Accurate Quasiparticle Spectra from Self-Consistent<i>GW</i>Calculations with Vertex Corrections

Self-consistent $GW$ calculations, maintaining only the quasiparticle part of the Green's function $G$, are reported for a wide class of materials, including small gap semiconductors and large gap insulators. We show that the inclusion of the attractive electron-hole interaction via an effective nonlocal exchange correlation kernel is required to obtain accurate band gaps in the framework of self-consistent $GW$ calculations. If these are accounted for via vertex corrections in $W$, the band gaps are found to be within a few percent of the experimental values.