0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Critical current in SFIFS junctions

A quantitative theory of the Josephson effect in SFIFS junctions (S denotes bulk superconductor, F is metallic ferromagnet, and I is insulating barrier) is presented in the dirty limit. A fully self-consistent numerical procedure is employed to solve the Usadel equations for arbitrary values of the F-layer thicknesses, magnetizations, and interface parameters. In the case of antiparallel ferromagnet magnetizations, the effect of critical current I _c enhancement by the exchange energy H is observed, while in the case of parallel magnetizations the junction exhibits a transition to the π state. In the limit of thin F layers, we study these peculiarities of the critical current analytically and explain them qualitatively; the scenario of the 0-πtransition in our case differs from those studied before. The effect of switching between 0 and π states by changing the mutual orientation of F layers is demonstrated.     

Critical current of an inhomogeneous Josephson junction at an intergrain boundary with a random distribution of dislocations

The critical current J _c(θ) of an intergrain boundary is calculated as a function of the contact misorientation angle θ of the granules. It is assumed that the ordering parameter is suppressed in regions near boundaries with an enhanced mechanical stress induced by randomly distributed surface dislocations. The stress distribution function is determined using a probabilistic approach. Assuming that the weak coupling at the boundary is Josephson coupling, an analytic expression is found for the angular dependence J _c(θ) (for tilt and twist boundaries). The magnitude of the residual critical current of a boundary in a strong magnetic field is estimated. Fiz. Tverd. Tela (St. Petersburg) 40, 393–402 (March 1998)     

Penetration of the magnetic field into a 3D ordered Josephson medium at very small values of the pinning parameter

The Meissner state of a 3D Josephson medium is analyzed for stability against small fluctuations of phase discontinuities at contacts. For any form of fluctuations, there exists value I ₀ of pinning parameter I such that the Meissner configuration remains stable if I < I ₀. Reasons why the configuration remains stable at small I are considered. Instability arises when the quadratic form of the second variation of Gibbs potential G is not a positively definite quantity. At small I, the contribution of the Josephson energy to G is small. The second variation of the magnetic energy, the other component of G, is always a positively definite quadratic form. Therefore, instability may arise only if I has a finite value. This statement holds true not only for the Meissner but also for any equilibrium configuration. At I < I ₀, stability persists up to the boundary of the Meissner state. Then, a sequence of plane vortices parallel to the boundary appears throughout the sample. Thus, vortices appearing at I < I ₀ are plane vortices rather than linear. The configurations of currents and the magnetic field profile inside the sample are calculated for I < I ₀. Calculation is based on analyzing the continuous variation of the current configuration toward a decrease in the Gibbs potential.     

Production of φ mesons in near-threshold πN and NN reactions

We analyze the production of φ mesons in πN and NN reactions in the near-threshold region, using throughout the conventional “non-strange” dynamics based on such processes which are allowed by the non-ideal ω-φ mixing. We show that the occurrence of the direct φNN interaction may show up in different unpolarized and polarization observables in πN→Nφ reactions. We find a strong non-trivial difference between observables in the reactions pp→ppφ and pn→pnφ caused by the different role of the spin singlet and triplet states in the entrance channel. A series of predictions for the experimental study of this effect is presented. Received: 27 January 2000     

Superconducting triplet spin valve

We study the critical temperature T _c of SFF trilayers (S is a singlet superconductor, F is a ferromagnetic metal), where the long-range triplet superconducting component is generated at noncollinear magnetizations of the F layers. We demonstrate that T _c can be a nonmonotonic function of the angle α between the magnetizations of the two F layers. The minimum is achieved at an intermediate α, lying between the parallel (P, α = 0) and antiparallel (AP, α = π) cases. This implies a possibility of a “triplet” spin-valve effect: at temperatures above the minimum T _c ^Tr but below T _c ^P and T _c ^AP, the system is superconducting only in the vicinity of the collinear orientations. At certain parameters, we predict a reentrant T _c (α) behavior. At the same time, considering only the P and AP orientations, we find that both the “standard” (T _c ^P < T _c ^AP) and “inverse” (T _c ^P > T _c ^AP) switching effects are possible depending on parameters of the system.     

