Electronic conductivity of quasiperiodic approximants to decagonal aluminum

We present ab initio calculations of the electronic transport properties of a hypothetical monoatomic quasiperiodic system, decagonal aluminum (d-Al). Our aim is to study the influence of quasiperiodicity on the transport properties in an example system that is sufficiently realistic to represent real Al-based quasicrystals, but does not involve the additional complexity of a strong s,p–d hybridization, which determines the properties of many crystalline and quasicrystalline Al-transition metal alloys. The investigation of the transport properties of a series of quasiperiodic approximants with increasing linear dimensions is based on a calculation of the electronic eigenstates and the Kubo–Greenwood formula. A scaling analysis demonstrates small deviations of the eigenstates from extended behavior and shows that the transport properties belong to the sub-ballistic regime, with a scaling exponent of the electronic diffusivity of β∼0.66 that is somewhat larger than the quantum-diffusion limit (β=0.5), but distinctly smaller than for ballistic transport (β=1). In this sub-ballistic or over-diffusive regime the conductivity diverges in the thermodynamic limit, leading to metallic behavior.