E. I. Isaev

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions.

Theory of elastic phase transitions in metals at high pressures. Application to vanadium

Structural transformations in elementary metals under high pressures are considered using the Landau theory of phase transitions, in which the finite strain tensor components play the role of the order parameter. As an example, the phase transition in vanadium observed at a pressure of 69 GPa is analyzed. It is shown that it is a first-order elastic phase transition, which is close to a second-order transition.

Quasicrystals: Structure and properties

The structure and properties of quasicrystals are discussed. The short-and long-range atomic orders and the effect of these factors on the physical characteristics are considered. It is noted that investigations of the physical properties of quasicrystals at temperatures above room temperature should be performed. Promising applications are briefly outlined.

Ground-state properties of boron-doped diamond

Boron-doped diamond undergoes an insulator-metal or even a superconducting transition at some critical value of the dopant concentration. We study the equilibrium lattice parameter and bulk modulus of boron-doped diamond experimentally and in the framework of the density functional method for different levels of boron doping. We theoretically consider the possibility for the boron atoms to occupy both substitutional and interstitial positions and investigate their influence on the electronic structure of the material. The data suggest that boron softens the lattice, but softening due to substitutions of carbon with boron is much weaker than due to incorporation of boron into interstitial positions. Theoretical results obtained for substitution of carbon are in very good agreement with our experiment. We present a concentration dependence of the lattice parameter in boron-doped diamond, which can be used for to identify the levels of boron doping in future experiments.

Transport properties of Al-Si solid solutions: theory

Abstract Al–Si solid solutions synthesized under high pressure demonstrate striking physical properties, among which are enhanced superconductivity and peculiarities of low-temperature transport properties. To find the reason behind the latter we have performed a first-principles study of the electronic spectra and Fermi surfaces of Al–Si solid solutions. Two electronic topological transitions (ETTs), taking place in the system with increasing concentration of Si and pressure, have been revealed. Based on these data and the theory of ETTs for substitutional solid solutions we have calculated concentration dependencies of the resistivity, thermoelectric power and Hall constant. We show the results to be in quantitative agreement with experiment and to reproduce nicely the experimentally observed peculiarities.

Charge state and diffusion of hydrogen in the TiZrNi icosahedral alloy

The electronic structure of a hydrogen atom in a 1/1 approximant of the Ti-Zr-Ni icosahedral quasicrystal is investigated using ab initio methods based on the density functional theory. The charge state of the hydrogen atom in Ti36Zr32Ni13 with different types of tetrahedral pores, as well as the charge state of hydrogen at a ratio H/M ≈ 1.7, is determined. The hydrogen atom is found to be in a nearly neutral state. The coefficient of hydrogen diffusion in Ti36Zr32Ni13 is calculated.

Phonon spectra of L12 Ni3Al and B2 NiAl: Ab initio calculations

Phonon spectra and phonon density of states of intermetallic compounds Ni3Al and NiAl are studied using the ab initio linear-response method. The calculated phonon dispersion curves agree well with the inelastic neutron scattering data available for the crystals under study.

Electron localization and conductivity in quasicrystals at low temperatures

Abstract 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

Electronic transport in quasicrystals

Mobility of electrons in quasicrystals is considered in the framework of the fractional Fermi surface (FS) model, i.e., a multiconnected FS with many electron-hole pockets. The Mott law for the variable range hopping conductivity is obtained when intervalley scattering processes with small momentum transfer are taken into account. The transition to the power-law temperature dependence is discussed.

Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.”