WEAK-COUPLING APPROACH TO THE SEMIINFINITE HUBBARD-MODEL - NONLOCALITY OF THE SELF-ENERGY

The Hubbard model on a semi-infinite three-dimensional lattice is cons idered to investigate electron-correlation effects at single-crystal s urfaces. The standard second-order perturbation theory in the interact ion U is used to calculate the electronic serf-energy and the quasi-pa rticle density of states (QDOS) in the bulk as well as in the vicinity of the surface. Within a real-space representation we fully account f or the non-locality of the serf-energy and examine the quality of the local approximation. Numerical results are presented and discussed for the three different low-index surfaces of the simple-cubic lattice. C ompared with the bulk significant differences can be found for the top -layer local self-energy, the imaginary part of which is energetically narrowed and has a reduced total weight. The non-local parts of the s elf-energy Sigma(ij)(E) decrease with increasing distance between the sites i and j. At the surface and far the three-dimensional bull-their decrease is faster than for a two-dimensional lattice. For all surfac es considered the effects of the non-local parts of the self-energy on the QDOS are found to be qualitatively the same as for the bulk: The weight of the quasi-particle resonance at the Fermi energy is lowered while the high-energy charge-excitation peaks become more pronounced. The main structures in the layer-dependent spectra are already recover ed within the focal approximation; taking into account the nearest-nei ghbor non-local parts turns out to be an excellent approximation. Due to the reduced coordination number for sites at the very surface, the top-layer QDOS is narrowed. Contrary to the the free (U = O) system, q uasi-particle damping results in a comparatively weak layer dependence of the QDOS generally. Pronounced surface effects that are related to surface Friedel oscillations show up as a fine structure within the r esonance around the Fermi level.