Coulomb repul sion of hole s and competition between $${d_{{x^2} - {y^2}}}$$ -wave and s-wave paring s in cuprate superconductor s

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO₂ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V _q does not appear in the kernel of the corresponding integral equation.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Fermion superfluid with hybridized <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-wave pairings

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized s- and p-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable s- and p-wave interactions, which is realizable in a two-component ⁴⁰K Fermi gas with close-by s- and p-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the s- and p-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Collision between two ortho-positronium (Ps) atoms: A four-body Coulomb problem

The elastic collision between two ortho-positronium (e.g. S = 1) atoms is studied using an ab-initio static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment S = 0, i.e., singlet (+) and S = 2, i.e., triplet (?) states are studied. An augmented Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section (σ), the quenching cross-section (σ_q) and ortho-to-para conversion ratio (σ/σ_q). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.     

Ground state pairing correlation competes in the doped triangular lattice Hubbard model

By using the constrained path quantum Monte carlo method, we study the ground state paring correlations in the t ? U ? V Hubbard model on the triangular lattice. It is shown that pairings with various symmetries dominate in different electron filling regions. The pairing correlation with fn-wave symmetry dominates over other pairings around half fillings, and as the electron filling decreases away from the half filling, the d + id-wave pairing correlation tends to dominate. As the electron filling is bellow the Van Hove singularity, the f-wave pairing dominates. These crossovers are due to the interplay of electronic correlation and geometric frustration, associating with the competition between the antiferromagnetic correlations and ferromagnetic fluctuations. Our findings reveal the possible magnetic origin of superconductivity, and also provide useful information for the understanding of superconductivity in Na _x CoO₂·H₂O and the organic compounds.     

Models of spin structures in Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript>

The mean-field method is used to calculate the bands, Fermi surfaces, and spin susceptibilities of a three-band model of the RuO₄ plane of Sr₂RuO₄ rutinate for states with different spin structures. In particular, the spiral state is studied with the “incommensurate” vector Q=2π(1/3, 1/3) corresponding to the nesting of bands with the population n=4. This state proves to be the lowest with respect to energy among other (paramagnetic, ferromagnetic, antiferromagnetic, and periodic) solutions. In the spiral state, in addition to the main α, β, and γ sheets of the Fermi surface, shadow Fermi boundaries along the Γ(0, 0)-M(π, 0) line (previously observed in the ARPES experiments) are revealed and explained. This may change the interpretation of the data on dispersionless peaks in photoemission, previously ascribed to surface states. The spin susceptibilities of the spiral state exhibit peaks in the dependence Im?(q, ω) at q=Q in accordance with the observed magnetic peak in neutron scattering. The hypothesis of the presence of spin structures with q=Q in the normal state of Sr₂RuO₄ and the methods of checking this hypothesis are discussed.     

Asymmetric Anderson model and spin excitations in the Kondo insulator YbB<Subscript>12</Subscript>

A cluster problem is analyzed as an example demonstrating that the observed three-mode behavior of spin-triplet excitations in YbB₁₂ can be described by the asymmetric Anderson model with insulating singlet ground state. In the case of an infinite system, it is argued that the behavior of the f subsystem can be analyzed by using an effective Hamiltonian ? _J with direct antiferromagnetic f-f exchange interaction. The spin excitation spectrum is shown to have a minimum at the antiferromagnetic vector, as observed experimentally. A distinctive feature of the analysis is the use of singlet and triplet basis operators.     

EPR study of impurity iron ion clusters in BaF<Subscript>2</Subscript> crystals

Tetragonal paramagnetic centers with spin S = 7/2 were detected in x-ray-irradiated BaF₂: Fe (c_Fe ≈ 0.002 at. %) crystals using the EPR method. Electronic transitions between the |±1/2〉 states of a Kramers doublet were observed in the X and Q ranges. In the EPR spectra of the tetragonal centers, a ligand hyperfine structure (LHFS) was observed corresponding to the interaction of the electron magnetic moment of the tetragonal center with eight equivalent ligands. The large spin moment, significant anisotropy of the magnetic properties, and the characteristic LHFS indicate that the tetragonal center is a Fe^1.5+?Fe^1.5+ dimer in which the two iron ions are bound via superexchange interaction. It is assumed that, before crystal irradiation, this dimer was in the Fe³⁺(3d⁵)?Fe⁺(3d⁷) state.     

Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chain

In spin-conversion (SC) compounds containing molecules organized around an iron (II) ion the fundamental level of the ion is low spin (LS), S = 0, and its first excited one is high spin (HS), S = 2. This energy diagram is due to the ligands field interaction on 3d electrons and to the spin pairing energy. Heating the compound increases the magnetic susceptibility which corresponds to a change of populations of both levels and consequently a change of spin value of the molecules. This mechanism, called spin conversion (SC), can be accompagnied by thermal hysteresis observed by studying magnetic susceptibility or high spin fraction. In that case one considers that the (SC) takes place through a first-order phase transition due to intermolecular interactions. In the atom-phonon coupling model the molecules are considered as two-level systems, or two-level atoms, and it is assumed that the elastic force constant value of the spring which links two atoms first neighbours is depending on the electronic states of both atoms. In this study we calculate the partition function of a linear chain of N atoms (N ≤ 16) and we describe the role of phonons and that of the parameter Δ which corresponds to the distance in energy between both levels. The chain free-energy function is F _atph . We introduce for the chain a free-energy function defined by the set (F _HS , F _LS , F _barr ) and we show that F _atph tends towards the previous set when N → ∞. The previous set allows to describe a first order phase transition between a (LS) phase and a (HS) one. At the crossing point between the function F _LS and F _HS , and around this point, there is an intermediate free-energy barrier which prevents the chain to change phase which can lead to thermal hysteresis. The energy gap between the free-energy function F _atph and that defined by the set (F _HS , F _LS , F _barr ) is small. So we can expect that a nanoparticule takes for free-energy function that defined by the set and then displays a thermal hysteresis.     

Effect of spin structures and nesting on the shape of the fermi surface and pseudogap anisotropy in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">t</Emphasis>′-<Emphasis Type="Italic">U</Emphasis> Hubbard models

The effect of two types of spin structures on the shape of the Fermi surface and on the map of photoemission intensities for the t-t′-U Hubbard model is investigated. The stripe phase with a period of 8α and the spiral spin structure are calculated in the mean field approximation. It is shown that, in contrast to electron-type doping, hole-doped models are unstable to the formation of such structures. Pseudogap anisotropy is different for h-and e-doping and is determined by the spin structure. In accordance with ARPES data for La_2?xSr_xCuO₄, the stripe phase is characterized by quasi-one-dimensional FS segments in the vicinity of points M(±π, 0) and by suppression of the spectral density for k _x =k _y . It is shown that spiral structures exhibit polarization anisotropy: different segments of the FS correspond to electrons with different spin polarizations.     

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J _H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J _H and high conduction electron density but a chiral \(d_{x^2 - y^2 } + id_{xy}\)-wave for large J _H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.     

Luminescence of water-soluble rh(III) porphyrins

The luminescent properties of complexes of rhodium(III) with three water-soluble porphyrins— meso-tetrakis(4-N-methyl pyridyl) porphyrin, meso-tetrakis(4-N,N,N-trimethyl aminophenyl) porphyrin, and meso-tetrakis(4-sulfonate phenyl) porphyrin—were studied. All three complexes were found to phosphoresce both at 77 K and in deaerated solutions at room temperature, with their fluorescence being very weak. The rate constants of radiative (k _p=40-60s^-1) and nonradiative deactivation of a triplet excited state were determined. It was ascertained that, in aqueous solutions, the phosphorescence is quenched by molecular oxygen via an energy-transfer mechanism that is accompanied by formation of singlet oxygen. The quantum yields of formation of singlet oxygen for all the metalloporphyrins studied were found to be close to unity, which is the quantum yield of formation of their triplet states.     

