Effect of interlayer single-particle hoppings on the superconducting transition temperature

It is well known that the superconducting transition temperature of high-T _c cuprates depends on the number of CuO₂ planes in the unit cell. The multilayer structure implies the possibility of interlayer hopping. Under the assumption that the interlayer hopping can be specified by the parameter t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))², the quasiparticle excitation spectrum for the bilayer cuprate in the superconducting state has been determined in the framework of the t − t′ − t″ − t _⊥ − J* model using the generalized mean-field approximation. It turns out that the interlayer hoppings does not create any additional mechanism of the Cooper paring and does not lead to an increase in T _c . The splitting of the upper Hubbard quasiparticle band attributed to the interlayer hoppings is manifested as two peaks in the doping dependence of the superconducting transition temperature at temperatures below the maximum T _c value for a single-layer cuprate. It has been found that antiferromagnetic interlayer correlations suppress the interlayer splitting. This probably leads to the common doping dependence of T _c for both single-layer and bilayer cuprates.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.     

The temperature dependence of the spectral width of singlet oxygen dimole emission

In the temperature range of T = 150–400 K, the dependence of spectral widths (cm⁻¹) on temperature, 182 + 0.38(±0.01)T and 217 + 0.48(±0.01)T, respectively, has been obtained for dimole emission of O₂(a, 0) + O₂(a, 0) → O₂(X, 1) + O₂(X, 0) + hν (λ = 703 nm) and O₂(a, 0) + O₂(a, 0) → O₂(X, 0) + O₂(X, 0) + hν (λ = 634 nm). It was shown that the ratio of dimole emission rate constants does not depend on temperature in the range of 150–400 K and is 1.06 ± 0.01.     

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)     

Vibrational spectrum of perfluoroethane

We have obtained IR absorption spectra of a C₂F₆ gas and a C₂F₆ cryosolution in Xe (T = 163 K) in the fundamental and overtone ranges. We have interpreted 28 bands of ¹²C¹²CF₆ and three bands of ¹³C¹²CF₆. In the spectral ranges that correspond to vibrations that are combinations with ν₁, ν₇, and ν₅, we observe multiplets, which we attribute to interactions of the type of Fermi resonances between the states ν₁(A _1g ) ∼ ν₆(A _1g ), ν₇(E _g ) ∼ ν₆ + ν₁₁(E _g ) ∼ 2ν₈(E _g ), ν₅(A _2u ) ∼ ν₈ + ν ₁₁(A _2u ). We reveal an anomalous intensity distribution in the spectrum of an asymmetric isotopologue. For the basic and isotopic configurations of perfluoroethane, we calculate the coefficients of shapes of vibrations and the intensities of absorption bands. We reveal that the behavior of the groups ¹²CF₃ and ¹³CF₃ is indifferent to the excitation of doubly degenerate stretching vibrations ν₇(E _g ) and ν₁₀(Eu).     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO<Subscript>2</Subscript> planes

The influence of interlayer hoppings on the superconducting transition temperature (T _c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))² and treated as a small perturbation for the states of two CuO₂ planes described by the t-t′-t″-J* model. In the generalized mean field approximation for d_{x² - y²}{d_{{x^2} - {y^2}}} symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO₂ layers provides an additional mechanism of Cooper pair formation or an increase in T _c. In the concentration dependence of T _c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T _c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Effect of hydrostatic compression on the indium-impurity-induced superconducting transition in Pb<Subscript>0.3</Subscript>Sn<Subscript>0.7</Subscript>Te

This paper reports on a study of the low-temperature conductivity and parameters of the superconducting state, namely, the critical temperature T _c and the second critical magnetic field H_c2, in the (Pb_0.3Sn_0.7)_0.95In_0.05Te solid solution under hydrostatic pressure P ≤ 9 kbar at T = 4.2 K. The choice of this material has been motivated by the fact that, according to earlier observations, it undergoes a superconducting transition at T _c ∼ 2.3 K, i.e., close to the maximum value T _c ∼ 2.9 K found for the (Pb _z Sn_{1 − z} )_0.95In_0.05Te solid solutions with a lead content z ∼ 0.15–0.25. It has been demonstrated that an increase in the pressure to P ≤ 9 kbar leads to a bell-shaped dependence T _c (P). The observed dependences are assigned to the effect of hydrostatic compression on the band structure of the solid solution and indicate a shift in the position of the Fermi level E _F with increasing pressure within the impurity band of the In quasi-local states. In this case, E _F passes through a maximum in the density of impurity states at P = 3–5 kbar.     

Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents

According to recent progresses in the finite size scaling theory of disordered systems, thermodynamic observables are not self-averaging at critical points when the disorder is relevant in the Harris criterion sense. This lack of self-averageness at criticality is directly related to the distribution of pseudo-critical temperatures T_c(i,L) over the ensemble of samples (i) of size L. In this paper, we apply this analysis to disordered Poland-Scheraga models with different loop exponents c, corresponding to marginal and relevant disorder. In all cases, we numerically obtain a Gaussian histogram of pseudo-critical temperatures T_c(i,L) with mean T_c^av(L) and width ΔT_c(L). For the marginal case c=1.5 corresponding to two-dimensional wetting, both the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay as L^-1/2, so the exponent is unchanged (ν_random=2=ν_pure) but disorder is relevant and leads to non self-averaging at criticality. For relevant disorder c=1.75, the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay with the same new exponent L^-1/νrandom (where ν_random ∼2.7 > 2 > ν_pure) and there is again no self-averaging at criticality. Finally for the value c=2.15, of interest in the context of DNA denaturation, the transition is first-order in the pure case. In the presence of disorder, the width ΔT_c(L) ∼L^-1/2 dominates over the shift [T_c(∞)-T_c^av(L)] ∼L^-1, i.e. there are two correlation length exponents ν=2 and that govern respectively the averaged/typical loop distribution.     

