Universal pseudogap at Fermi energy in quasicrystals

Abstract

The electronic structures are calculated for several crystalline approximants of quasicrystals, AlCuLi and AlFe. The densities of states of these systems, and also of AIMn, suggest universality of the pseudogap at the Fermi energy in quasicrystals. The pseudogap satisfies a Hume-Rothery-type relation. The origin of the pseudogap is attributed to strong electron scattering by the lattice and the pseudogap causes an enhancement of cohesive energies. The characteristics of the states in the pseudogap and the electric resistivity are also discussed.PACS numbers: 65.40.Em, Since the discovery of quasicrystals, 1,2 theoretical investigations have focused mainly on their structures and phasons. Recently, the electronic properties have received much attention. The main interest is twofold: One is electronic transport or localization 3 " 5 and the other is the electronic mechanism of cohesion. 6 " 9 The diffraction pattern in quasicrystals is a sum of densely distributed 8 functions with crystallographically disallowed orientational symmetry. The anomalous diffraction pattern suggests that electrons in quasicrystals may be always and everywhere scattered strongly and the electron wave functions oscillate at all scales. This is the case in the one-dimensional Fibonacci lattice and the energy spectrum has gaps at almost every energy value. 3 In the two-dimensional case, the situation is not essentially changed. The energy spectrum of the twodimensional Penrose lattice is not smooth and most of the wave functions are critical, i.e., neither extended nor exponentially localized, and presumably with power-law decay. 4 Recently, high quality samples of stable quasicrystals with only small amounts of structural disorder and phasonlike defects were prepared, and their electric resistivity has been observed to be anomalously large. The electric resistivity in icosahedral AlCuLi is 6 times larger than in crystals, whereas the coefficient of the linear-temperature-dependent term of the specific heat is almost the same in two phases. 10 The electric resistivity of stable icosahedral AlCuRu has been observed to increase drastically, up to 2500 p. Cl cm or more at 4.2 K. 11 Therefore, we presume that electronic states in threedimensional quasicrystals are also critical. The anomalous diffraction pattern also suggests a strong electronlattice interaction and one may expect it has a crucial role for stability, such as in the Hume-Rothery or Peierls mechanism.In this paper, we present the electronic structures of crystalline approximants of realistic quasicrystals, AlCu-Li and AlFe, and discuss an electronic mechanism of cohesion and stability in realistic quasicrystals. Discussions are concerned with R-AlCuLi and Alj 4 Fe3, together with a-AlMn. 8 These are the crystalline approximants of typical quasicrystals: the stable icosahedral quasicrystal /-AlCuLi, the metastable icosahedral quasicrystal /-AlMnSi, and the metastable decagonal quasicrystal rf-AlFe. The crystalline phase of AlCuLi, i.e., /^-AlCuLi, reveals the typical structure of...

Electronic transport properties of quasicrystals

“…The L.M.T.O. results obtained by T. Fujiwara et al 56 , have confirmed that conductivity is very weak, and more concretely they get σDC ∼ 10 − 150(Ωcm) −1 for the α−AlMn(Si) phase (cubic lattice of Mackay icosahedra), which are anomalously low for metallic alloys. Their adjustable parameter is the scattering time τ for which they take standard values ∼ 10 −14,−15 s. In addition, their study of the decagonal phase d − AlCuCo agrees with the observed experimental anisotropy 18 between quasiperiodic and periodic directions(σDC ∼ 3000(Ωcm) −1 )for the quasiperiodic one, whereas for periodic (σDC ∼ 15000(Ωcm) −1 ) 57 .…”

“…From ab-initio calculations, the main features can be summarized by the existence of a deep pseudo-gap at the Fermi level 56 , and by an overall structure composed of a high concentration of bands with small dispersion (see figure figSTB2) (from ref. 57,58 ).…”

Quantum Transport of Slow Charge Carriers in Quasicrystals and Correlated Systems

“…Its total density of states is characterized [14] by a depletion near the Fermi energy E F , called pseudo-gap, which is observed experimentally. This is due to a Hume-Rothery mechanism [13,17] of band energy minimization that is strong in quasicrystals and their approximants [17]. Following the HumeRothery condition, it is expected that the most realistic value of E F in the actual α-phase corresponds to the minimum of the pseudo-gap, i.e.…”

Electron Localization and Conduction Mechanism of Icosahedral Quasicrystal Al-Pd-Ru

“…In addition, in views of the ab initio calculations [6,7], Tamura et al [8] have suggested strongly the creation of the virtual bond states or confinement of electrons, in the icosahedral clusters of TM atoms.…”