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arXiv · 1009.0136

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

Guy Trambly De Laissardière·Christophe Oguey·Didier Mayou
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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 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.

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Guy Trambly De Laissardière, Christophe Oguey, Didier Mayou. 2010-09-01. Breakdown of the semi-classical conduction theory in approximants of the octagonal tiling. https://doi.org/10.1080/14786435.2010.523718

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