Electronic transport in AlMn(Si) and AlCuFe quasicrystals: Breakdown of the semiclassical model

Abstract

The semiclassical Bloch–Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semiconductors. 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 breakdown 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, and 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 also confirm the validity of this anomalous quantum diffusion scheme. This provides us with an ab initio model of transport in approximants such as α-AlMnSi and AlCuFe 1/1 cubic approximant.