QSGW calculations for point defects using a cut-and-paste approach for the self-energy

The self-energy in quasiparticle self-consistent GW (QSGW) approximation is usually represented in the basis set of density functional theory (DFT) eigenstates. The real space representation of the self-energy matrix obtained by expanding these eigenstates in an atom-centered basis set, such as linearized muffin-tin orbitals, has great advantages.  In this work, we show that the self-energy matrix is relatively short-ranged in the real space representation. This allows us to create a practical “cut-and-paste” method to construct the self-energy matrix of a large system from those of smaller subunits. This method can be used for the study of point-defects in a large supercell by constructing the real space matrix elements Σ_{RL,R’+TL’} in terms of the host and defect Σ, with the latter obtained from a much smaller defect containing cell. In the case of the As_Ga point-defect in GaAs, we show that the defect can already be represented in the 8 atom conventional fcc unit cell. We show that the band structure of a 64 atom defect supercell using the cut-and-paste method is in good agreement with the exact QSGW calculation for the same cell. The defect band position relative to the valence band maximum and dispersion are virtually identical.