Coherent Potential Approximation

A detailed report is given of the fundamental aspects of the coherent potential theory which serves as the best single-site approximation to the ensemble-averaged one-particle Green's function 〈G〉 for restricted model Hamiltonian of elementary excitations in certain random lattices. The concept of the approximation is illustrated in a unified framework of the general perturbation method. Applications of the theory to various model systems and realistic problems of practical interest are reviewed and a wide range of physical properties in these systems are discussed. Particular attention is paid to the advantageous feature of the approach, and the successful results obtained in the applications are described in comparison with the conclusions due to the previous methods. Limitations of the theory are stated with emphasis on the problems which are left open and several recent attempts to extend the applicability of the method are also mentioned.