ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

Abstract

We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the nonequilibrium Keldysh formalism. The scheme is general and can be used with any quasiparticle self-energy, but for practical reasons, we mainly specialize to the so-called $GW$ self-energy, widely used to describe the quasiparticle band structures and spectroscopic properties of extended and low-dimensional systems. We restrict the $GW$ self-energy to a finite, central region containing the molecule, and we describe the leads by density functional theory (DFT). A minimal basis of maximally localized Wannier functions is applied both in the central $GW$ region and the leads. The importance of using a conserving, i.e., fully self-consistent, $GW$ self-energy is demonstrated both analytically and numerically. We introduce an effective spin-dependent interaction which automatically reduces self-interaction errors to all orders in the interaction. The scheme is applied to the Anderson model in and out of equilibrium. In equilibrium at zero temperature, we find that $GW$ describes the Kondo resonance fairly well for intermediate interaction strengths. Out of equilibrium, we demonstrate that the one-shot ${G}_{0}{W}_{0}$ approximation can produce severe errors, in particular, at high bias. Finally, we consider a benzene molecule between featureless leads. It is found that the molecule's highest occupied molecular orbital--lowest unoccupied molecular orbital gap as calculated in $GW$ is significantly reduced as the coupling to the leads is increased, reflecting the more efficient screening in the strongly coupled junction. For the $I\text{\ensuremath{-}}V$ characteristics of the junction, we find that Hartree--Fock (HF) and ${G}_{0}{W}_{0}[{G}_{\mathrm{HF}}]$ yield results closer to $GW$ than does DFT and ${G}_{0}{W}_{0}[{G}_{\mathrm{DFT}}]$. This is explained in terms of self-interaction effects and lifetime reduction due to electron-electron interactions.