Electroproduction of <Emphasis Type="Italic">J/ψ</Emphasis> mesons within the semihard QCD approach and the color-singlet model

The deep-inelastic production of J/ψ mesons in electron-proton interactions at the HERA collider is considered within the semihard (k_T-factorization) QCD approach and within the color-singlet model. The dependence of the Q², p _T ² , z, y* and W distributions of J/ψ mesons on various sets of unintegrated gluon distributions and the dependence of the spin parameter α on p _T ² and Q² are investigated. The results of the calculations are compared with the latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider. It is shown that experimental investigations of the polarization properties of J/ψ mesons over the kinematical region Q²<1 GeV² may provide an additional test of the statement that the dynamics of gluon distributions is governed by the Balitsky-Fadin-Kuraev-Lipatov equations.     

Role of critical fluctuations in the formation of a skyrmion lattice in MnSi

The region in the H–T phase diagram near the critical temperature (T _c ) of the cubic helicoidal MnSi magnet is comprehensively studied by small-angle neutron diffraction. Magnetic field H is applied along the [111] axis. The experimental geometry is chosen to simultaneously observe the following three different magnetic states of the system: (a) critical fluctuations of a spin spiral with randomly orientated wavevector k _f , (b) conical structure with k _c ∥ H, and (c) hexagonal skyrmion lattice with k_sk ⊥ H. Both states (conical structure, and skyrmion lattice) are shown to exist above critical temperature T _c = 29 K against the background of the critical fluctuations of a spin spiral. The conical lattice is present up to the temperatures where fluctuation correlation length ξ becomes comparable with pitch of spiral d _s . The skyrmion lattice is localized near T _c and is related to the fluctuations of a spiral with correlation length ξ ≈ 2d _s , and the propagation vector is normal to the field (k_sk ⊥ H). These spiral fluctuations are assumed to be the defects that stabilize the skyrmion lattice and promote its formation.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Zur Bestimmung der Spin-Polarisation aus Transparenz-Messungen beim Optischen Pumpen

A simple method of measuring the degree of polarization achieved by optical pumping has been described recently for the case of sodium vapor, illuminated with the single circularly polarizedD ₁ line. The assumption had to be made, however, that the atomic absorption cross sectionQ, depending on the degree of polarizationP and the frequency of lightν, may be approximated byQ(P, ν)=(1?P)·Q(P=O,ν). The purpose of this paper is to discuss the qualification of this assumption. A theoretical analysis of the pumping process is tried, showing that the measured polarization corresponds in good approximation to the degree of the valence electron spin polarization. — For the case of weak absorption and equal intensity of the two hyperfine components of theD ₁ line a diagramm is given, relating the measured polarization to the polarization of the nuclear spin.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Vibronic-spin-orbit interactions in heterocyclic analogues of fluorene with the N and O heteroatoms

The transition dipole moments P _0n ^s for the transitions from the electronic triplet state ³ B ²(ππ*) to vibrational sublevels of the vibrational out-of-plane modes n of the carbazole and dibenzofuran molecules are calculated. The values of the radiative deactivation rate constant k _rad ^s of the triplet sublevels T ^s are determined along with the components k _SO ^s and k _VSO ^s of this constant, which depend on the intramolecular spin-orbit (SO) and vibronic-spin-orbit (VSO) interaction. It is ascertained that k _rad ^z > k _rad ^y . For different structural units of the molecules (the heteroatom and the carbon atoms of the dibenzene fragment), the effect of the SO coupling on the constant k _VSO～Σ_{s, n} (P _0n ^s )² is studied. A competition between the effects on k _VSO from the SO coupling in the carbon atoms and in the light N and O heteroatoms is revealed. This competition accounts for the weak influence of the heteroatom on this component of the rate constant k _rad in these molecules. It is ascertained that the intensity distribution among the vibronic lines in the phosphorescence spectra of carbazole and dibenzofuran I _0n ～Σs (P _0n ^s )² is different due to the substantially different influence of the N and O heteroatoms on the deactivation of the triplet sublevel T ^y .