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

Guy Trambly de Laissardière (1) , Christophe Oguey (1) , Didier Mayou (2)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
2 NEEL - OPTIMA - Optique et Matériaux

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 Boltzmann terms decreases, whereas the magnitude of non-Boltzmann terms increases. It shows that, in large approximants, the non-Boltzmann contributions should dominate the transport properties of electrons. This confirms the break-down of the Bloch-Boltzmann theory to understand the transport properties in approximants with very large unit cells, and then in quasicrystals, as found in actual Al-based approximants.

Mots clés: quantum diffusion; quasicrystals; octagonal tiling

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Guy Trambly de Laissardière, Christophe Oguey, Didier Mayou. Breakdown of the semi-classical conduction theory in approximants of the octagonal tiling. Philosophical Magazine, 2011, 91 (19-21), pp.2778-2786. ⟨10.1080/14786435.2010.523718⟩. ⟨hal-00512757⟩