### Abstract

The electronic trace-map for one-dimensional tight-binding binary chains with a constant nearest-neighbour interaction, whose atomic sequence is generated by the stacking rule C(1) = B, C(2) = A and C(n + 1) = C(n)^{p}C(n - 1)^{q}, have been examined. Here A and B are the two types of atoms with different site energies, and p and q are integers >0. The invariant of the map for q = 1 becomes a 'quasi-invariant' for q > 1. Vanishing of the quasi-invariant defines a manifold in the trace space, on which the wave function is essentially Bloch-like. The wavefunction is therefore extended at a dense subset of the entire spectrum. The study of cyclic orbits on this manifold suggests that an invariant exists only when q = 1 or q = p + 1. The bandwidth distribution has fractal structure only when q = 1. For q > 1, most of the states are extended, but are interspersed with localized states whose distribution appears to be fractal.

Original language | English |
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Pages (from-to) | 944-948 |

Number of pages | 5 |

Journal | Journal of Non-Crystalline Solids |

Volume | 156-158 |

Issue number | PART 2 |

DOIs | |

Publication status | Published - 1993 May 2 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Condensed Matter Physics
- Materials Chemistry

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## Cite this

*Journal of Non-Crystalline Solids*,

*156-158*(PART 2), 944-948. https://doi.org/10.1016/0022-3093(93)90102-4