GENERALIZED FIBONACCI LATTICES - DYNAMIC MAPS, ENERGY-SPECTRA AND WAVE-FUNCTIONS

Electronic properties of the generalized Fibonacci lattices are studied using the dynamical system technique, for which the off-diagonal tight-binding model is employed. The matrix and trace maps are obtained and investigated in a unified way. It is found that the energy spectra are Cantor-like and the wavefunctions are critical at many energies. For some systems, it is also shown that there are extended and localized wavefunctions. In addition, according to the degree of spatial extension or localization, two other types of wavefunctions are further distinguished, of which one has the tendency to be extended and the other has the tendency to be localized.