Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Time-resolved Stark effect in rapidly varying fields

The cycle-averaged ac Stark effect associated with the ^[ A _]2Σ⁺v^′=2?^[ X _]2Π1/2v^′=0 two-photon absorption of NO at intensities between 7.7 and 15.2 TW cm^-2 has been characterized in real time through a synergic combination of bichromatic laser experiments and quantum-dynamics calculations. Measurements of the fluorescence emitted by the Rydberg ^[ A _]2Σ⁺v^′=2 level as a function of time between Stark and probe components of a bichromatic field exhibit a characteristic evolution in temporal peak structure with Stark-field intensity, which is interpreted in terms of a time-dependent Floquet analysis of the laser–matter interaction. The experimental observations are consistent with a dynamic Stark shift of Δε_s(ω₁,ω₂)≤0.23 eV of the optical transition at these intensities. Received: 18 January 2002 / Revised version: 6 March 2002 / Published online: 24 April 2002     

Lattice dynamics of a Pd0.90Rh0.10 crystal

Using inelastic neutron scattering, the phonon dispersion relations along the [100], [110] and [111] directions of a single crystal of Pd_0.90Rh_0.10 have been measured at 296K. From these results and phonon data for Pd, the phonon frequency shifts,(q), and the self-energy function, _j (q, _j (q)), have been determined for all branches. The frequency changes exhibit large wave vector and polarization dependence and behave non linearly with the increase concentration of Rh. The seventh neighbour tensor Born-von Kármán model has been fitted to the experimental phonon dispersion curves, and the force constants and elastic constants calculated. Correlations between the phonon anomalies, displayed in the slope ofT ₁ [110] branch, and the structure of the generalized susceptibility function, ₀(q), for Pd were discussed. From which follows the influence of the electron-electron interaction on theT ₁ [110] branch in Pd and Pd-Rh alloys.     

Electronic plus phonon-exchange mechanism for high-temperature superconductivity in layered crystals

A general mathematical formulation is developed for calculating the effective electron-electron interaction in layered crystals like YBa₂Cu₃O_7−δ, and for finding the resulting superconducting transition temperatureT _c in such systems within the framework of the conventional BCS pairing arising from various possible excitations in the medium. This differs considerably from the usual case of an effective three-dimensional homogeneous system, and should be relevant in the calculation ofT _c for the new class of high-T _c perovskites in which oxygen deficiencies in Cu-O layers and their distribution in the crystal play a crucial role. The explicit form of the effective interactionV _jj(q _t,ω) in a given layerj in the unit cell of the crystal is found to be determined not only by the true polarization functionπ _j(q _t,ω) of that layer, but also of other layers. The exchange of electronic excitations of a nearby insulating layer by carriers in a conducting layer thus becomes possible to get highT _c, with or without the usual phonon exchange.     

Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s-wave superconductor: E=(n+1/2)ω₀, with integral n. In class II the corresponding spectrum is E=nω₀ and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period ΔE=2ω₀ and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 9, 601–606 (10 November 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Observation of multiple superconducting gaps in the infrared reflectivity spectra of Ba(Fe<Subscript>0.9</Subscript>Co<Subscript>0.1</Subscript>)<Subscript>2</Subscript>As<Subscript>2</Subscript>

The results of infrared reflectivity measurements for the iron-based high-temperature superconductor Ba(Fe_0.9Co_0.1)₂As₂ are reported. The reflectivity is found to be close to unity at frequencies ω lower than 2Δ/h (2Δ is the superconducting gap and h is Planck’s constant). This is evidence for the s ^+/− or s ^+/+ symmetry of the superconducting order parameter in the studied compound. The infrared reflectivity spectra of Ba(Fe_0.9Co_0.1)₂As₂ manifest opening of several superconducting gaps at temperatures lower than critical T _c .     

