Inelastic scattering in nanoscale devices: One-shot current-conserving lowest-order approximation

Abstract

We describe a lowest-order approximation (LOA) to the nonequilibrium Green's function in the presence of interactions, and generally address how one can build $\ensuremath{\Phi}$-derivable one-shot approximations that satisfy the continuity equation. These approximations produce conserved electronic currents in one shot, requiring only one self-energy evaluation and, when applicable, they are as accurate as but much faster than the corresponding self-consistent approximation. This challenges the currently adopted view that heavy self-consistent calculations are necessary to get a satisfactory prediction of transport in nanoscale structures. We illustrate this with the case of electron-phonon scattering expressed within the self-consistent Born approximation (SCBA). In the LOA, the SCBA is further approximated by accounting only for one-phonon processes. LOA and SCBA are compared in one-dimensional wire where electrons interact with one optical phonon mode at room temperature. The LOA is found to provide a considerable reduction in computational time. Its limitations and extensions to include two-phonon processes are discussed.