Electronic properties of the generalized Fibonacci lattices: energy spectrum and wavefunction

The authors study the electronic properties of a one-dimensional diagonal tight-binding model with potentials (V n ) arranged in generalized Fibonacci (GF) sequences. Using the negative-eigenvalue theorem, they calculate the density of states (DOS). The DOS and the V dependence of energy spectra for silver-mean (SM) and copper-mean (CM) series clearly show distinctive features. The relation of the energy spectral feature to the geometry of the underlying lattices is emphasized. Various states of the CM lattice are examined in detail by means of wavefunctions, resistances and a multifractal analysis. Critical states are characterized both by scaling transformations and by multifractal behaviours. They find that states with a strongly localized wavefunction under a given system size exhibit additional wavepackets with increasing system size. This shows that the localized behaviour of allowed states is a feature of the finite size of the system, and implies the absence of strongly localized states in a system of infinite size.