Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.Comment: (16 pages, submitted to Phys. Rev. B

Electron transport through strongly interacting quantum dot coupled to normal metal and superconductor

We study the electron transport through the quantum dot coupled to the normal metal and BCS-like superconductor (N - QD - S) in the presence of the Kondo effect and Andreev scattering. The system is described by the single impurity Anderson model in the limit of strong on-dot interaction. We use recently proposed equation of motion technique for Keldysh nonequilibrium Green's function together with the modified slave boson approach to study the electron transport. We derive formula for the current which contains various tunneling processes and apply it to study the transport through the system. We find that the Andreev conductance is strongly suppressed and there is no zero-bias (Kondo) anomaly in the differential conductance. We discuss effects of the particle-hole asymmetry in the electrodes as well as the asymmetry in the couplings.Comment: Supercond. Sci. Technol. - accepted for publicatio

Time-Dependent Partition-Free Approach in Resonant Tunneling Systems

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in order to deal with the time-dependent current response of a resonant tunneling system. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No fictitious partitions are used. Besides the steady-state responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under what circumstances a steady-state current develops and compare our result with the one obtained in the partitioned scheme. We prove a Theorem of asymptotic Equivalence between the two schemes for arbitrary time-dependent disturbances. We also show that the steady-state current is independent of the history of the external perturbation (Memory Loss Theorem). In the so called wide-band limit an analytic result for the time-dependent current is obtained. In the interacting case we propose an exact non-equilibrium Green function approach based on Time Dependent Density Functional Theory. The equations are no more difficult than an ordinary Mean Field treatment. We show how the scattering-state scheme by Lang follows from our formulation. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is obtained. As an example the time-dependent current response is calculated in the Random Phase Approximation.Comment: final version, 18 pages, 9 figure