The optical conductivity of quasicrystals: evidence of a Weyl semimetal with 3D Dirac spectrum

The optical conductivity of quasicrystals is characterized by an absence of the Drude peak and a conductivity that rises linearly over a wide range of frequencies. The absence of the Drude peak has been attributed to a pseudogap at the Fermi surface but a detailed explanation of the linear behavior has not been found. This unusual behavior is seen in all icosahedral quasicrystal families and their periodic approximants. A simple model that assumes that the entire Fermi surface is gapped, with the exception at a finite set of Dirac points, fits the data. There is no evidence of a semiconducting gap in any of the materials suggesting that the massless Dirac spectrum is protected by topology leading to a Weyl semimetal. The model gives rise to a linear conductivity with only one parameter, the Fermi velocity. In accord with this picture decagonal quasicrystals should have a frequency independent conductivity, without a Drude peak. This is in accord with the experimental data as well.