Conductivity Of Quasicrystals Research Articles

On Modified Mott (Т–1/4) Law in the Conductivity of Quasicrystals

On Modified Mott (Т–1/4) Law in the Conductivity of Quasicrystals

Variable range hopping conductivity in quasicrystals

Variable range hopping conductivity in quasicrystals

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

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.

Electron localization and conductivity in quasicrystals at low temperatures

In the quasicrystalline case the electronic states at the Fermi level might be localized by the quasiperiodic potential itself, and there is only the formal analogy with Anderson type localization. A perfect quasicrystal at low temperatures exists at the “critical” state of metal–insulator transition. The power-law temperature dependence of electronic conductivity experimentally observed at T<5 K in i-Al-Pd-Re quasicrystal is obtained on “critical” wave functions. A “scenario” is proposed to explain the existence of the Mott law for the variable range hopping conductivity in quasicrystals.

Variable range hopping conductivity in quasicrystals

The Fermi surface of a perfect icosahedral quasicrystal at zero temperature consists of infinite number of electron-hole pockets, and therefore electronic states are localized. It is shown that in this state the Mott law for the variable range hopping conductivity is fulfilled at very low temperatures.

Variable-range hopping conductivity in quasicrystals

The electronic density of states (DOS) of 1D quasicrystals looks like that of a highly doped, p-type semiconductor: the Fermi level lies in the “impurity band”, which consists of localized states. At low temperatures, the conductivity of an electronic structure of this type is by variable-range hopping, as observed recently in i-Al–Pd–Re.

Breakdown of metallic conductivity in quasicrystals

In the icosahedral phases i-AlCuFe, i-AlPdMn and i-AlPdRe, the electrical conductivity is in the same range as for doped semiconductors. Strong similarities are observed between the direct and tunneling conductivity for the i-AlPdRe phase and for disordered systems on both sides of the metal–insulator (MI) transition.

Investigation of the intrinsic conductivity of Al-Cu-Fe quasicrystals in a zero-gap semiconductor model

Experimental proofs are obtained for the fact that the intrinsic conductivity of quasicrystals at low temperatures satisfies the T3/2 law.

Conductivity in quasicrystals via hierarchically variable-range hopping.

This paper takes the structure example of the AlPdMn quasicrystal, as determined from diffraction data, to derive useful self-similarity rules in consistency with composition and atomic valence constraints. These rules are then accounted for to explain inelastic-neutron-scattering data and thermal conductivity behavior. Basically, three regimes can be identified: extended low-energy phonon conductivity at low temperature following roughly a ${\mathit{T}}^{2}$ power law which transforms into a plateau of constant conductivity and, at higher temperature, a phonon assisted localized-state hopping mechanism with a ${\mathit{T}}^{3/2}$ power law and hierarchically distributed hopping distances. Electrical conductivity is also briefly analyzed along the same approach: accordingly, pure perfect quasicrystals should show a \ensuremath{\sigma}(T)\ensuremath{\propto}T behavior with deviation in ${\mathit{T}}^{0.5}$ at low temperature and in ${\mathit{T}}^{3/2}$ at high temperature coming from quasiperiodicity breaking. \textcopyright{} 1996 The American Physical Society.

Electronic structures in quasicrystals

The electronic structures are calculated for crystalline approximants of icosahedral quasicrystals, i-AlMn and i-AlCuLi. The density of states shows, commonly, a large depression, called a pseudogap, at the Fermi energy. The origin of the pseudogap is attributed to the electron-lattice interaction known as the Hume-Rothery mechanism. The density of states has also a structure of dense and fine spiky peaks. These may cause a large effective mass and may be one of the causes of abnormal transport phenomena and optical conductivity in quasicrystals.

特集・準結晶研究の発展 準結晶の電子構造

Abstract The electronic structures are calculated for crystalline approximants of icosahedral quasicrystals, i-AlMn and i-AlCuLi. The density of states shows, commonly, a large depression, called a pseudogap, at the Fermi energy. The origin of the pseudogap is attributed to the electron-lattice interaction known as the Hume-Rothery mechanism. The density of states has also a structure of dense and fine spiky peaks. These may cause a large effective mass and may be one of the causes of abnormal transport phenomena and optical conductivity in quasicrystals.

Perturbation theory for the electrical conductivity of quasiperiodic lattices.

Small energy denominators are argued not to cause difficulties for studies of the electrical conductivity of quasicrystals by the present author, using perturbation theory.