The semiclassical model of electron transport, which successfully describes the behavior of electrons in ordinary crystals, encounters serious difficulties in explaining the electronic properties of quasicrystals such as AlMn(Si) and AlCuFe. These materials, which have long-range order without translational invariance, exhibit anomalous electron transport behavior that cannot be explained within the framework of traditional concepts of band structure and electron scattering.
One of the key aspects indicating the failure of the semiclassical model is the anomalously low electrical conductivity of quasicrystals. Unlike metals, where electrical conductivity is due to the high concentration of free electrons and their relatively free movement in the crystal lattice, quasicrystals demonstrate electrical conductivity comparable to semiconductors or even dielectrics. This is due to the presence of a pseudogap in the electron density of states near the Fermi level, which significantly limits the number of charge carriers participating in conductivity.
The Bloch-Boltzmann theory, which combines classical and quantum approaches, is the cornerstone of the explanation of conductivity in solids, covering a wide range of materials, from metals to semiconductors. In this regard, systems where this theory fails are of considerable scientific interest. Quasicrystals and related complex metallic compounds appear to demonstrate a new mechanism for deviation from this theory, due to the specifics of electron propagation.
In this paper, we develop a theory of quantum transport that can be applied to both standard ballistic motion and nonstandard diffusion regimes. We demonstrate that phenomenological models developed on the basis of this theory adequately describe the anomalous conductivity observed in quasicrystals. First-principles calculations performed on approximating structures also confirm this model of anomalous quantum diffusion. This allows us to construct an ab initio transport model for approximations such as the 1/1 cubic approximations for α-AlMnSi and AlCuFe.
In addition, the temperature dependence of electrical conductivity in quasicrystals also contradicts the predictions of the semiclassical model. In ordinary metals, electrical conductivity decreases with increasing temperature due to increased scattering of electrons on phonons. However, in quasicrystals, the temperature dependence of electrical conductivity can be weak, non-monotonic, or even exhibit a semiconductor character, which indicates the predominance of other scattering mechanisms not taken into account in the semiclassical model.
Finally, the Hall effect, which in the semiclassical model allows one to determine the concentration and sign of charge carriers, manifests itself in an anomalous way in quasicrystals. The Hall coefficient can have unusual values or even change sign depending on the temperature and composition of the material, which indicates the complex nature of charge carriers and their interactions in the quasicrystalline structure.
Author: G. Trembley de Laissardiere, J.-P. Julien, D. Maillot
Institute: Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA; Neel Institute, National Center for Scientific Research and Joseph Fourier University, Building D, 25 avenue des Martyrs, P.O. Box 166, 38042 Grenoble, France