Quantum electronic transport: Linear and nonlinear conductance from the Keldysh approach

This is a review of the derivation of the Landauer conductance using the Keldysh non-equilibrium Green's function (NEGF) formalism and the equations-of-motion (EOM) method. We consider the elastic quantum electronic transport through a multi-lead device and treat the conductor in the mean-field approximation. This is suitable for open quantum dots as well as for several molecular systems where charging effects are negligible. The focus of the presentation is to unveil the technical issues involved in the formalism. We show how the Landauer conductance emerges as a linear term in the current-voltage I-V characteristics and indicate how to go beyond this regime. We address the connection of the NEGF approach to recent developments in molecular transport and discuss the problems that arise when one tries to include interaction effects beyond the mean field.