Localization of electrons in ordered and disordered systems II. Bound bands

摘要: The question is: how should we describe the electron states in an assembly of `atoms' with overlapping bound-state wave functions? In a regular lattice, these are non-localized Bloch functions, forming band width B, say. Attention is focused on effects `cellular disorder', where statistical variation wl imposed energy bound state lth atom. A very simple version argument Anderson (1958) demonstrates his conclusion that all become localized if distributed uniformly over range somewhat greater than B. same applied to `equiconcentration binary alloy', takes values ±½W at random, shows propagating not destroyed, but splits into two narrower bands when W>>B. attempt confirm results, successive approximations for average Green function such system formulated, starting from propagator `ordered' and treating as perturbation. problem allowing correlations induced by repeated scatterings centre demonstrated type self-consistent t-matrix formula - nearly various other published formulae based upon principles developed. It turns out, however, none `medium propagator' methods leads splitting equiconcentration alloy. technique Matsubara et al. then sketched shown be entirely different principle. As theory, expanded powers overlap integral, which `perturbs' isolated atoms. By Fourier transformation, cumulant averaging, approximation, obtained rather complicated appear consistent criteria localization. This is, therefore, much best approach problem. consequences `structural' disorder also discussed, inconclusively.