M. Potthoff et W. Nolting, WEAK-COUPLING APPROACH TO THE SEMIINFINITE HUBBARD-MODEL - NONLOCALITY OF THE SELF-ENERGY, Zeitschrift fur Physik. B, Condensed matter, 104(2), 1997, pp. 265-277
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.