On the spectrum of spatially disordered systems
- 10 April 1981
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 14 (10), 1435-1443
- https://doi.org/10.1088/0022-3719/14/10/011
Abstract
The spectral density of states in systems where the atoms are completely randomly distributed in space with the concentration c is studied with the locator expansion of Matsubara and Toyozawa in the case of low concentration beta =c alpha -3<-1 is a characteristic length of the exponentially decreasing transfer integral. It is demonstrated that the nature of the spectrum in the vicinity of the level of an isolated atom is closely connected with the degree of localisation of the eigenstates. The limits of validity of the Lifshitz model, that predicts a minimum in the middle of the band, and of the Matsubara and Toyozawa approximation are established. The estimate beta c approximately=9.4*10-4 for the concentration beta c of the Anderson transition in this spatially disordered system is obtained by the application of the bond percolation theory to the Lifshitz model.Keywords
This publication has 11 references indexed in Scilit:
- Molecular model of impurity bands in semiconductorsJournal of Physics C: Solid State Physics, 1978
- Electron localization in disordered systems (the Anderson transition)Uspekhi Fizicheskih Nauk, 1978
- Localisation and conductivity studies on two-dimensional spatially disordered systemsJournal of Physics C: Solid State Physics, 1977
- The Hubbard Model for the Structurally Random SystemJournal of the Physics Society Japan, 1976
- On the electronic structure of an impurity band: a cumulant approachJournal of Physics C: Solid State Physics, 1974
- Density of states from moments. Application to the impurity bandJournal of Physics C: Solid State Physics, 1973
- Energy spectrum structure and quantum states of disordered condensed systemsUspekhi Fizicheskih Nauk, 1964
- Theory of Impurity Band Conduction in SemiconductorsProgress of Theoretical Physics, 1961
- Cluster Size in Random Mixtures and Percolation ProcessesPhysical Review B, 1961
- Absence of Diffusion in Certain Random LatticesPhysical Review B, 1958