The collective excitations of the order parameter in HTSC and heavy fermion superconductors (HFSC) underD-pairing

Within the path integral model ofd-pairing for HTSC and HFSC developed recently by P. N. Brusov and N. P. Brusova¹, the whole collective mode spectrum has been calculated for the first time for five states of HTSC that arise in their symmetry classification as well as for three states of HFSC. For HTSC the calculations have been made for the state which is a candidate for the superconducting state of HTSC in light of numerous recent experiments as well as for , d_xy, d_xz, d_yz states. For HFSC we considered three states, among themdγ and Y₂₋₁ states treated by Hirashima and Namaizawa² who used the theory of response. The number of the collective modes in each phase of both superconducting systems is equal to 10, among which five are high frequency modes while five others are Goldstone or Goldstone-like ones. The spectrum can be used to identify the superconducting states through ultrasound and microwave absorption experiments as well as to interpret these experiments.     

Spin dynamics and implications for superconductivity: some problems with thed-wave scenario

We review the spin dynamics of the normal state of the cuprates with special emphasis on neutron data in both the YBa₂Cu₃O_7– and La_2–x Sr _x CuO₄ systems. When realistic models of the Fermi surface shapes are incorporated, along with a moderate degree of spin fluctuations, we find good semiquantitative agreement with experiment for both cuprates. Building on the success of this Fermi-liquid-based scheme, we explore the implications ford-wave pairing from a number of vantage points. We conclude that our present experimental and theoretical understanding is inadequate to confirm or refute thed-wave scenario.     

Specific Heat Jump at Tc of High Tc Superconductors: Effect of Van Hove Singularity

In the BCS framework, exact expressions for the ratio between the jump in the specific heat at T _c and the normal phase specific heat are derived within the Van Hove singularity scenario. Analytical results are obtained for an isotropic s-wave and anisotropic d-wave pairing symmetries. Graphical solutions of the ratio as functions of _D /T _c and E _F /T _c , where _D is the cutoff energy and E _F is the Fermi energy, show significant deviations from the BCS value of 1.43.     

Doping-Dependent Superconducting Symmetry in Hubbard Systems

The d-wave superconducting state is studied by using a generalized Hubbard model, in which a next-nearest-neighbor correlated-hopping interaction (t ₃) is included. The results obtained within the BCS framework suggest the existence of a critical hole concentration, below which a d_x ^{2-y 2}-wave superconducting gap is observed. However, above this critical concentration the maxima of the single-particle excitation energy gap are rotated by /4 and no real nodes exist, as observed in tunneling experiments. In this study, the parameters estimated by first-principle calculations for cuprate superconductors are used.     

Intrinsic surface depression of the order parameter under mixed (s+id)-wave pair symmetry and its effect on the critical current of high-Tc SIS Josephson junctions

An intrinsic gap depression at the superconductor-insulator interface due to the very short value of the coherence length in high-T _c superconductors [HTS] is considered in the framework of a mixed (s+id)-wave pair symmetry for the order parameter ranging from pures to pured-wave. This gap depression acts as the main physical agent causing the relevant reduction ofI _c (T)R _n (T) values with respect to BCS expectations in HTS SIS Josephson junctions. Good agreement with various experimental data is obtained with both pures-wave and pured-wave symmetries of the order parameter, but with amounts of gap depression depending on the pair symmetry adopted. Regardless of the apir symmetry considered, these results prove the importance of the surface order-parameter depression in the correct interpretation of theI _c (T)R _n (T) data in HTS SIS junctions. In the case of a planar YBCO-based junction the use of the de Gennes condition allowed us to tentatively obtain an upper limit for the amount ofd-wave present in the gap of YBCO.     

