The Unique Properties of Superconductivity in Cuprates

Copper oxides are the only materials that have transition temperatures, T _c, well above the boiling point of liquid nitrogen, with a maximum \(T_{\mathrm {c}}^{\mathrm {m}}\) of 162 K under pressure. Their structure is layered, with one to several CuO₂ planes, and upon hole doping, their transition temperature follows a dome-shaped curve with a maximum of \(T_{\mathrm {c}}^{\mathrm {m}}\) . In the underdoped regime, i.e., below \(T_{\mathrm {c}}^{\mathrm {m}}\) , a pseudogap Δ* ∝ T* is found, with T* always being larger than T _c, a property unique to the copper oxides. In the superconducting state, Cooper pairs (two holes with antiparallel spins) are formed that exhibit coherence lengths on the order of a lattice distance in the CuO₂ plane and one order of magnitude less perpendicular to it. Their macroscopic wave function is parallel to the CuO₂ plane near 100 % d at their surface, but only 75 % d and 25 % s in the bulk, and near 100 % s perpendicular to the plane in yttrium barium copper oxide (YBCO) [1]. There are two gaps with the same T _c [2]. As function of doping, the oxygen isotope effect is novel and can be quantitatively accounted for by a vibronic theory or by the presence of bipolarons [2, 3]. These cuprates are intrinsically heterogeneous in a dynamic way. In terms of quasiparticles, bipolarons are present at low doping and aggregate upon cooling [2] so that probably ramified clusters and/or stripes are formed, leading over to a more Fermi liquid-type behavior at large carrier concentrations.     

Effect of Structural Relaxation on the In-Plane Electrical Resistance of Oxygen-Underdoped ReBa_2Cu_3O_{7-\delta } (Re = Y,Ho) Single Crystals

The effect of jumpwise temperature variation and room-temperature storing on the basal-plane electrical resistivity $\rho _{ab}$ of underdoped ReBa $_2$ Cu $_3$ O $_{7-\delta }$ (Re = Y, Ho) single crystals is investigated. Reducing the oxygen content has been revealed to lead to the phase segregation accompanied by both, labile component diffusion and structural relaxation in the sample volume. Room-temperature storing of ${\text {YBa}}_2{\text {Cu}}_3{\text {O}}_{7-\delta }$ single crystals with different oxygen hypostoichiometries leads to a substantial widening of the rectilinear segment in $\rho _{ab}(T)$ in conjunction with a narrowing of the temperature range of existence of the pseudogap state. It is established that the excess conductivity obeys an exponential law in a broad temperature range, while the pseudogap’s temperature dependence is described satisfactory in the framework of the BCS-BEC crossover theory. Substituting yttrium with holmium essentially effects the charge distribution and the effective interaction in CuO planes, thereby stimulating disordering processes in the oxygen subsystem. This is accompanied by a notable shift of the temperature zones corresponding to transitions of the metal-insulator type and to the regime of manifestation of the pseudogap anomaly.     

Is There a Unified Description of Conductivity of Layered Cuprates ?

We present a novel approach to the analysis of the normal state in-plane $\sigma _{ab} $ and out-of-plane σ_c conductivities of anisotropic layered crystals such as oxygen deficient YBa ₂ Cu ₃ O _x . It can be shown that the resistive anisotropy is determined by the ratio of the phase coherence lengths in the respective directions; i.e., $\sigma _{ab} /\sigma _c = \ell _{ab}^2 /\ell _c^2 $ . From the idea that at all doping levels and temperatures T the out-of-plane transport in these crystals is incoherent, follows that $\ell _c $ is T-independent, equal to the spacing $\ell _0 $ between the neighboring bilayers. Thus, the T-dependence of $\ell _{ab} $ is given by the measured anisotropy, and $\sigma _{ab} (\ell _{ab} )$ dependence is obtained by plotting $\sigma _{ab} {\text{ }}vs{\text{ }}\ell = {\text{ (}}\sigma _{ab} /\sigma _c )^{1/2} \ell _0 $ .The analysis of several single crystals of YBa ₂ Cu ₃ O _x (6.35 < x < 6.93) shows that for all of them $\sigma _{ab} (\ell ) $ is described by a universal dependence $\sigma _{ab} /\overline \sigma = f(\ell /\overline \ell ) $ with doping dependent parameters $\overline \sigma {\text{ }}and{\text{ }}\overline \ell $ .     

