Unusual transport of excitations in quasiperiodic systems

Abstract

This paper presents a theoretical study of excitation transport in quasiperiodic systems whose eigenstates are critical. Numerical experiments for the one-dimensional tight-binding electron model with diagonal or off-diagonal Fibonacci modulation shown that the width of an initially localized wavepacket grows with time t in a power-law form ∼ t α (0<α<1), where α decreases with increasing the strength of quasiperiodic modulation. Of particular importance is that the power α is smaller or larger than the value α = sol1 2 of ordinary diffusion, depending upon the modulation strength. Besides the overall power-law behavior, the wavepacket dynamics involve many oscillatory components, which appear on all time and lenght scales in a self-similar fashion. These results are interpreted in terms of a renormalization group argument. The unusual transport phenomena shown here will be experimentally observable in Fibonacci semiconductor superlattices and quasicrystals.