Layer Korringa-Kohn-Rostoker theory for close-spaced planes of atoms

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Abstract
Layer Korringa-Kohn-Rostoker (LKKR) approaches that calculate interlayer scattering using a plane-wave basis set cannot treat systems in which the interplanar spacing becomes small. This problem is most acute at band energies at which electronic lifetimes are long and the scattering strong. Taking a face-centered-cubic material as an example, solutions for the simplest of grain boundaries, the Σ5 tilt, requires the stacking together of (210) planes. The planar spacing for this system is too small to allow the conventional LKKR methods to be applied. We estimate needing over 500 plane waves to converge the interlayer scattering in this case. We describe here a solution to layer coupling that allows for this situation. The technique optimizes the sizes of the angular momentum and plane-wave basis sets and thus provides an important extension to LKKR schemes. The ideas developed can be easily applied to both low-energy electron diffraction and photoemission.