Quantum Transport in Interacting Nanojunctions

Senz, Volkmar

健仁 上出

Luca Magazzù, Milena Grifoni

We present a nonperturbative and formally exact approach for the charge transport in interacting nanojunctions based on a real-time path-integral formulation of the reduced system dynamics. For reservoirs of noninteracting fermions, the exact trace over the leads' degrees of freedom results in the time-nonlocal Feynman-Vernon influence functional, a functional of the Grassmann-valued paths of the nanojunction, which induces correlations among the tunneling transitions in and out of the nanojunction. An expansion of the influence functional in terms of the number of tunneling transitions, and integration of the Grassmann variables between the tunneling times, allows us to obtain a still exact generalized master equation for the populations of the reduced density matrix in the occupation-number representation, as well as a formally exact expression for the current. By borrowing the nomenclature of the famous spin-boson model, we parametrize the two-state dynamics of each single-particle fermionic degree of freedom, in the occupation-number representation, in terms of blips and sojourns. We apply our formalism to the exactly solvable resonant level model (RLM) and to the single-impurity Anderson model (SIAM), the latter being a prototype system for studying strong correlations. For both systems, we demonstrate a hierarchical diagrammatic structure. While the hierarchy closes at the second tier for the RLM, this is not the case for the interacting SIAM. Upon inspection of the current kernel, known results from various perturbative and nonperturbative approximation schemes to quantum transport in the SIAM are recovered. Finally, a noncrossing approximation for the hierarchical kernel is developed, which enables us to systematically decrease temperature at each next level of the approximation. Analytical results for a simplified fourth-tier scheme are presented both in equilibrium and nonequilibrium and with an applied magnetic field.

David K. Ferry, Mihail Nedjalkov

H. Ness, L. K. Dash

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green function technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalized Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalized lead self-energies. The second set characterizes inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems.

David K. Ferry