On the dimensionality of superconductivity in cuprate superconductors

The question of the dimensionality of superconductivity is considered within the framework of a model of superconductivity via asymmetric, delocalized “crystalline” π orbitals (analogous to the corresponding molecular orbitals) extending along chains of covalently bonded copper and oxygen ions. It is shown that superconductivity is preceded by a separation of the bonds in the CuO₂ layer into covalent and ionic bonds with ordering of the covalent bonds into chains. Such an ordering facilitates the formation of a crystalline π orbital lowering the crystal energy by the resonance energy of the π bond and is therefore favored. The superconducting current is created by non-dissipative motion of π-electron pairs along the asymmetric, “crystalline” π orbitals extending along chains of covalently bonded copper and oxygen ions, in the presence of an ionic bond between neighboring chains extending through the easily polarizable O²⁻ ions. This ionic bond correlates the motion of the electron pairs along all the π orbitals and stabilizes the superconducting state. Only in this sense is the apparent “onedimensionality” of superconductivity in cuprate superconductors to be understood. Zh. Tekh. Fiz. 68, 82–84 (November 1998)     

Medium effects in the production and π0γ decay of ω-mesons in pA collisions in the GeV region

The ω resonance production and its π⁰γ decay in pA reactions close to threshold is considered within the Intranuclear Cascade (INC) model. The π⁰γ invariant-mass distribution shows two components which correspond to the ω decay “inside” and “outside” the nucleus, respectively. The “inside” component is distorted by medium effects, which introduce a mass shift as well as collisional broadening for the ω-meson and its decaying pion. The relative contribution of the “inside” component is analyzed in detail for different kinematical conditions and nuclear targets. It is demonstrated that a measurement of the correlation in azimuthal angle between the π⁰ and γ momenta allows to separate events related to the “inside”ω decay from different sources of background when uncorrelated π⁰'s and γ's are produced. Received: 2 April 2001 / Accepted: 5 June 2001     

Josephson current in superconductor/ferromagnet/ superconductor junctions

The Bogoliubov-de Gennes equation and Nambu spinor Green's function approach are applied to studying the Josephson current in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions in the clean limit. It is found that the critical current exhibits a damped oscillation with the F thickness d, the oscillation period equal to 2πξ_F with ξ_F the coherence length of the F. The change of the critical current from positive to negative is determined by factor cosφ^′ with φ^′=d/ξ_F as the F-induced phase difference. The exponent decay of the critical current is close related to that of the superconductor order parameter in the F, both of them having the same decay length.     

Reconciling φ radiative decays with other data for a0(980), f0(980), ππ→KK and ππ→ηη

Data for φ→γ(ηπ⁰) are analysed using the KK loop model and compared with parameters of a₀(980) derived from Crystal Barrel data. The ηπ mass spectrum agrees closely and the absolute normalisation lies just within errors. However, BES parameters for f₀(980) predict a normalisation for φ→γ(π⁰π⁰) at least a factor 2 lower than is observed. This discrepancy may be eliminated by including constructive interference between f₀(980) and σ. The magnitude required for σ→KK is consistent with data on ππ→KK. A dispersion relation analysis by Büttiker, Descotes-Genon and Moussallam of ππ→KK leads to a similar conclusion. Data on ππ→ηη also require decays of σ to ηη. Four sets of ππ→KK data all require a small but definite f₀(1370) signal. PACS 13.25.Gv; 14.40.Gx; 13.40.Hq     

Supercurrent and its Fano effect in a Josephson Aharonov-Bohm ring

The Josephson current through an Aharonov-Bohm (AB) interferometer, in which a quantum dot (QD) is situated on one arm and a magnetic flux Φ threads through the ring, has been investigated. In the presence of the magnetic flux, the relation between the Josephson current and the superconductor phase is complex, and the system can be adjusted to π junction by either modulating the magnetic flux or the QD’s energy level ε_d. Due to the electron-hole symmetry, the Josephson current I has the property I(ε_d,Φ)=I(-ε_d,Φ+π). The Josephson current exhibits a jump when a pair of Andreev bound states aligns with the Fermi energy. The condition for the current jump is given. Particularly, we find that the position of the current jump and the position of the maximum value of the critical current I_c are identical. Due to the interference between the two paths, the critical current I_c versus the QD’s level ε_d shows a typical Fano shape, which is similar to the Fano effect in the corresponding normal device. However they also show some differences. For example, the critical current never reaches zero for any parameters, while the current in the normal device can reach zero at the destruction point.     

