We derive a generalized Drude formula for the optical conductivity of quasicrystals, assuming a diffusion law in a perfect quasicrystal $L\left(t\right)\propto t^{\beta }$, where $L\left(t\right)$ measures the spreading of a wave packet in a time $t$. We show that the so-called Drude peak in the optical conductivity, characteristic of metals, is strongly modified. If $\beta <1\mathrm{}/2$ the Drude peak is even replaced by a dip and the dc conductivity increases when disorder increases. An interpretation of the experimental results on icosahedral and decagonal phases is proposed.

• Received 2 December 1999

DOI:https://doi.org/10.1103/PhysRevLett.85.1290