Viscous dark cosmology with account of quantum effects

The analytic properties of the energy density ρ(t) of the cosmic fluid and the Hubble parameter H(t) are investigated close to the future singularity t=t _s assuming different forms for the equation of state. First, it is shown that the inclusion of quantum effects coming from the conformal anomaly modifies the singularity. Thereafter, we consider the effect coming from the bulk viscosity in the fluid. The viscosity tends to reduce the magnitude of t _s, but does not alter the singularity itself (the exponent). The main emphasis is laid on the simple case when the equation of state is p=w ρ, with w a constant.     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

KNΛ and KNΣ coupling constants from the Chiral Bag Model

The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤g _KNΛ≤−3.67 and 1.15 ≤g _KNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K ^*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants g _KNΛ and g _KNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings. Received: 17 August 1998 / Revised version: 22 December 1998     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

Relation between the reduced and unreduced hardness in nanomicroindentation tests

Hooke’s law is generalized to the case of arbitrary elastic or plastic indentation , where ɛ=q/E _r is the elastic strain, q is the average pressure over the contact area, E _r is the reduced elastic (Young’s) modulus, A is the projected area of the contact, w ₁ is the deformation in elastic indentation by a flat punch. On this basis a relation is obtained between the reduced hardness H and unreduced hardness H _h, which depends on the ratio w _s/w₁=m _s; w _s is the elastic deformation along the perimeter of the indent, and m _s≅0.78. It is shown that the correction ΔE _r to the elastic modulus E _r determined from the condition of linearity of the initial part of the unloading diagram, is ΔE _r=0.27(ΔP/P _m), where ΔP is the value used in the calculation of E _r for the length of the linear part of the diagram, reckoned from the maximum load P _m. It is shown that for metallic construction materials of medium hardness one has q=HM, where HM is the Meyer hardness. With increasing HM and increasing angle ϕ at the tip of the indenter, the ratio HM/q grows by an exponential law. Zh. Tekh. Fiz. 69, 42–48 (July 1999)     

Temperature dependence of surface impedance of Tl2Ba2CaCu2O8−δ and YBa2Cu3O6.95 single crystals measured in the microwave band

The real part R _s and the imaginary part X _s of the surface impedance Z _s=R _s+ iX _s of Tl₂Ba₂CaCu₂O_8−δ and YBa₂Cu₃O_6.95 single crystals have been measured with high precision at frequency ω/2π=9.4 GHz in the temperature range 0<T<140 K. In the Tl₂Ba₂CaCu₂O_8−δ crystal a linear temperature dependence R _s(T) has been found for T⩽50 K, and the magnetic field penetration depth λ(4.2 K)=X _s(4.2 K)/ω μ ₀≈3760 Å has been measured. Along with well known features of the function Z _s(T) in high-quality YBa₂Cu₃O_6.95 single crystals, such as the linearity of λ(T) and R _s(T) for T<T _c/3 and a maximum of R _s(T) at T∼T _c/2, the linearity range of λ(T) extends to T≃50 K, and this curve has a plateau in the range 60<T<85 K. The curve of R _s(T) in both the superconducting and normal states of YBa₂Cu₃O_6.95 is well described by a two-fluid model with the electron-phonon mechanism of quasiparticle relaxation. A formula describing the curve of λ ²(0)/λ ²(T) throughout the studied temperature range is also given. Zh. éksp. Teor. Fiz. 112, 2210–2222 (December 1997)     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Kinetics of formation of O2(1Σ) molecules in reactions involving excited O2(1Δ) oxygen molecules and I(2P1/2) iodine atoms

The results of our experimental study of the kinetics of formation of O₂(¹Σ) molecules in energy-exchange reactions O₂(¹Δ) + I(⁵ p,² P _1/2) and O₂(a,¹Δ) + O₂(a,¹Δ) are presented. The ratio of rate constants was obtained for these reactions (4800 ± 300). Setting the rate constant of the deactivation of O₂(¹Σ) molecules on CO₂ molecules at 4.1 · 10^–13 cm³/s, we evaluated the rate constants for these reactions at a temperature of approximately 330 K: (1.7 ± 0.2) · 10⁻¹³ and (3.6 ± 0.5) · 10⁻¹⁷ cm³/s, respectively.     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000