STM Spectroscopy on Anisotropic Superconductors

The superconducting phase of organic superconductors -(BEDT-TTF)₂Cu(NCS)₂ and (MDT-TTF)₂AuI₂ was investigated by the electron tunneling spectroscopy using low temperature STM. The tunneling differential conductance at the lateral surface of -(BEDT-TTF)₂Cu(NCS)₂ varies its shape depending on the tip direction. The in-plane anisotropy of the conductance is well explained by the d-wave symmetry with line nodes along the direction 45° from the c-axis. For (MDT-TTF)₂AuI₂, the tunneling conductance at T = 1.4 K shows the superconducting energy gap structure clearly. The finite conductance inside the gap edge suggests the gap anisotropy. The tunneling spectrum is explained by the d-wave pairing. The obtained gap ₀ = 2 meV (2₀/kT _c = 12) is larger than that of the weak coupling limit. The pseudogap structure is observed near T _c .     

X-ray diffraction study of compositionally homogeneous, nanocrystalline yttria-doped zirconia powders

The crystal structure of compositionally homogeneous, nanocrystalline ZrO₂ - X mol% Y₂O₃ (X = 2.8, 4, 5, 6, 7, 8, 9, 10, 11, and 12) powders synthesized by a nitrate-citrate gel-combustion process has been studied by X-ray diffraction. By applying the Rietveld method, it was found that all the powders presented the tetragonal phase (P4 ₂/nmc space group). The axial ratio c/a _f decreased with increasing Y₂O₃ content and became almost unity at 9 mol% Y₂O₃. However, powders in the compositional range of ZrO₂ - 9 to 12 mol% Y₂O₃ exhibited the oxygen atoms displaced from their ideal sites of the cubic phase along the c axis, which is known as the t-form of the tetragonal phase. A conjunct analysis of crystallite size and microstrain of all the powders is also presented.     

Thermal Conductivity of the Accidental Degeneracy and Enlarged Symmetry Group Models for Superconducting UPt3

We present theoretical calculations of the thermal conductivity for the accidental degeneracy and enlarged symmetry group models that have been proposed to explain the phase diagram of UPt ₃ . The order parameters for these models possess point nodes or cross nodes, reflecting the broken symmetries of the ground state. These broken symmetries lead to robust predictions for the ratio of the low-temperature thermal conductivity for heat flow along the axis and in the basal plane. The anisotropy of the heat current response at low temperatures is determined by the phase space for scattering by impurities. The measured anisotropy ratio, _c/ _b, provides a strong constraint on theoretical models for the ground state order parameter. The accidental degeneracy and enlarged symmetry group models based on no spin-orbit coupling do not account for the thermal conductivity of UPt ₃. The models for the order parameter that fit the experimental data for the and directions of the heat current are the 2D E_1g and E _2u models, for which the order parameters possess line nodes in the ab-plane and point nodes along the axis, and the A_1gE _1g model of Zhitomirsky and Ueda. This model spontaneously breaks rotational symmetry in the ab-plane below T_c2 and predicts a large anisotropy for the ab-plane heat current.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Spin-Triplet Superconductivity in Sr2RuO4

We study the doping and temperature dependence of the order parameter for the triplet states of the layered perovskite material Sr₂RuO₄. The tight binding model that includes orthorhombic distortion and second nearest neighbor hopping, has been considered to study the doping and temperature dependence of the p- and f-wave states. We also calculate the temperature dependence of specific heat and thermal conductivity. We compare our results with the corresponding singlet -results of the cuprates. d _xy -wave has also been considered. The jump in the specific heat at T _c (critical temperature) and its temperature dependence agree well with the experiment.     

Point-contact spectroscopy for itinerant-magnetic material of Fe x TiS2

The nonlinear current-voltage characteristics of a homojunction point contact of 1T-CdI₂-type layered crystal TiS₂ and its intercalation compound of itinerantmagnetic Fe _x TiS₂ have been measured at 1.4 K. For the magnetic samples, both a maximum and a minimum in thedI/dV-V curves are observed within a restricted range of the initial differential resistancesR _d(0). Electron-magnon scatterings are responsible for the appearance of the minimum at a bias voltageV _B(min), which depends onR _d(0). These results are discussed using the conventional spherical spreading out model, together with a heating model. The agreement between experiment and theory is apparently good if a large background is taken into account, but with unusually large andR _d(0)-dependent Lorenz number.     

