The Specific Heat and the Fermi Surface Anisotropy in Sr2RuO4

The influence of the Fermi surface anisotropy on the specific heat jump is studied for the p-wave superconductor with a gap function d = z^(k _x ± ik _y ) in connection with Sr₂RuO₄. It is shown that the normalized specific heat jump, C/T _c , is reduced from its universal value, 1.43, in accordance with experimental findings. We show that this behavior fits well into our present understanding of the quasiparticle spectrum and the impurity effects.     

Chemical potential pinning near a van Hove singularity in the cuprates

The Fermi energy is shown to be pinned near a van Hove singularity for an extended doping range in the one-band and three-band Hubbard models as a consequence of filling dependent band renormalizations.     

Theory of Josephson Effect in Sr2RuO4/Diffusive Ferromagnet/Sr2RuO4 Junctions

We study Josephson effect in Sr₂RuO₄/insulator/diffusive ferromagnet (DF)/insulator/Sr₂RuO₄ junctions, solving the Usadel equation under a new boundary condition for DF/Sr₂RuO₄ interface. Josephson current is calculated changing temperatures, resistances of the interfaces between the DF and Sr₂RuO₄, the exchange field in the DF, and a length of the DF. We find that the exchange field can induce the 0–π transition in these junctions.     

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.     

Normal-state and superconducting properties of Sr2RuO4

We discuss some of the current issues on the copper-free layered perovskite superconductor Sr₂RuO₄, for which a sharp transition at T_c = 1.2 K has been reproducibly obtained. The normal state is characterized as an essentially twodimensional Fermi liquid, and the coherent interlayer transport is established only at low temperatures. The cylindrical Fermi surface observed by de Haas-van Alphen experiments is consistent with other thermodynamic and transport properties. Although the specific heat jump across T_cconfirms the bulk superconductivity, the large residual T-linear term which correlates with the variation in T_cis unusual and suggestive of unconventional pairing.On leave from Hiroshima University.     

p-Wave Superconductors in Sr2RuO4 and Bechgaard Salts

We review our recent works on the vortex state in p-wave superconductors. First, in a magnetic field parallel to the c-axis, the square vortex lattice is most stable, except in the immediate vicinity of T = T _c0. Second, the effect of impurities on H _c2 is studied, which exhibits characteristics of unconventional superconductors. Finally, the a–b anisotropy in the upper critical field in a magnetic field is considered. This anisotropy provides important information about the fourfold term arising from the Fermi surface effect.     

The Unconventional Superconductivity of Sr2RuO4

We review the evidence for unconventional superconductivity in Sr ₂ RuO ₄ ; the pairing in this material is certainly non-s-wave, and most of the current observations can be accounted for by a particular p-wave state, which is doubly degenerate and breaks time-reversal symmetry. Our observations of the flux lattice by small-angle neutron scattering contribute to this picture. The square flux lattice and the intensity of the diffracted signal indicate that superconductivity resides primarily on the sheet of the Fermi surface, which is derived from the Ru - d _xy orbitals. This is in agreement with the orbital-dependent p-wave scenario. Furthermore, the shape of the flux lines derived from these measurements is strongly indicative of a two-component order parameter.     

Fermi surface studies of the borocarbide superconductor YNi2B2C

The Fermi surface of the nonmagnetic borocarbide superconductor YN_i2B₂C was studied by the de Haas-van Alphen (dHvA) effect. Five branches of dH-vA frequencies are observed in the normal state for B c and the angular dependence was investigated with magnetic fields in the (110) plane. Together with the effective cyclotron masses, m_c, the result is discussed in the context of electronic band-structure calculations.This work has been supported by the Human Capital and Mobility Programme of the European Community through Grant No. ERBCH-BICT941212.     

Experimental Evidence for Spin-Triplet Superconductivity in Sr2RuO4

We review the experimental evidence for spin-triplet superconductivity in Sr₂RuO₄. The Knight shift experiments decisively demonstrated that the Cooper-pair symmetry is spin triplet. We discuss the most probable wave function of the Cooper pairs on the basis of the results of a number of key experiments. We point out that a simple picture of the unitary state with the isotropic gap is not compatible with the observed behavior of the specific heat, and that a profound modification of the pairing wave function is needed. We also present the in-plane angular dependence of the upper critical field, with the field applied exactly parallel to the quasi-two-dimensional plane. We discuss the possible implication of the observed fourfold anisotropy in connection with the proposed second superconducting state with a line-node gap.     

Electronic Theory for the Magnetic Anisotropy in Sr2RuO4

Using a three-band Hubbard Hamiltonian we calculated within the random-phase-approximation the spin susceptibility, χ(q, ω), and NMR spin-lattice relaxation rate 1/T ₁, in the normal state of the triplet superconductor Sr₂RuO₄, and obtained quantitative agreement with experimental data. Most importantly, we found that because of spin–orbit coupling the out-of-plane component of the spin susceptibility χ ^zz (q, ω) becomes two times larger than the in-plane one at low temperatures. We analyze in particular the role of the xy-band in the magnetic anisotropy.     