Cryptanalysis of a key exchange protocol based on the endomorphisms ring End{(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}

Climent et?al. (Appl Algebra Eng Commun Comput 22:91?C108, 2011) identified the elements of the endomorphisms ring End ${(\mathbb{Z}_p \times \mathbb{Z}_{p^2})}$ with elements in a set, E _p , of matrices of size 2?× 2, whose elements in the first row belong to ${\mathbb{Z}_{p}}$ and the elements in the second row belong to ${\mathbb{Z}_{p^2}}$ . By taking advantage of matrix arithmetic, they proposed a key exchange protocol using polynomial functions over E _p defined by polynomials in ${\mathbb{Z}[X]}$ . In this note, we show that this protocol is insecure; it can be broken by solving a set of 10 consistent homogeneous linear equations in 8 unknowns over ${\mathbb{Z}_{p^2}}$ .     

Superconductivity of YBa2−x Nd x Cu3O y Solid Solution

The solubility of Nd at the Ba sites and the superconductivity of YBa_2?x Nd _x Cu₃O _y were investigated by X-ray powder diffraction and measurements of the electrical resistance and ac susceptibility. The single Re123 phase was obtained for x≤0.30. The onset transition temperature $T_{\text{c}}^{{\text{on}}}$ is insensitive to the Nd content x in the region of x≤0.40. All are higher than 95 K. The zero resistance transition temperatures $T_{\text{c}}^{{\text{zero}}}$ , however, exhibits two-step variation with the increase of x. For x≤0.25, $T_{\text{c}}^{{\text{zero}}}$ are all above 92 K. The highest $T_{\text{c}}^{{\text{zero}}}$ of 94 K was obtained for x=0.25. For x≥0.3 $T_{\text{c}}^{{\text{zero}}}$ drops sharply to about 84 K. Finally $T_{\text{c}}^{{\text{zero}}}$ falls to 30 K and $T_{\text{c}}^{{\text{zero}}}$ is below 10 K for x=0.5. The two-step variation of T _c might be an indication of the existence of two trap levels for holes.     

How the Surface Resistance R s of Patterned High-T c Superconducting Thin Film Is Affected by the Film's Edge

This paper defines an effective microwave surface resistance $R_{\text{s}}^{{\text{eff}}}$ for the nonuniform distribution of microwave surface resistance R _s in the strip of a microstrip. It is proved that $R_{\text{s}}^{{\text{eff}}}$ is equivalent to the expression of R _s used in experiments, and that the $R_{\text{s}}^{{\text{eff}}}$ is dominated by the edge part, i.e., the area of width λ²/2t from the strip edge, where λ is the magnetic penetration depth and t is the film thickness. Under the assumption that $R_s \sim \left( {H_{{\text{rf}}}^y } \right)^n$ where $H_{{\text{rf}}}^y$ is the component of rf magnetic field along the film thickness and n is an integer, the ratio of the contributions of the edge part and the rest of the strip to $R_s^{{\text{eff}}}$ is calculated by using an approximate analytical expression of the surface current density distribution J _s in the strip and $H_{{\text{rf}}}^y$ calculated by the London equation. The effect of film's edge on R _s was studied using a microstrip resonator. It is found that the perfectness of the edge could affect the magnitude of the power dependence of R _s significantly, which agreed with our analysis.     

