Weak absence of diffusion in two dimensions in the weak-disorder limit

Abstract

Working within the single-electron picture of two-dimensional disordered systems in the crucial weak-disorder regime, the authors calculate the average two-particle Green function by summing the maximally crossed diagrams occurring in the approximation of Neal and Langer (1966) as developed by Abrahams and Ramakrishnan (1980) to show that Anderson's criterion for location is not satisfied, while there is only a weak absence of diffusion in the sense of Ishii (1973). Summation of ladder diagrams appearing in the Langer-Neal scheme gives an identical result in the small-disorder regime. They reach the same conclusion upon using the CPA to perform the required averaging. Recent mathematical results associate such a weak absence of diffusion with a singularly continuous spectrum.