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

TL;DR

This paper demonstrates that in large octagonal approximants, non-Boltzmann contributions dominate electron transport, indicating a breakdown of traditional semi-classical conduction theory in quasicrystal-like structures.

Contribution

It provides numerical evidence that non-Boltzmann effects become dominant in large approximants, challenging the applicability of the Boltzmann theory for quasicrystals.

Findings

Non-Boltzmann contributions increase with approximant size.

Boltzmann terms decrease as unit cell size grows.

Transport properties are dominated by non-Boltzmann effects in large approximants.

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.