Quantum diffusion of electrons in quasiperiodic and periodic approximant lattices in the rare earth-cadmium system

Abstract

Icosahedral quasicrystals are characterised by the absence of a distinct Drude peak in their low-frequency optical conductivity and the same is true of their crystalline approximants. We have measured the optical conductivity of i-GdCd, an icosahedral quasicrystal, and two approximants, GdCd and YCd. We find that there is a significant difference in the optical properties of these compounds. The approximants have a zero frequency peak, characteristic of a metal, whereas the quasicrystal has a striking minimum. This is the first example where the transport properties of a quasicrystal and its approximant differ in such a fundamental way. Using a generalised Drude model introduced by Mayou, we find that our data are well described by this model. It implies that the quantum diffusion of electron wave packets through the periodic and quasiperiodic lattices is responsible for these dramatic differences: in the approximants, the transport is superdiffusive, whereas the quasicrystals show subdiffusive motion of the electrons.

Keywords:

• Quasicrystal
• approximant
• quantum diffusion
• optical conductivity
• reflectivity
• Drude model

Acknowledgements

We would like to thank Jules Carbotte for helpful discussions. Work at McMaster University was supported by the Natural Sciences and Engineering Research Council of Canada and the Canadian Institute for Advanced Research.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research performed at the Ames Laboratory was supported by the US Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358. Work at UCSD was supported by [grant number ARO w911NF-13-1-0210].