Calculating Quantum Corrections to Electronic Transport in Disordered Nanostructures

Electronic transport in nanostructures shows strong dependencies on disorder and related quantum effects. The leading-order quantum corrections to the diffusive transport were identified as the weak-localization (WL) and the Altshuler-Aronov (AA) effects. An important issue is to develop a numerical method for computing these quantum corrections starting from the atomistic arrangement. To this end, a diagrammatic scheme based on nonequilibrium Green functions is put forward. We employ a nonlocal expansion technique to generate Cooperon diagrams in oder to capture WL. We implement this approach using a tight-binding Anderson model to simulate finite wires containing disorder. In WL regime, our computed conductance agrees well with the exact numerical solution, and the WL corrected resistance shows a nonlinear scaling versus the channel length. The WL induced negative magnetoresistance is also investigated. For AA correction, we extend the numerical GW method by dressing interaction vertices with diffusons, and we apply it to a finite Anderson-Hubbard model. Density of states anomalies are found at energies corresponding to bias voltages, and their size dependence is analyzed. The AA effect in nonlinear transport will also be reported.