Sub-diffusive electronic states in octagonal tiling

Abstract

We study the quantum diffusion of charge carriers in octagonal tilings. Our numerical results show a power law decay of the wave-packet spreading, $L(t)\propto t^{\beta }$, characteristic of critical states in quasicrystals at large time $t$. For many energies states are sub-diffusive, i.e. $\beta <0.5$, and thus conductivity increases when the amount of defects (static defects and/or temperature) increases.

4 pages, 1 figure