-equilibrium charge susceptibility and dynamical conductance still holds even in the presence of crossing interaction. I. INTROThe theory of quantum transport in nano-scale devices has evolved rapidly over the past decade, as advances in experimental techniques have made it possible to probe transport properties (at different temperatures) down to the single-molecule scale. Furthermore simultaneous measurement of charge and heat transport through single molecules is now also possible 1 . The development of accurate theoretical methods for the description of quantum transport at the single-molecule level is essential for continued progress in a number of areas including molecular electronics, spintronics, and thermoelectrics.One of the longstanding problems of quantum charge transport is the establishment of a theoretical framework which allows for quantitatively accurate predictions of conductance from first principles. The need for methods going beyond the standard approach based on density functional theory combined with Landauer-like elastic scattering 2-12 has been clear for a number of years. It is only recently that more advanced methods to treat electronic interaction have appeared, for example those based on the many-body GW approximation 13-15 . Alternative frameworks to deal with the steady-state or timedependent transport are given by many-body perturbation theory based on the non-equilibrium (NE) Green's function (GF) formalism: in these approaches, the interactions and (initial) correlations are taken into account by using conserving approximations for the many-body self-energy [16][17][18][19][20][21][22][23][24][25] . Other kinds of interactions, e.g. electron-vibron coupling, also play an impo...