Weak-coupling approach to the semi-infinite Hubbard model: Non-locality of the self-energy

TL;DR

This paper investigates electron correlations at surfaces of a semi-infinite Hubbard model using second-order perturbation theory, highlighting the importance of non-local self-energy effects and their impact on surface electronic properties.

Contribution

It provides a real-space analysis of non-local self-energy effects at surfaces, demonstrating that local approximations are often sufficient for describing surface electronic structure.

Findings

Non-local self-energy decreases rapidly with distance between sites.

Surface local self-energy differs significantly from bulk, especially at the top layer.

Local approximation captures main features of surface spectra effectively.

Abstract

The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the electronic self-energy and the quasi-particle density of states (QDOS) in the bulk as well as in the vicinity of the surface. Within a real-space representation we fully account for the non-locality of the self-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. Compared 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 self-energy Sigma(ij)(E) decrease with increasing distance between the sites i and j. At the surface and for the three-dimensional bulk their decrease is faster than for a two-dimensional lattice. For all surfaces 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 recovered within the local approximation; taking into account the nearest-neighbor 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=0) system, quasi-particle damping results in a comparatively weak layer dependence of the QDOS generally.