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)pC(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.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Condensed Matter Physics
- Materials Chemistry