Features in the formation of Ge/Si multilayer nanostructures under ion-beam-assisted crystallization

A method of combined ion-beam crystallization of the Ge/Si multilayer nanostructures is proposed. Using atomic-force microscopy and electron microscopy, we observed the formation of an array of germanium quantum dots with lateral dimensions 〈a〉 = 12–15 nm at the following conditions: silicon-substrate temperature T = 330–350°C, ion-beam energies E _Ge + = 30–40 eV, $E_{Ar^ + }^0 = 230 - 240$ eV (primary pulsed defect formation mode), $E_{Ar^ + } = 130 - 140$ eV (permanent diffusion stimulation mode), and ion-beam fluences $f_{Ge^ + } = 1.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ , $f_{Ar^ + } = 5 \times 10^{12} cm^{ - 2} s^{ - 1} $ . The Raman spectroscopy data indicate the experimental possibility of low-temperature ion-stimulated growth of the spacer layers of silicon (T = 420–450°C, $E_{Ar^ + } = 80 - 90$ eV, $E_{Si^ + } = 30 - 40$ eV, $f_{Si^ + } = 3.5 \times 10^{14} cm^{ - 2} s^{ - 1} $ ) and the formation of multilayer structures with Ge _x Si_{1 ? x} quantum dots (x > 0.85).     

Rational formulas for traces in zero-dimensional algebras

We present a rational expression for the trace of the multiplication map Times _r : A → A in a finite-dimensional algebra ${A := \mathbb {K}[x_1,\ldots,x_n] /\mathcal {I}}$ in terms of the generalized Chow form of ${\mathcal{I}}$ . Here, ${\mathcal{I} \subset \mathbb {K}[x_1,\ldots,x_n]}$ is a zero-dimensional ideal, ${\mathbb {K}}$ is a field of characteristic zero, and r(x ₁,..., x _n ) a rational function whose denominator is not a zero divisor in A. If ${\mathcal {I}}$ is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.     

Pulsed Nuclear Magnetic Resonance on 3He Adsorbed on Bare and 4He Preplated MCM-41 Using DC SQUID Detection

We report low field DC SQUID NMR measurements down to 1.5 K of ³He adsorbed in the pores of the mesoporous molecular sieve MCM-41. In the first experiment measurements were made on ³He adsorbed onto the bare pore walls of MCM-41 with coverages ranging from $n_{^{3}\mathrm{He}}=0.86n_{1}$ to full pores at $n_{^{3}\mathrm{He}}=1.79n_{1}$ , where n ₁ is the coverage for monolayer completion. A second experiment was performed with low ³He coverages ( $n_{^{3}\mathrm{He}}\sim0.01n_{1}$ ) on ⁴He preplated pores, where a crossover to a quasi-1D state is expected to occur at temperatures sufficiently below 700 mK. In both experiments relaxation times T ₁ and T ₂ ^* were measured as a function of temperature and coverage at frequencies from 80 to 240 kHz. The frequency dependence of the linewidth in the pure ³He experiment is extremely weak therefore T ₂ ^* ≈T ₂. The 1.5 K isotherm shows a small minimum in T ₂ ^* at a coverage corresponding to monolayer completion. In the experiment with ⁴He preplating there was no significant change in T ₁ or T ₂ ^* when the ³He coverage was doubled from $n_{^{3}\mathrm{He}}=0.01n_{1}$ to 0.02n ₁ at a ⁴He preplating of $n_{^{4}\mathrm{He}}=1.05n_{1}$ . This suggests that the relaxation times are dominated by single particle effects in the low density regime.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

Angular Dependence of the Fluctuation Magnetization Vector Above the Superconducting Transition of a Highly Anisotropic High-T c Cuprate

In highly anisotropic cuprate superconductors it is generally accepted that the reversible magnetization vector, $\vec{M}$ , is essentially perpendicular to the superconducting CuO₂ layers in a wide range of crystal orientations with respect to the applied magnetic field, $\vec{H}$ . In a recent work (Mosqueira et al. in Phys. Rev. B 84:134504, 2011) it is shown, however, that the dependence of $\vec{M}$ on the $\vec{H}$ orientation in the reversible mixed state of a high-quality Tl-based cuprate presents a notable deviation from this behavior. Here we extend these measurements to the fluctuation region above T _c , in order to check whether the above-mentioned effect is also present.     

