HIERARCHICAL MOBILITY EDGES IN A CLASS OF ONE-DIMENSIONAL GENERALIZED FIBONACCI QUASI-LATTICES

The electronic energy spectrum and localization of the wave functions for a class of one-dimensional generalized Fibonacci quasilattices, whose substitution rules are A→ABB and B→A, have been studied. It has been found that the spectrum has a peculiar trifurcating structure and there are three kinds of wave functions in the spectrum: extended, localized, and intermediate states. The middle part of the central subband in every hierarchy of the spectra is always continuous and the corresponding wave functions are all extended while the rest of the wave functions are intermediate or localized, i.e., there exist mobility edges in the subband. For the whole spectra the mobility edges possess a type of hierarchical structure. © 1995 The American Physical Society.