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We report on the optical conductivity of the structurally ordered icosahedral quasicrystal A17QPd2QRe IQ and the crystal A12Ru obtained from the reflectance measured over a wide frequency range. Our results show that both the crystal and the quasicrystal are semiconductors and have quite similar band structure.

We consider a simple model of a quasi-one-dimensional conductor in which two order parameters (OP) may coexist, i.e., the superconducting OP ∆ and the OP W that characterizes the amplitude of a chargedensity wave (CDW). In the mean field approximation we present equations for the matrix Green's functions G i k , where the first subscript i relates to the one of the two Fermi sheets and the other, k, operates in the Gor'kov-Nambu space. Using the solutions of these equations, we find stationary states for different values of the parameter describing the curvature of the Fermi surface, µ, which can be varied, e.g., by doping. It is established, in particular, that in the interval µ 1 < µ < µ 2 the self-consistency equations have a solution for coexisting OPs ∆ and W . However, this solution corresponds to a saddle point in the energy functional Φ(∆,W ), i.e., it is unstable. Stable states are: 1) the W-state, i.e., the state with the CDW (W = 0, ∆ = 0) at µ < µ 2 ; and 2) the S-state, i.e., the purely superconducting state (∆ = 0, W = 0) at µ 1 < µ. These states correspond to minima of Φ. At µ < µ 0 = (µ 1 + µ 2 )/2, the state 1) corresponds to a global minimum, and at µ 0 < µ, the state 2) has a lower energy, i.e., only the superconducting state survives at large µ. We study the dynamics of the variations δ∆ and δW from these states in the collisionless limit. It is characterized by two modes of oscillations, the fast and the slow one. The fast mode is analogous to damped oscillations in conventional superconductors. The frequency of slow modes depends on the curvature µ and is much smaller than 2∆/ħ if the coupling constants for superconductivity and CDW are close to each other. The considered model can be applied to high-T c superconductors where the parts of the Fermi surface near the "hot" spots may be regarded as the considered two Fermi sheets. We also discuss relation of the considered model to the simplest model for Fe-based pnictides.

We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous studies, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values |ε(π, 0) − EF | Γ, where EF is the Fermi energy, ε (π, 0) is the energy in the middle of the Brillouin zone edge, and Γ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a d-form factor Fermi surface deformation (Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a d-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the d-form factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.