Band- andk-dependent self-energy effects in the unoccupied and occupied quasiparticle band structure of Cu

Abstract

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.

Resonant coherent three-photon photoemission from Cu(001)

“…2 usually does not describe experimental photoemission data quantitatively. 22,23 Because of this, we assume in the following that the calculation still describes the dispersion of the bands correctly but we make the absolute values for the critical points adjustable to known experimental data. Then we try to find k-conserving resonances in the band structure as a function of photon energy.…”

Higher Order Photoemission from Metal Surfaces

“…As is well known, a theoretical band structure such as shown in Figure 2.2 usually does not describe experimental photoemission data quantitatively [22,23]. Because of this, we assume in the following that the calculation still describes the dispersion [20] of Cu(001) with the proposed three-photon resonance for a photon energy near 3 eV.…”

“…In addition, the dispersing unoccupied spband can supply states near simultaneous one-photon resonance to the d-bands and the image potential, respectively. Adjusting the critical points of the bulk band structure, the d-bands are assumed to have X 5 at À1.99 eV and X 2 at À2.18 eV [22]. Due to spin-orbit coupling, the band with D 5 spatial symmetry is split into D 5 7 and D 5 6 bands with reported experimental splittings between 100 [24] and 170 meV [25] in the region of interest near the X point.…”

“…Due to spin-orbit coupling, the band with D 5 spatial symmetry is split into D 5 7 and D 5 6 bands with reported experimental splittings between 100 [24] and 170 meV [25] in the region of interest near the X point. For comparison, the theoretical value is 160 meV [22] at the X point. The upper sp-band is assumed with X 1 at 7.67 eV [22] and thus cannot be reached resonantly with the photon energies in our experiment.…”

“…For comparison, the theoretical value is 160 meV [22] at the X point. The upper sp-band is assumed with X 1 at 7.67 eV [22] and thus cannot be reached resonantly with the photon energies in our experiment. In Figure 2.3, we show the bands after shifting up the IP state by one photon energy, the sp-band by two photon energies, and the d-bands by three photon energies to the final-state energy.…”