Breakdown of semi-classical conduction theory in approximants of the octagonal tiling

Abstract

We present numerical calculations of quantum transport in perfect octagonal approximants. These calculations include a Boltzmann (intra-band) contribution and a non-Boltzmann (inter-band) contribution. When the unit cell size of the approximant increases, the magnitude of the Boltzmann terms decreases, whereas the magnitude of the non-Boltzmann terms increases. This shows that, in large approximants, the non-Boltzmann contributions should dominate the transport properties of electrons. This confirms the breakdown of the Bloch–Boltzmann theory for understanding the transport properties in approximants with very large unit cells, and then in quasicrystals, as found in actual Al-based approximants.

Keywords:

• quasicrystals
• electronic transport
• quantum critical phenomena
• numerical simulation

Acknowledgements

The computations have been performed at the Service Informatique Recherche (S.I.R.), Université de Cergy-Pontoise. We thank Y. Costes, S.I.R., for computing assistance.