Gaps in the Spectra of Nonperiodic Systems
There are bipartite networks, in which the tight-binding spectrum for electrons presents a gap and localized states at the center of the band. This anomalous situation is analyzed by renormalizing one of the sublattices. Then, the states near the center of the band map into the lower band edge, and the localized states of interest become low-energy excitations. The existence of a gap between the ground state and the rest of the excitation spectra is then revealed to be due to frustration of perfectly coherent antibonding states. A detailed analysis of electrons in the random binary alloy in two dimensions and in the Penrose lattice is performed and compared with numerical calculations. Predictions from this theory agree with former numerical calculations and recent experimental findings in quasi-crystals. The same theoretical considerations might be applied to other cases, such as electron, phonon and magnetic excitation spectra in disordered solids.
KeywordsWave Function Bipartite Network Mobility Edge Lower Frustration Inverse Participation Ratio
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- 1.R. M. White, and T. H. Geballe, Long Range Order in Solids ( Academic Press, New York, 1979 ), p. 37.Google Scholar
- 2.M. F. Thorpe, in Excitations in Disordered Systems, edited by M. F. Thorpe, NATO Advanced Summer Institute Series, Vol. B78, ( Plenum, New York, 1982 ), p. 85.Google Scholar
- 5.J. M. Ziman, Models of Disorder (Cambridge University Press, 1979 ).Google Scholar
- 7.R. A. Barrio and C. Wang, J. Non-Cryst. Solids, 153 and 154, 375 (1993).Google Scholar
- D. N. Basov et al., Phys. Rev. Lett. 73, 1865 (1994).Google Scholar
- 10.M. H. Cohen, in Topological Disorder in Condensed Matter, edited by F. Yonezawa and T. Ninomiya, Springer Series in Solid State Science. 46, ( Springer-Verlag, New York, 1983 ), p. 122.Google Scholar
- 12.G. G. Naumis, R. A. Barrio and C. Wang, Proc. V int. Conf. on Quasicrystals, edited by C. Janot and R. Mosseri, ( World Scientific, Singapore, 1995 ), p. 431.Google Scholar