Optical conductivity of the R-Cd quasicrystals and approximants

Recently, a new family of R-Cd binary icosahedral quasicrystals has been discovered [1]. Using optical reflectance spectroscopy, we have examined the quasicrystal GdCd₇.₉₈ and the approximants GdCd₆ and YCd₆. To explain the unique behaviour of electrons in a quasiperiodic lattice Mayou [2] created a model of electron transport due to anomalous diffusion of wave packets scattering from the quasiperiodic lattice. We have determined the optical conductivity of the above-mentioned materials from 7.5 meV to 5.5 eV and have used Mayou's model of optical conductivity for approximants and quasicrystals, σ₁ ∝ Re[ (1/(γ-iω))^(2β-1) ], to describe the low frequency behaviour. Despite the concern of Mayou of not being able to differentiate experimentally between normal metallic conductivity of ballistic electrons, β=1, and sub-ballistic conductivity, 1/2<β<1, we clearly see β≍3/4 in the intraband peak of the icosahedral approximants, which has not been observed before. Before this work, the only unambiguously Drude-like peak seen in any quasicrystal or their approximant occurred in the decagonal approximant γ-brass, which was fit with exactly β=1 [3]. However, unlike the approximants in our study, this sample of γ-brass was admittedly not a good approximant to a quasicrystal with its small lattice constant. In the GdCd₇.₉₈ quasicrystal, we observe low frequency behaviour that lacks a Drude peak but is not nearly perfectly linear as seen by others. In this case, the low frequency behaviour is qualitatively similar to the diffusive regime, 0<β<1/2, that is often seen. However, it is not adequately modelled by Mayou's generalized Drude model. With these results, unlike in previous optical conductivity studies, we have a striking difference in the low frequency conductivity that suggests that there is a difference in the physics of the optical conductivity of periodic and quasiperiodic lattices that needs to be explored.