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Coherent potential approximation

About: Coherent potential approximation is a(n) research topic. Over the lifetime, 1930 publication(s) have been published within this topic receiving 36805 citation(s).

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Journal ArticleDOI
Paul Soven1
Abstract: We introduce a model of a substitutional alloy based on the concept of an effective or coherent potential which, when placed on every site of the alloy lattice, will simulate the electronic properties of the actual alloy. The coherent potential is necessarily a complex, energy-dependent quantity. We evaluate the model for the simple case of a one-dimensional alloy of $\ensuremath{\delta}$-function potentials. In order to provide a basis for comparison, as well as to see if a simpler scheme will suffice, we also calculate the spectrum of the same alloy using the average $t$-matrix approximation introduced by Beeby. On the basis of these results, we conclude that the average $t$-matrix approximation is not adequate for the description of an actual transition-metal alloy, while the coherent-potential picture will provide a more reasonable facsimile of the density of states in such an alloy.

1,744 citations

Journal ArticleDOI
Abstract: We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

1,192 citations

08 Mar 1995
Abstract: Quantum and Classical Waves.- Wave Scattering and the Coherent Potential Approximation.- Coherent Waves and Effective Media.- Diffusive Waves.- The Coherent Backscattering Effect.- Renormalized Diffusion.- The Scaling Theory of Localization.- Localized States and the Approach to Localization.- Localization Phenomena in Electronic Systems.- Mesoscopic Phenomena.

1,157 citations

Journal ArticleDOI
Abstract: A single-band model Hamiltonian is used to describe the electronic structure of a three-dimensional disordered binary alloy. Several common theories based on the single-site approximation in a multiple-scattering description are compared with exact results for this Hamiltonian. The coherent-potential theory of Soven and others is shown to be the best of these. Within the appropriate limits, it exhibits dilute-alloy, virtual-crystal, and well separated impurity-band behavior. Hubbard and Onodera's and Toyozawa's simple model density of states is employed in numerical calculations for a wide variety of concentrations and scattering-potential strengths. Explicit results are exhibited for the total density of states, the partial density contributed by each component, and such $k$-dependent properties as the Bloch-wave spectral density and the distribution function. These illustrate the general conclusions as well as the limitations of the quasiparticle description.

1,019 citations

01 Jul 1999
Abstract: 1. Essentials 1.1 Lorentz field 1.2 Clausius-Mossotti 1.3 Maxwell-Garnett 1.4 Bruggeman 1.5 Green's functions formulation 1.6 Summary and equivalence 2. Rigorous results 2.1 Introduction 2.2 Variational bounds 2.3 The concentric shell model 2.4 Spectral representation 2.5 Exactly soluble models 2.6 Reciprocity theorems 3. Dynamical theory 3.1 Introduction 3.2 Review 3.3 Macroscopic electrodynamics 3.4 Quasi-static regime 3.5 Displacement current and wave scattering 3.6 Mie scattering 3.7 Dynamical effective medium theory 3.8 Open problems 4. Limitations and beyond 4.1 Introductory remarks 4.2 Higher order terms 4.3 Percolation and criticality 4.4 Mie resonances 4.5 Multiple scattering 4.6 Competing interactions 4.7 Two body effective medium 4.8 Non-equilibrium 5. Related theories 5.1 Comments 5.2 Coherent potential approximation 5.3 Feynman diagrams 5.4 Localization of light 5.5 Classical theory of liquids 5.6 Density functional theories 5.7 Hubbard model, CPA and DFT 5.8 Summary 6. EMT applications 6.1 Introduction 6.2 Electric and magnetic properties 6.3 Optical properties 6.4 Granular high Tc superconductors 6.5 Hydrodynamics of suspensions 6.6 Mechanical properties 6.7 Nonlinear composites 6.8 Conclusions Appendices A.1 Stationery properties of UP and UR A.2 Evaluation of the last term in equation (2.18)

625 citations

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