Effects of phonons and antiferromagnetic spin fluctuations on the pairing and density of states in high-T c superconductors

We solve the Eliashberg equations for a two-dimensional, tight-binding band and anisotropic interaction due to exchange of phonons and antiferromagnetic spin fluctuations. For small band fillings, a mixture of simple and extendeds-wave pairing is stable, while for band fillings closer to half-filling thed-wave pairing state becomes stable. The density of statesN() becomes highly asymmetric in for smaller band fillings, which is an effect of particle-hole asymmetry. For thed-wave stateN() is linear in for small and exhibits a logarithmic singularity at the gap amplitude. For the mixeds-wave stateN() shows the BCS singularity at the gap edge. Antiferromagnetic spin fluctuations give rise to a pseudogap inN() for the normal state.     

Symmetries of Vortex Lattice Solutions of the Bogoliubov–de Gennes Equation in a Two-Dimensional Square Lattice

This report describes symmetry properties of tetragonal vortex lattice solutions of the Bogoliubov–de Gennes equation in a two-dimensional square lattice in a uniform magnetic field. The invariance group of a tetragonal vortex lattice solution is expressed in a form of G _(l) = (e + tC _2x ) (l = 0, 2, ± 1), where tC _2x is a space rotation around the x-axis accompanied with time reversal, is a kind of fourfold rotation group, and L is the magnetic translational group of the vortex lattice state. We give a new, refined definition of local symmetric order parameters (OPs) (s-wave, d-wave, and p-wave), which have a well-defined nature such that the OP (e.g., s-wave OP) at the translated site by a lattice vector (of the vortex lattice) from a site (m, n) is expressed by the OP (e.g., s-wave) at the site (m, n) times a phase factor. Winding numbers around the origin of s-wave and d-wave OPs are obtained for four types of solutions G _(l) (l = 0, 2, ± 1). It is shown that all energy bands of quasiparticles of a vortex lattice state are doubly degenerate.     

Inhibition of the formation of the B metastable phase in yttrium oxide plasma-spray coatings by the addition of zirconia

Yttrium oxide plasma-spray deposits show a metastable B phase together with the cubic stable form. This B form is prejudicial for thermal applications of these coatings (i.e. weakens mechanical properties, etc.). Attempts have been made to avoid the formation of this metastable phase during the plasma-spraying operation by use of an inhibitor, such as ZrO₂. A large solid solution with cubic C phase was found to form between ZrO₂ and Y₂O₃ (Y_1–xZr_xO_{1.5 + x/2 0.5 – /2}). A method is described for preparing powders suitable for plasma spraying. Several compositions were tested. B phase is no longer formed for ZrO₂ additions as low as x = 0.03. The influence of ZrO₂ addition on Y₂O₃ coatings properties is discussed.     

Specific Heat Jump at T<Emphasis Type="Italic">c</Emphasis> of High T<Emphasis Type="Italic">c</Emphasis> Superconductors: Effect of Van Hove Singularity

In the BCS framework, exact expressions for the ratio between the jump in the specific heat at T _c and the normal phase specific heat are derived within the Van Hove singularity scenario. Analytical results are obtained for an isotropic s-wave and anisotropic d-wave pairing symmetries. Graphical solutions of the ratio as functions of ω _D /T _c and E _F /T _c , where ω _D is the cutoff energy and E _F is the Fermi energy, show significant deviations from the BCS value of 1.43.     

Study of the Order Parameter Symmetry in Overdoped Y1−x Ca x Ba2Cu3O7−δ by Measurement of Andreev Reflection, Evidence for Enhancement of the Sub Dominant Order Parameter Amplitude in High Transparency Contacts

We have measured the differential conductance of Au/Y_1–x Ca _x Ba₂Cu₃O_7– point contacts in the regime where it is dominated by Andreev reflection, which enhances its value at low bias. We find that the characteristics can not be fitted by a pure d-wave Order Parameter (OP). Using the formalism developed by Kashiwaya and Tanaka, the best fits are obtained by adding a sub-dominant imaginary OP, whose amplitude appears to depend on the transparency of the contact. At high transparencies it can reach up to 60% of the total amplitude of the OP, for lower transparencies it is substantially smaller. We attribute this enhancement, at high transparencies to a proximity effect between the Au tip and the superconducting electrode.     

