All-Electron GW Quasiparticle Band Structures of Group 14 Nitride Compounds

We have investigated the group 14 nitrides (M$_3$N$_4$) in the spinel phase ($\gamma$-M$_3$N$_4$ with M= C, Si, Ge and Sn) and $\beta$ phase ($\beta$-M$_3$N$_4$ with M= Si, Ge and Sn) using density functional theory with the local density approximation and the GW approximation. The Kohn-Sham energies of these systems have been first calculated within the framework of full-potential linearized augmented plane waves and then corrected using single-shot G$_0$W$_0$ calculations, which we have implemented in the modified version of the Elk full-potential LAPW code. Direct band gaps at the $\Gamma$ point have been found for spinel-type nitrides $\gamma$-M$_3$N$_4$ with M= Si, Ge and Sn. The corresponding GW-corrected band gaps agree with experiment. We have also found that the GW calculations with and without the plasmon-pole approximation give very similar results, even when the system contains semi-core $d$ electrons. These spinel-type nitrides are novel materials for potential optoelectronic applications because of their direct and tunable band gaps.