Electronic transport in AlMn(Si) and AlCuFe quasicrystals: Break-down of the semiclassical model

TL;DR

This paper investigates the failure of the semiclassical Bloch-Boltzmann theory in quasicrystals, proposing a quantum transport model that explains their anomalous conductivity through ab-initio calculations.

Contribution

It introduces a new quantum transport theory applicable to quasicrystals, explaining their anomalous conductivity beyond traditional semiclassical models.

Findings

Phenomenological models match experimental conductivity data

Ab-initio calculations confirm anomalous quantum diffusion

Validates transport model in specific quasicrystal approximants

Abstract

The semi-classical Bloch-Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semi-conductors. Physical systems that are beyond the range of applicability of this theory are thus of fundamental interest. It appears that in quasicrystals and related complex metallic alloys, a new type of break-down of this theory operates. This phenomenon is related to the specific propagation of electrons. We develop a theory of quantum transport that applies to a normal ballistic law but also to these specific diffusion laws. As we show phenomenological models based on this theory describe correctly the anomalous conductivity in quasicrystals. Ab-initio calculations performed on approximants confirm also the validity of this anomalous quantum diffusion scheme. This provides us with an ab-initio model of transport in approximants such as alpha-AlMnSi and AlCuFe 1/1 cubic approximant.