New layer method for the investigation of the electronic properties of two-dimensional periodic spatial structures: First applications to copper and aluminum

Abstract

A new formalism, the ``assembly of boundary-controlled monolayers'' (ABCM) method, has been developed for the calculation of the electronic structure of general three-dimensional physical systems exhibiting two-dimensional translational symmetry. By outlining the underlying basic concepts, it is shown that there is indeed no physically relevant restriction with regard to the form of the electronic potential nor to the number of layers of which the structure is composed. It is characteristic of the method that, in a first step, the properties of each monolayer of the structure considered are represented by a Green's operator; then, by application of the ``layer composition process'' to these operators, the entire structure is synthesized. Special interest is paid to the case of a crystal surface; it is shown that the ABCM method provides direct access to the complex band structure, and enables a natural classification of the electronic states of a half-crystal. A first numerical realization of the method was used to demonstrate its reliability in practical applications: Thusly have comprehensive investigations of the complex band structure and of the surface states and resonances of the Al(100), Al(110), and Cu(100) surfaces been performed. These calculations are not only high-accuracy refinements of previous work, but they also provide the missing continuation in regions of (k,E) space where no theoretical results have been obtained up to now, hereby yielding confirmation of some speculative interpretations of the experimental data.