Electrical conductivity of polycrystalline tin dioxide and its solid solution with ZnO

Electrical conductivity (σ) of “pure” and ZnO doped SnO₂ has been measured at different temperatures and oxygen partial pressures ( \(p_{{\text{O}}_{\text{2}} } \) )- From the variation of electrical conductivity of these materials three partial pressure ranges have been identifieD. In the high partial pressure rangeσ increases with decreasing \(p_{{\text{O}}_{\text{2}} } \) followed by a \(p_{{\text{O}}_{\text{2}} } \) independent region at lower \(p_{{\text{O}}_{\text{2}} } \) ´s and finally increases once again with a further decrease of \(p_{{\text{O}}_{\text{2}} } \) . These variations have been explained on the basis of an anti-Frenkel type defect structure and an interstitial solid solution of ZnO in SnO₂. The activation energy for the conduction process has been estimated and the values are found to differ in two different temperature ranges. In the low temperature range the conductivity is attributed mainly to the chemisorption of oxygen on the surface of the specimen.     

Dislocation structure at a \{ {\overline{1} 2\overline{1} 0} \}/ {\langle} 10\overline{1} 0 {\rangle} low-angle tilt grain boundary in LiNbO3

LiNbO₃ is a ferroelectric material with a rhombohedral R3c structure at room temperature. A LiNbO₃ bicrystal with a $ \{ {\overline{1} 2\overline{1} 0} \}/ {\langle}10\overline{1} 0{\rangle}$ 1° low-angle tilt grain boundary was successfully fabricated by diffusion bonding. The resultant boundary was then investigated using high-resolution TEM. The boundary composed a periodic array of dislocations with $ b = { 1}/ 3{\langle} \overline{1} 2\overline{1} 0{\rangle} $ . They dissociated into two partial dislocations by climb. A crystallographic consideration suggests that the Burgers vectors of the partial dislocations should be $ 1/ 3{\langle}01\overline{1} 0{\rangle} $ and $ 1/ 3{\langle}\overline{1} 100{\rangle} $ , and a stacking fault on $ \{ {\overline{1} 2\overline{1} 0} \} $ is formed between the two partial dislocations. From the separation distance of a partial dislocation pair, a stacking fault energy on $ \{ {\overline{1} 2\overline{1} 0} \} $ was estimated to be 0.25?J/m² on the basis of isotropic elasticity theory.     

Photoluminescence,thermally stimulated luminescence and electron paramagnetic resonance studies of U6+ doped BaSO4

U⁶⁺ doped BaSO₄ samples were synthesized by precipitation route. PL, TL and EPR investigations of γ and self α irradiated samples were carried out. PL spectra of these samples give structured broad band peaking around 518 nm with five vibronic bands centred around 498·4, 516·0, 533·7, 554·0 and 575·1 nm, respectively and the average frequency of symmetric stretching of O=U=O in the ground electronic state was found to be 674 cm^?1. Trap level spectroscopic studies of U doped BaSO₄ give glow peaks at 411, 488 and 512 K, respectively and their spectral characteristics are typical of UO \(_{2}^{2+}\) emission. EPR studies of γ-irradiated U⁶⁺:BaSO₄ sample have shown the presence of sulphoxy centred radicals like SO \(_{4}^{-}\) and SO \(_{3}^{-}\) in addition to OH^?, O \(_{3}^{-}\) and SH^2?. TSL peaks at 411 and 488 K were correlated with thermal destruction of SO \(_{4}^{-}\) and SO \(_{3}^{-}\) radicals.     

