Study of a mobility edge by a new perturbation theory
- 1 January 1978
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine Part B
- Vol. 37 (1) , 97-109
- https://doi.org/10.1080/13642817808245310
Abstract
The recursion method is applied to the Anderson model of disorder on a Cayley tree, i.e. a Bethe lattice. For small disorder an infinite order perturbation theory is applied which determines the distributions of parameters of a tight-binding linear chain which is exactly equivalent to the original system. The linear chain possesses localized states and extended states separated in energy by mobility edges. Analysis of the linear chain gives the position of the mobility edges, the nature of the singularity at the mobility edge, and the spatial extent of the localized states. A universal property of the Gaussian distribution is demonstrated and comments are made about a Cauchy distribution.Keywords
This publication has 14 references indexed in Scilit:
- The Anderson transition in silicon inversion layers: the origin of the random field and the effect of substrate biasProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1977
- Van Hove singularities and continued fraction coefficientsJournal de Physique Lettres, 1977
- Vibrational spectra and topological structure of tetrahedrally bonded amorphous semiconductorsPhilosophical Magazine, 1976
- Conductivity and mobility edges for two-dimensional disordered systemsJournal of Physics C: Solid State Physics, 1975
- Electronic structure based on the local atomic environment for tight-binding bands. IIJournal of Physics C: Solid State Physics, 1975
- The inverse of a linear operatorJournal of Physics A: Mathematical, Nuclear and General, 1974
- Self-consistent theory of localization. II. Localization near the band edgesJournal of Physics C: Solid State Physics, 1974
- The CPA and Anderson's model of cellular disorderPhilosophical Magazine, 1973
- Electrons in disordered structuresAdvances in Physics, 1967
- Absence of Diffusion in Certain Random LatticesPhysical Review B, 1958