Coexistence of Localized and Extended States?
The localized electronic states of a simple model of a substitutional alloy are studied in the strong scattering or separated subband limit, using the tight-binding approximation. We observe states localized in small isolated clusters (as studied in percolation theory), and localized states decaying exponentially at large distances (as in the Anderson model), plus a class of small localized states which have not been discussed before. These last states occur at special energies in the middle of the band, yet are not physically isolated from the rest of the material, or from the extended states of the system.
KeywordsLocalize State Monte Carlo Sample Extended State Localize Excita Coherent Potential Approximation
Unable to display preview. Download preview PDF.
- 1.P. Dean, Proc. Royal Soc. (London) A, 254, 507 (1960). Sharp structure in the density of states had previously been observed by R. Landauer and J. C. Helland, J. Chem. Phys. 22, 1655 (1954). For a review of Monte Carlo calculations on alloys, and description of numerical techniques, see P. Dean, Rev. Mod. Phys. 44, 127 (1972).CrossRefGoogle Scholar
- 4.S. Kirkpatrick and T. P. Eggarter, to appear in Phys. Rev. B15.Google Scholar
- 7.S. Kirkpatrick, J. Non-Cryst. Solids 8, to appear as part of the proceedings, Int’l. Conf. on Liquid and Amorphous Semiconductors, Ann Arbor, Mich., 1971.Google Scholar
- 10.W. Kohn and J. T. Olson, Proceedings of Conf. on Electronic Properties of Ordered and Disordered Solids, Menton, France, 1971 (to appear).Google Scholar
- 11.M. H. Cohen, Proceedings, Tenth Int’l. Conf. on the Physics of Semiconductors, Cambridge, Mass., (1970) p. 645.Google Scholar
- 13.J. E. Gubernatis and P. L. Taylor, J. Phys. C4, L94 (1971).Google Scholar
- 15.J. T. Edwards and D. J. Thouless, J. Phys. C5, 807 (1972).Google Scholar
- 17.B. G. Nickel, Phys. Rev. B4, 4354 (1971); L. Schwartz and E. Siggia, Phys. Rev. B5, 383 (1972); and private communications.Google Scholar