The Korringa-Kohn-Rostoker nonlocal coherent-potential approximation : a new method for calculating the electronic structure of disordered metallic systems
The limitations of the current 'first-principles' effective medium approach to calculating the electronic structure of disordered systems are described. These limitations can be addressed by a cluster theory, and only very recently the first satisfactory cluster theory, the nonlocal coherent potential approximation, has been developed within a tight-binding framework. However an approach based on KKR multiple scattering is needed in order to treat the problem from first principles for ab-initio calculations. In this thesis, these ideas are reformulated in terms of multiple scattering theory and the Korringa-Kohn-Rostoker non-local coherent potential approximation (KKR-NLCPA) is introduced for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used local mean-field KKR-CPA approach and includes nonlocal correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalisation of the KKR-CPA; it determines a site-to-site translationally-invariant effective medium, it is herglotz analytic, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density functional theory to give an ab-initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys and spin fluctuations in magnets amongst others are very promising. The method is illustrated by application to a simple one-dimensional model.