Breakdown of the 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 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.

8 pages, 8 figures

References in corpus (4)

• Quantum dynamics in two and three-dimensional quasiperiodic tilings
• Quantum transport of slow charge carriers in quasicrystals and correlated systems
• Energy levels and their correlations in quasicrystals
• Electronic transport in AlMn(Si) and AlCuFe quasicrystals: Break-down of the semiclassical model

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