Gaps in the Spectra of Nonperiodic Systems

  • R. A. Barrio
  • Gerardo G. Naumis
  • Chumin Wang


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.


Wave Function Bipartite Network Mobility Edge Lower Frustration Inverse Participation Ratio 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • R. A. Barrio
    • 1
  • Gerardo G. Naumis
    • 1
  • Chumin Wang
    • 2
  1. 1.Instituto de FísicaUniversidad Nacional Autónoma de MéxicoMéxico, D. F.Mexico
  2. 2.Insituto de Invegtigaciones en MaterialesUniversidad Nacional Autónoma de MéxicoMéxico, D. F.Mexico

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