Electronic structure of Co doped ZnO from the \textit{GW} perspective

In transition metal doped ZnO, the energy position of dopant 3$d$ states relative to host conduction and valence bands is crucial in determining the possibilty of long range ferromagnetism. Density functional theory based estimates of the energy position of Co-3$d$ states in Co doped ZnO differ substantially depending upon the choice of exchange-correlation functional. In this work we investigate many-body $GW$ corrections on top of DFT$+U$ and hybrid-DFT groundstates to provide a theoretical benchmark for the quasiparticle energies in wurtzite ZnO:Co. Both single shot $G_0W_0$ as well as partially self-consistent $GW_0$ wherein the wavefunctions are held fixed at the DFT level but the eigenvalues in G are iterated, are considered. The predicted energy position of the minority spin Co-$t_2$ states is 3.0-3.6 eV above the ZnO conduction band minimum which is closer to hybrid-DFT based estimates.