Band- and k-dependent Self-Energy Effects in the Unoccupied and Occupied   Quasiparticle Band Structure of Cu
  Excited-state self-energy effects in the electronic structure of Cu, a prototype weakly correlated system containing states with different degrees of localization, are investigated with emphasis on the unoccupied states up to 40 eV above the Fermi level. The analysis employs the experimental quasiparticle states mapped under full control of the 3-dimensional wavevector k using very-low energy electron diffraction for the unoccupied states and photoemission for the occupied states. The self-energy corrections to the density-functional theory show a distinct band- and k-dependence. This is supported by quasiparticle GW calculations performed within the framework of linearized muffin-tin orbitals. Our results suggest however that the GW approximation may be less accurate in the localized d-bands of Cu with their short-range charge fluctuations. We identify a connection of the self-energy behavior with the spatial localization of the one-electron wavefunctions in the unit cell and with their behavior in the core region. Mechanisms of this connection are discussed based on the local-density picture and on the non-local exchange interaction with the valence states. 
V.N. Strocov, R. Claessen, F. Aryasetiawan, P. Blaha, P.O. Nilsson