Molecular beam epitaxy of semipolar AlN(11\bar{2}2) and GaN(11\bar{2}2) on m-sapphire

We report on the plasma-assisted molecular-beam epitaxy of semipolar $\hbox{AlN}(11\bar{2}2)$ and GaN( $11\bar{2}2$ ) films on $(1\bar{1}00)$ m-plane sapphire. AlN deposited on m-sapphire settles into two main crystalline orientation domains, $\hbox{AlN}(11\bar{2}2)$ and $\hbox{AlN}(10\bar{1}0),$ whose ratio depends on the III/V ratio. Growth under moderate nitrogen-rich conditions enables to isolate the $(11\bar{2}2)$ orientation. The in-plane epitaxial relationships of $\hbox{AlN}(11\bar{2}2)$ on m-plane sapphire are $[11\bar{2}\bar{3}]_{\rm AlN} \vert \vert [0001]_{\rm sapphire}$ and $[1\bar{1}00]_{\rm AlN} \vert \vert [11\bar{2}0]_{\rm sapphire}.$ GaN deposited directly on m-sapphire results in ( $11\bar{2}2$ )-oriented layers with ( $10\bar{1}\bar{3}$ )-oriented inclusions. A ～100 nm-thick AlN( $11\bar{2}2$ ) buffer imposes the ( $11\bar{2}2$ )-orientation for the GaN layer grown on top. By studying the Ga-desorption on GaN( $11\bar{2}2$ ), we conclude that these optimal growth conditions corresponds to a Ga excess of one monolayer on the GaN( $11\bar{2}2$ ) surface.     

Anisotropy of the Adiabatic Relaxation Time of Adsorbed 3He Monolayer

This paper investigates the anisotropy of the adiabatic relaxation time $T_{2}^{\prime}$ (T ₂(ω), ω→∞, where ω is the Larmor frequency) of adsorbed monolayer solid ³He. We calculate $T_{2}^{\prime}$ based on the phenomenological Heisenberg Hamiltonian with the nearest-neighbor and the next nearest-neighbor exchange interactions. Furthermore, the four particle exchange in the triangular plane is also incorporated. To calculate  $T_{2}^{\prime}$ , it is necessary to compute the second and the fourth moments of the resonance line $M_{2}^{0}$ and $M_{4}^{0}$ . To obtain them, we can use the formulas published in previous studies. From the results, we can observe no significant difference between the nearest-neighbor Heisenberg model and the four particle spin interaction models. A comparison of the present results and the experimental data is briefly discussed.     

Mixed-mode crack-tip stress fields for orthotropic functionally graded materials

Quasi-static mixed mode stress fields for a crack in orthotropic inhomogeneous medium are developed using asymptotic analysis coupled with Westergaard stress function approach. In the problem formulation, the elastic constants E ₁₁, E ₂₂, G ₁₂, ν ₁₂ are replaced by an effective stiffness ${E=\sqrt {E_{11} E_{22}}}$ , a stiffness ratio ${\delta =\left({{E_{11}}\mathord{\left/ {\vphantom {{E_{11}} {E_{22}}}}\right. \kern-0em} {E_{22}}} \right)}$ , an effective Poisson’s ratio ${\nu =\sqrt {\nu_{12}\nu _{21}} }$ and a shear parameter ${k=\left({E \mathord{\left/ {\vphantom {E {2G_{12}}}}\right. \kern-0em} {2G_{12}}}\right)-\nu }$ . An assumption is made to vary the effective stiffness exponentially along one of the principal axes of orthotropy. The mode-mixity due to the crack orientation with respect to the property gradient is accommodated in the analysis through superposition of opening and shear modes. The expansion of stress fields consisting of the first four terms are derived to explicitly bring out the influence of nonhomogeneity on the structure of the mixed-mode stress field equations. Using the derived mixed-mode stress field equations, the isochromatic fringe contours are developed to understand the variation of stress field around the crack tip as a function of both orthotropic stiffness ratio and non-homogeneous coefficient.     

