Effect of propagator renormalization on the band gap of insulating solids

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, $Phi$-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.