Spectral properties of quasiperiodic superlattices and study of wave functions

Abstract

We report the study of the spectral properties of a quasiperiodic superlattice within a tight binding model. Numerical work is carried out using the transfer matrix method. An approximate analytical scheme is used to obtain expressions for the band gaps which explain all the features obtained numerically. Due to the fact that blocks of atoms are repeated quasiperiodically, the gaps are shown to vanish at specific energies. These states have much the same behaviour as the extended states but the amplitude is a quasiperiodic function of the site index. The total number of such extended states are estimated. Since it is known that other states in quasiperiodic systems are critical, these states are expected to exhibit a cross-over behaviour to the critical states as a function of the energy. Multifractal analysis of the quasiperiodic wave function show that it has the same signature as the extended wave function. We briefly comment on the cross-over behaviour.