Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity

TL;DR

This paper demonstrates that the optical conductivity of quasicrystals can be explained by a model featuring massless Dirac fermions at certain points on the Fermi surface, revealing a topologically protected Weyl semimetal state.

Contribution

It introduces a simple model linking linear optical conductivity in quasicrystals to Dirac points, suggesting a topologically protected Weyl semimetal phase.

Findings

Linear conductivity is universal across Al-based icosahedral quasicrystals.

Absence of a Drude peak indicates a pseudogap at the Fermi surface.

Model predicts frequency-independent conductivity similar to graphene.

Abstract

The optical conductivity of quasicrystals is characterized by two features not seen in ordinary metallic systems. There is an absence of the Drude peak and the interband conductivity rises linearly from a very low value up to normal metallic levels over a wide range of frequencies. The absence of a Drude peak has been attributed to a pseudogap at the Fermi surface but a detailed explanation of the linear behavior has not been found. Here we show that the linear conductivity, which seems to be universal in all Al based icosahedral quasicrystal families, as well as their periodic approximants, follows from a simple model that assumes that the entire Fermi surface is gapped except at a finite set of Dirac points. There is no evidence of a semiconducting gap in any of the materials suggesting that the Dirac spectrum is massless, protected by topology leading to a Weyl semimetal. This model gives rise to a linear conductivity with only one parameter, the Fermi velocity. This picture suggests that decagonal quasicrystals should, like graphene, have a frequency independent conductivity, without a Drude peak. This is in accord with the experimental data as well.