Exact-exchange based quasiparticle energy calculations applied to (transition) metal nitrides: ScN, InN and more

The transition metal nitride ScN is emerging as a versatile material for promising technological applications, e.g. in spintronics and optoelectronics. Like for InN the electronic band structure of ScN -- a key quantity for devices -- has been difficult to access experimentally (due to growth related problems) and theoretically (due to strong self-interaction effects in the local-density approximation (LDA) to density functional theory (DFT)). Here we show that removing the self-interaction by applying DFT in the exact-exchange optimized effective potential approach (OEPx) correctly predicts ScN and InN to be semiconductors and not (semi)metals as found in the LDA. The OEPx ground state then provides a suitable starting point for quasiparticle energy calculations in the $G_0W_0$ approximation. Our OEPx+$G_0W_0$ gap supports recent experimental observations [1] that ScN has a much lower indirect band gap than previously thought [2]. We further show how a meaningful comparison to LDA based $G_0W_0$ calculations can be constructed that allows us to make contact with self-consistent $GW$ calculations.\\ $[$1$]$ A. A. Al-Brithen {\it et al.}, Phys.\ Rev.\ B {\bf 70}, 045303 (2004)\\ $[$2$]$ P. Rinke {\it et al.}, cond-mat/0611435