LOWEST-ORDER CORRECTIONS TO THE RPA POLARIZABILITY AND GW SELF-ENERGYOF A SEMICONDUCTING WIRE

We present the results of the addition of lowest-order vertex and self -consistency corrections to the RPA polarizability and the GW self-ene rgy for a semiconducting wire. It is found that, when starting from a local density approximation zeroth-order Green function and systematic ally including these corrections in both the polarizability and the se lf-energy, the correction to the non-self-consistent RPA-GW band gap i s small. Partial inclusion of these corrections leads to very differen t band gaps. This sheds new light on the puzzling question why non-sel f-consistent RPA-GW calculations of band gaps have been so very succes sful.