The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres

We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and inelastic Maxwell molecules (ν = 0). We develop a new asymptotic method for analyzing large deviations from Gaussian behavior for the velocity distribution function f(c). The framework is that of the spatially uniform nonlinear Boltzmann equation and special emphasis is put on the situation where the system is driven by white noise. Depending on the value of exponent ν, three different situations are reported. For ν < −2, the non-equilibrium steady state is a repelling fixed point of the dynamics. For ν > −2, it becomes an attractive fixed point, with velocity distributions f(c) having stretched exponential behavior at large c. The corresponding dominant behavior of f(c) is computed together with sub-leading corrections. In the marginally stable case ν = −2, the high energy tail of f(c) is of power law type and the associated exponents are calculated. Our analytical predictions are confronted with Monte Carlo simulations, with a remarkably good agreement.     

A new optical method for measuring the electron-phonon interaction parameter λ〈Ω2〉 using the spectral dependence of the relaxation rate

The spectral dependence of the electron-phonon relaxation rate γ_e−ph(ℏω) in metals is studied in pump-supercontinuum-probe (PSCP) experiments with femtosecond time resolution. Investigation of this spectral dependence, which exhibits a substantial slowing of the relaxation rate γ_e−ph(ℏω) near the Fermi level E _F , using the parametrization γ_e−ph(ℏω)∝λ〈Ω²〉 (ℏω−E _F )² makes it possible to determine directly the electron-phonon interaction parameter λ〈Ω²〉. The parameter λ〈Ω²〉 for YBa₂Cu₃O_7−δ is analyzed using this method. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 329–332 (10 September 1999)     

Ion transport in the anion-deficient nonstoichiometric phases La0.95(Ba1−x Srx)0.05F2.95 (0⩽x⩽1)

The fluoride-ion conductivity of the nonstoichiometric tysonite phases La_0.95(Ba_1−x Sr_x)_0.05Fe_2.95 (0⩽x⩽1) is investigated by impedance spectroscopy. Electrophysical measurements are performed in the frequency range 5–5×10⁵ Hz and temperature range 300–700 K. A discontinuity is observed in the temperature dependence of the conductivity at T _c=410–430 K. The behavior of the temperature dependence of the electrical conductivity is explained within a transport model taking into account the migration of fluoride ions between different inequivalent structural sites. The maximum value of the conductivity at room temperature (293 K) is 2×10⁻⁴ Ω⁻¹ cm⁻¹ for the solid solution La_0.95Sr_0.05F_2.95. The fluorine-ion conductivity in La_0.95(Ba_1−x Sr_x)_0.05F_2.95 single crystals is almost an order of magnitude larger than the value for the commercial solid electrolyte La_0.992Eu_0.008F_2.992 (a fluorine-selective membrane) having a tysonite structure. Fiz. Tverd. Tela (St. Petersburg) 40, 658–661 (April 1998)     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Intrinsic Josephson junctions in Bi2Sr2CaCu2O8+δ single crystals

We report on thec-axis superconducting energy gap parameter Δ _c (T) of intrinsic Josephson tunnel junctions inBi ₂ Sr ₂ CaCu ₂ O _8+δ (Bi2212) single crystals. Δ _c (4.2K)≈10−13 meV, which is approximately a factor of two smaller than reported in the majority of tunneling experiments. Δ _c (T) deviates strongly from the BCS temperature dependence. These observations may be explained by a multilayer model of Bi2212 which assumes that theBi−O layers are superconducting due to the proximity effects. The Josephson tunneling then takes place between adjacentBi−O layers while there is a strong proximity coupling betweenBi−O andCu−O layers. The work is supported by Swedish Supercon-ductivity Consortium and NUTEK, and, in part, by Russian Foundation for Basic Research, grant #95-02-04307     

Correlation between the electric-field effect and weak-link type in YBa2Cu3−x Oy and YBa2Cu3−x Oy /Agx high-T c superconducting ceramics

An experimental study is reported of the effect of an electric field E⩽120 MV/m and of temperature T on the critical current I _c and I-V characteristics of yttrium-based high-T _c superconducting ceramics. The materials studied were copper-deficient ceramics, YBa₂Cu_3−x O_y (D samples), and YBa₂Cu_3−x O_y/Ag_x ceramics [S samples with silver present in amounts equal to the copper deficiency (0⩽x⩽0.4)]. It has been established that in D samples at 77 K, the electric field increases I _c and reduces substantially R for I>I _c, whereas in S samples no field effect is observed. Measurements of the I _c(T) dependence near the critical temperature showed that they can be described for all samples by a relation of the type I _c =const(1−T/T _c )^α, where α≈1 for the D samples, and α≈2 for the S samples. The results obtained suggest that the electric-field effect correlates with the existence in the ceramic of SIS-type weak links at grain boundaries. Fiz. Tverd. Tela (St. Petersburg) 40, 1195–1198 (July 1998)