Effect of correlations on the localization properties of electrons and phonons in the long-wavelength limit

Abstract

The problem of Anderson localization in a spatially correlated disordered potential is formulated in the framework of the self-consistent theory of Vollhardt and Wolfle in conjunction with the self-consistent Born approximation for both tight-binding electrons and phonons. An approximation which is exact in the weak scattering limit is introduced for the coherent backscattering contribution to the irreducible two-particle vertex. For the case of electrons in three dimensions, the phase diagrams in the near-band-edge region are studied numerically for the binary alloys with short-range correlations and the idea of quasiuniversality is examined. For the case of phonons in one and two dimensions, the complete expressions for the localization length are obtained in the long-wavelength limit for both short-range and long-range correlations. The universality holds when the correlations are short range. In the presence of long-range correlations, different expressions for the localization length are obtained depending on the definition of the mean free path used in the theory. When the single-phonon mean free path is used, our results give the same asymptotic behaviors found previously by using the replica method. In one dimension, different asymptotic behavior appears when the transport mean free path is used. Discussions are given.