Korringa-Kohn-Rostoker nonlocal coherent-potential approximation

Abstract

We introduce the Korringa-Kohn-Rostocker nonlocal coherent-potential approximation ͑KKR-NLCPA͒ for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used 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 generalization of the KKR-CPA; it remains fully causal, 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. We illustrate the method by application to a simple one-dimensional model.

Theory of electronic transport in random alloys with short-range order: Korringa-Kohn-Rostoker nonlocal coherent potential approximation

“…This nonlocal CPA ͑NLCPA͒ theory is based on reciprocal space coarse-graining ideas introduced by Jarrell and Krishnamurthy, 42 originating from the dynamical cluster approximation ͑DCA͒. [43][44][45] The KKR-NLCPA 36,37 introduces an effective ͑translationally invariant͒ disorder term ␦G, which represents an effective propagator that accounts for all nonlocal scattering correlations on the electronic propagation due to disorder configurations and modifies the structure constants accordingly. By coarse-graining reciprocal space, one naturally introduces real space periodically repeating clusters.…”

Generalized inclusion of short-range ordering effects in the coherent potential approximation for complex-unit-cell materials

“…2 in reciprocal space, to correctly describe a finite cluster still representative for the whole bulk. Jarrell et al, 20 and subsequently Rowlands et al, 21 have shown how this can be accomplished through a partitioning of the original Brillouin zone domain of integration respectful of the underlying lattice symmetries. This is now coarse-grained into N c tiles around a discrete set of cluster momenta K n , which remain defined only up to an arbitrary phase factor, further discussed below 24 .…”

“…20 To this date the technique has been developed only for simple lattices with just one element per unit cell, in the case of Strukturberichte A h , A2, A1 geometries. 21 Furthermore, this coarse-graining of the Brillouin zone leads to discontinuities in the k -dependent integrand of Eq.12, whenever tile boundaries are crossed. 24,26 We note here however a recent suggestion to overcome such limitation through an additional averaging step over various phase choices, to reobtain a smooth k -dependence 18 .…”

“…Our approach to overcome such limitation picks up from the non-local extension of the method, 21 which we now briefly proceed to review.…”

“…14 Along the latter line of research, the non-local coherent potential approximation (NLCPA) has been recently developed based on insights provided by the Dynamical Cluster Approximation (DCA). 20 The method has shown its capability to describe SRO effects both within model Hamiltonian studies 18,[21][22][23][24] and when reimplemented within a completely self-consistent DFT-KKR framework for realistic systems. [25][26][27] This technique inherits however from its derivation a practical restriction to simple, one atom per unit cell lattices in Strukturberichte A h , A2 or A1 structures.…”