Topological Investigations of Excess Molar Volumes and Excess Isentropic Compressibilities of Ternary Mixtures Containing Pyrrolidin-2-one at 308.15 K

Excess molar volumes, ${V^{\rm E}_{ijk}}$ , and speeds of sound, u _ijk , of pyrrolidin-2-one (2-Py) (i)+benzene or methyl benzene (j)+propan-1-ol (k) ternary mixtures and speeds of sound, u _ij , of benzene or methyl benzene (i)+propan-1-ol (j) binary mixtures have been measured dilatometrically and interferrometrically over the complete mole fraction range at 308.15 K. Speed-of-sound data have been utilized to evaluate excess isentropic compressibilities for binary and ternary mixtures. ${V^{\rm E}_{ijk}}$ and ${\left({\kappa_S^{\rm E}}\right)_{ijk}}$ values have been fitted to a Redlich–Kister equation to predict ternary adjustable parameters and standard deviations. Topological investigations employed for predicting excess molar volumes and excess isentropic compressibilities, ${\left({\kappa _S^{\rm E}} \right)_{ij}}$ , of 2-Py + benzene or methyl benzene or propan-1-ol binary mixtures have been extended to ternary mixtures (by employing the concept of a connectivity parameter of third degree, ³ ξ, of a molecule) to obtain an expression that describes well the measured ${V^{\rm E}_{ijk}}$ and ${\left({\kappa_S^{\rm E}}\right)_{ijk}}$ values.     

Evaluating geometric queries using few arithmetic operations

Let ${\mathcal{P}:=(P_1,\ldots,P_s)}$ be a given family of n-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by d and h, respectively. Suppose furthermore that for each 1??? i??? s the polynomial P _i can be evaluated using L arithmetic operations (additions, subtractions, multiplications and the constants 0 and 1). Assume that the family ${\mathcal{P}}$ is in a suitable sense generic. We construct a database ${\mathcal{D}}$ , supported by an algebraic computation tree, such that for each ${x\in [0,1]^n}$ the query for the signs of P ₁(x), . . . , P _s (x) can be answered using ${h d^{\mathcal{O}(n^2)}}$ comparisons and nL arithmetic operations between real numbers. The arithmetic-geometric tools developed for the construction of ${\mathcal{D}}$ are then employed to exhibit example classes of systems of n polynomial equations in n unknowns whose consistency may be checked using only few arithmetic operations, admitting, however, an exponential number of comparisons.     

Dislocation structures in a { \bar{1} 104}/��11 \bar{2} 0�� low-angle tilt grain boundary of alumina (��-Al2O3)

An alumina (??-Al₂O₃) bicrystal with a ( $ \bar{1} $ 104)/[11 $ \bar{2} $ 0] 2^o low-angle tilt grain boundary was fabricated by diffusion bonding at 1500 °C in air, and the grain boundary was observed by transmission electron microscopy (TEM). High-resolution TEM observations revealed that the grain boundary consists of at least two kinds of dislocations. One is a perfect dislocation which has a Burgers vector of 1/3[ $ \bar{1} $ 2 $ \bar{1} $ 0]. The other is dissociated into two partial dislocations with a stacking fault on the (0001) plane, and each partial dislocation has a 1/6[ $ \bar{1} $ 101] edge component. It is suggested from structural considerations that the dissociated-dislocation pair originates from a b = 1/3[02 $ \bar{2} $ 1] perfect dislocation (i.e., 1/3[02 $ \bar{2} $ 1] ?? 1/6[02 $ \bar{2} $ 1] + 1/6[02 $ \bar{2} $ 1]). This dissociation produces a stacking fault in the anion sublattice. The stacking fault energy is estimated to be roughly 1.3 Jm^?2 based on the elastic theory. The authors discuss the dislocation structures and the stacking fault formed on the (0001) plane in detail.