Layer-by-layer low-energy electron diffraction and two-dimensional space group symmetry

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Abstract
The wave field of LEED in a 2D structure is symmetrised with respect to the structure's 2D space group (2D structure meaning diperiodic structure composed of one or several 2D periodic overlayers lying in register on the 2D periodic face of a crystal). Attention is focused on the layer-KKR (Korringa-Kohn-Rostoker) method, the wave representations of which are beams outside layers and partial waves inside layers. It is shown how the field of beams and the field of partial waves are made globally symmetric representations of the 2D space group, how the 2D translations of an individual layer (giving rise to local 2D von Laue diffraction conditions) divide the beams into independent bundles and, further, how local point-group symmetry arranges the bundles in 'irreducible sequences' and combines the partial waves into 'irreducible showers'. The theory is applied to three examples of overlayer structures on surfaces of face-centered cubic crystals, and the coding of the scheme of symmetrisation is discussed.