Measurement of pionium lifetime with the Dirac spectrometer

Pionium ( π ⁺ π ^- bound state) lifetime is measured with improved precision with respect to earlier work, and the ππ s-wave scattering length difference between I = 0 and I = 2 amplitudes | a ₀ - a ₂| is determined to 5% precision.     

On lower scalar quark-antiquark nonets

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I ^G J ^PC = 0⁺0⁺⁺ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f₀ resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.     

Penetration of the magnetic field into a 3D ordered Josephson medium at small values of the pinning parameter

The current configurations and the profile of the magnetic field penetrating into a 3D ordered Josephson medium are calculated for I < I _C . The calculation algorithm (modified for finite-length samples) is based on analyzing the continuous variation of the configuration toward a decrease in the Gibbs potential. This algorithm makes it possible to find a configuration into which the Meissner state passes when I < I _C and an external field slightly exceeds H _max and trace the evolution of this configuration with a further rise in the field. At H > H _max, the magnetic field penetrates into the sample as a quasi-uniform sequence of plane vortices. When H is roughly equal to H ₀/2, where H ₀ is the outer field at which one fluxoid Φ₀ passes through each cell, the plane vortices disintegrate into linear ones centered in cells neighboring along the diagonal. As the field grows, the vortex pattern condenses: zero-fluxoid cells are gradually “filled” starting from the boundary. When the field approaches H ₀, a sequence of plane vortices centered in adjacent rows arises near the boundary. With a further increase in the field, sequences of linear vortices with a double fluxoid form at the boundary. Then, such a scenario is periodically repeated with a period H ₀ in the external field.     

Correlations of polarizations and entangled states in the two-photon system

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π⁰ → 2γ, η → 2γ, K _L ⁰ → 2γ, K _S ⁰ → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.     

Mixing angles of quarks and leptons in quantum field theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2) _L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2) _f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns on the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ ₂₃ is maximal and tan (2θ ₁₂)=2. The Cabibbo angle fulfills the condition tan (2θ _c )=1/2 and θ ₁₂ for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θ _c +θ ₁₂=π/4. θ ₁₃=±5.7⋅10⁻³ are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly broken symmetry of the Standard Model is outlined.     

Ferromagnetic 0–<Emphasis Type="BoldItalic">π</Emphasis> Josephson junctions

We present a study on low-T_c superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop of either 0 or π. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0–π Josephson junction, in which 0 and π ground states compete with each other. At a certain temperature the 0 and π parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum Φ₀. PACS  74.50.+r; 74.78.Fk; 74.81.-g; 85.25.Cp     

Feasibility study of model-independent approach to φ3 measurement using Dalitz plot analysis

In this paper, we present results of a feasibility study of a model-independent way to measure the angle φ₃ of the unitarity triangle. The method involves B^±→DK^± decays where the neutral D decays to the K⁰ _Sπ⁺π^- final state, together with the sample of decays of CP-tagged D mesons (produced, e.g. in ψ(3770)→DD̄ process) to the same final state. We consider different approaches to the extraction of φ₃ and obtain the expected statistical accuracy of the φ₃ measurement as a function of B and D_CP statistics. PACS 11.30.Er, 12.15.Hh     

Comments on preliminary data on the reactions e + e −→φ→γ f 0(980)→γπ0π0

Preliminary data on the reactions e ⁺ e ⁻→φ→γ f ₀(980)→γπ⁰π⁰ together with data on ππ scattering and the reactions J/ψ→φπ⁺π⁻ and K ⁻ p→π ⁺π⁻(Λ,Σ) are analyzed. The analysis shows that the mass of the f ₀(980) meson is = 950 MeV, and BR(φ→γf ₀→γπ⁰π⁰)≃ 1× 10⁻⁴, indicating that the f ₀(980) resonance is of a four-quark nature. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 445–449 (10 April 1998)