CHARACTERISTIC WAVEFUNCTIONS OF ONE-DIMENSIONAL PERIODIC, QUASIPERIODIC AND RANDOM LATTICES

We obtain analytically a universal expression of the resonant energies for any one-dimensional (1D) models with the defects having symmetric internal structures. In a 1D periodic system with the on-site energy ε0=0 and a nearest-neighbor matrix element t0=1.0, two classes of the most interesting and simplest wavefunction behaviors are numerically obtained for the resonant energies around (a) 0, ±1, (b) [Formula: see text], respectively. We show that similar wavefunction behaviors can be found widely in many quasiperiodic and random systems where the delocalization phenomena are predicted. We suggest that the envelope of these wavefunctions can be generally used as a criterion of delocalization of electronic states in 1D random and quasiperiodic lattices.