Dimer-Type Correlations and Band Crossings in Fibonacci Lattices

Abstract

Fibonacci system with both diagonal and off-diagonal disorder is mapped to a model with dimer type 'defects'. The model exhibit resonance transition corresponding to zero reflectance condition resulting in extended states in the system. These Bloch-type states reside on the line of inversion symetry of the energy spectrum and include states at the band crossings. The resonant states at the band crossings are related to the harmonics of the sine wave and have transmission coefficient equal to unity in quasiperiodic limit. This is in contrast to other resonant states where the transmission coeffiecient oscillates. An exact renormalization scheme confirms the fact that all resonant states are Bloch type waves as they are described by trivial attractors of the renormalization flow.