The microstructure and mechanical properties of yttria-stabilized zirconia prepared by arc-melting

The microstructure of ZrO₂-Y₂O₃ alloys prepared by arc-melting was examined mainly by electron microscopy. It was found that the microstructure changed markedly with yttria content between 0 and 8·7 mol%. Pure zirconia was a single monoclinic phase, while ZrO₂-8·7 mol% Y₂O₃ alloy was single cubic phase as expected from ZrO₂-Y₂O₃ phase diagram. Tetragonal phase was found in alloys with 1 to 6 mol% Y₂O₃ together with monoclinic or cubic phase. The tetragonal phase found in present alloys normally had a lenticular shape with a length 1 to 5m and a width 0.1 to 0.3m, which is much larger than that formed by annealing. The phase with a herring-bone appearance was found in alloys with Y₂O₃ between 2 and 3 mol%, which was recognized to be a metastable rhombohedral phase. The structure of the present alloys is likely to be formed by martensitic or bainitic transformation during fairly rapid cooling from the melt temperature. The change in hardness and toughness with yttria content of the alloys is discussed on the basis of microstructural observations.     

Top-Seeded Melt-Growth of YBa2Cus3Ox Crystals for Neutron Diffraction Studies

We have grown cubic centimeter-size crystals of YBa₂Cu₃O _x suitable for neutron studies, by a top-seeded melt-growth technique. Growth conditions were optimized with an eye toward maximizing phase purity. It was found that the addition of 2% Y₂BaCuO₅ and 0.5% Pt (by mass) were required to prevent melt loss and to obtain the highest crystallinity. A neutron diffraction study on a mosaic of six such crystals found that the final Y₂BaCuO₅ concentration was 5%, while other impurity phases comprised less than 1% by volume. The oxygen content was set to x = 6.5, the crystals were detwinned, and then carefully annealed to give the well-ordered ortho-II phase. The neutron study determined that 70% of the mosaic's volume was in the majority orthorhomic domain. The neutron (006) and (110) rocking curve widths were 1° per crystal and 2.2° for the mosaic, and the oxygen chain correlation lengths were >100 Å in the a- and b-directions and 50 Å in the c-direction.     

The influence off-wave pairing fluctuations on sound propagation in superfluid3He-A

The theory of sound propagation in pair-correlated Fermi liquids developed previously by Wölfle, with additionalf-wave pairing fluctuations, is applied to the ABM state. Expressions for the anisotropic sound absorption and velocity at arbitrary temperature and frequency in the collisionless limit are derived. Thef-wave pairing fluctuations give a large effect on the normal-flapping mode frequency at low temperatures. The corresponding shift in the sound attenuation peak of this collective mode provides a sensitive probe of thef-wave pair coupling constantg ₃. There is also a pronounced effect on the super-flapping mode attenuation peak, which becomes well defined whenf-wave pairing fluctuations are considered.     

Microwave Measurements of Overdoped Y0.9Ca0.1Ba2Cu3O7−δ Thin Films

In the present report we show, for the first time, that a complex order parameter is not just a surface effect, but a bulk property in overdoped Y_0.9Ca_0.1Ba₂Cu₃O_7– thin films. The penetration depth change versus temperature is very well fitted to a complex order parameter of the form d_x ^{2-y 2} + id _xy , where = 14.5 meV and = 2meV. This result contrasts our previous results for optimally doped YBCO thin films where a power law for the penetration depth, versus temperature was reported, corresponding to a d_x ^{2-y 2}-wave order parameter. The penetration depth behavior is accompanied by a rapid reduction of the scattering rate at low temperatures, in contrast with a flattening of this quantity for the optimally doped YBCO films.