Sub-diffusive electronic states in octagonal tiling

TL;DR

This paper investigates quantum diffusion in octagonal tilings, revealing sub-diffusive states with power-law wave-packet spreading, indicating increased conductivity with more defects, characteristic of critical quasicrystal states.

Contribution

It provides numerical evidence of sub-diffusive quantum states in octagonal tilings, highlighting their critical nature and unusual conductivity behavior.

Findings

Wave-packet spreading follows a power law, $L(t) \,\propto\, t^{\beta}$.

Most states are sub-diffusive with $\beta < 0.5$.

Conductivity increases with more static defects or higher temperature.

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.