Modeling electronic transport in disordered mesoscopic systems

The aim of this thesis is to extend the theoretical framework of nonequilibrium electronic transport to incorporate quantum effects in disordered mesoscopic systems.Our theoretical methods are developed based on the diagrammatic perturbation technique formulated with the Keldysh nonequilibrium Green's functions.Given the real-space Hamiltonian of the transport system together with thermal reservoir parameters, we seek to compute the electronic structure and the charge current taking the various quantum effects into account.Following this methodology, the three most important and ubiquitous disordered mesoscopic effects are addressed, viz.weak localization, energy relaxation, and the Altshuler-Aronov (AA) effect, all of which give rise to corrections to the classical Drude description of electronic transport.Specialized theoretical methods are developed for the respective physical effects.For weak localization we develop a Cooperon-based diagrammatic scheme using the so-called dual fermion (DF) technique in order to take into account nonlocal interference processes which have been neglected in the prevailing coherent potential approximation (CPA).Numerical simulations have shown that, compared to CPA, our DF method yields more accurate results for transport properties of disordered quantum wires, and that in particular it is able to predict the negative magnetoresistance effect which is a signature of weak localization.The energy relaxation in disordered interacting wires is tackled with a self-consistent GW -CPA scheme.Using this computational method we study how the energy distribution of interacting electrons evolves under increasing interaction and external field strengths.In addition, the same computational scheme is also employed to simulate the Coulomb drag effect between parallel quantum wires.The interesting dependence of nonequilibrium drag current on the chemical potentials of reservoirs is discussed.As to the AA effect, the original diagrammatic formulation by Altshuler and Aronov is generalized to the real-space Keldysh formalism.Then, both theoretical and numerical diagram calculations show that for a disordered wire at nonequilibrium the AA effect leads to anomalous DOS corrections at its respective Fermi energies, and that the magnitudes of these (local) DOS corrections are position-dependent.The AA effect on transport properties is also analyzed, which shows nontrivial behaviors with respect to system sizes and bias voltages.i I gratefully thank my supervisor Prof. Hong Guo

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