Ferromagnetic Correlations in Ca-Doped Sr2RuO4: 87Sr NMR Study

Magnetic properties on Sr_2–x Ca _x RuO₄ have been investigated by a microscopic probe of ⁸⁷Sr-NMR in order to understand the magnetic character on spin-triplet superconductor of Sr₂RuO₄, which has multibands on the Fermi surface. With substituting Ca for Sr which gives rise to crystal distortion, the Knight shift (K) and the nuclear spin-lattice relaxation rate divided by temperature (1/T _{1 T}) increases progressively up to x=1.5. The Korringa relation from K and 1/T ₁ T becomes smaller, indicative of development of ferromagnetic fluctuations with increasing Ca content. This suggests that the q-independent spin fluctuations originating from the 2-dimensional band are changed to the ferromagnetic ones by the Ca doping.     

LCAO analysis of Sr2RuO4 band structure

A simple tight-binding model for the conduction band of Sr₂Ru0₄ is presented. The Ru4d and 02p orbitals of RuU₂ conduction plane are taken into account. In momentum representation the LCAO Hamiltonian has a block structure, containing hopping amplitudes between the in-plane orbitals O_a2p_y, O_b2p_x, Ru4d_xy, and those vertical to RuO₂ plane — Ru4d_yz, Ru4d_zx, O_a2_pz and O_b2_pz. This simple structure allows an analytical derivation of electron band dispersions (p_x,P_y) and constant energy contours (p_x,p_y) = const. The energy surfaces (p_x,P_y) (numerically calculated) are also related to angle-resolved photoemission spectra. Based on the analytical results a fitting philosophy for both the available experimental data and ab initio calculations is discussed. The tight-binding parameters calculated within the adopted model are found to be in acceptable agreement with the first principles calculations.     

Tunneling and Phase-Sensitive Studies of the Pairing Symmetry in Sr2RuO4

Results obtained from several tunneling experiments on the pairing symmetry in Sr₂RuO₄ are reported. A normal surface layer was found to be present on the ab face of single-crystalline Sr₂RuO₄ in the c-axis tunnel junctions. Measurements in the in-plane junctions, however, revealed features suggesting a suppressed, but non-zero superconducting gap and Andreev bound states (ABSs) associated only with an unconventional superconductor. Josephson coupling between a conventional s-wave superconductor and Sr₂RuO₄ has been used to probe the pairing symmetry in the latter, through both the selection rule and the phase sensitive experiments. All results indicate that Sr₂RuO₄ is unconventional, most likely spin-triplet superconductor. Finally, some recent studies of several newly-characterized ruthenates are reviewed.     

Theoretical Consideration on Triplet Superconductivity in UPt3 and Sr2RuO4

Two representative superconductors, UPt₃ and Sr₂RuO₄, are comparatively studied on the basis of a general symmetry argument. The existing experimental data set for both systems strongly and commonly points to a triplet pairing. For the former, heavy fermion material, UPt₃, a non-unitary bipolar state is the most possible candidate, whereas for the latter system, Sr₂RuO₄, determination of a precise pairing symmetry class, either unitary or non-unitary, is debated.     

Crossover from 3D to 2D metallic conduction in Sr2RuO4

We have investigated the normal-state conduction of superconducting Sr₂RuO₄ (T_c 1K), which is isostructural to La_2–xSr_xCuO₄. The resistivity of single crystals shows a crossover at T_M130K from 3D metallic conduction at lower temperatures to 2D one at higher temperatures. Concerning the temperature dependence of the out-of-plane resistivity, we present a systematic interpretation based on competition between the life time of the quasiparticles and the time for the quasiparticles to travel between the adjacent RuO₂ planes.     

17O Knight shift study in the superconducting state of Sr2RuO4

¹⁷O Knight shift measurements in Sr₂RuO₄ were performed over the wide range of magnetic field 3.2-11.4kOe parallel to the basal RuO₂ planes. The spin susceptibility is totally unchanged through its T_c, evidencing that the spin-triplet superconducting state is realized in Sr₂RuO₄. The result indicates that the Cooper pairs consist of the parallel spin pairs | > and | > with their quantization axis perpendicular to the c-axis direction. The in-plane 2D nearly ferromagnetic spin fluctuations may play a role for the stabilization of this state among various representations of spin-triplet order parameter.     

Optical Conductivity in the van Hove Scenario

We calculate the conductivity in the ab plane for a superconductor assumed to have a saddle point in the energy surface due to the logarithmic density of states. The influence of the optical phonons was taken into account. At sufficient high temperatures (corresponding to the normal phase) the conductivity is characterized by a Drude-like behavior.     

Superconducting Properties of the 3-K Phase of Sr2RuO4 near Hc2

The superconducting transition temperature, T _c , of the impurity-free, intrinsic Sr₂RuO₄ is as high as 1.50 K. However, we recently showed that T _c is remarkably increased up to 3 K in the Sr₂RuO₄–Ru eutectic system, in which plate-like microdomains of Ru metal are embedded in the primary-phase Sr₂RuO₄. The phase diagram of the anisotropic upper critical field of the 3-K phase indicates that H _c2 for the field parallel to the RuO₂ plane is strongly suppressed at low temperatures. We argue that the reorientation of the Cooper-pair spin direction near the Sr₂RuO₄–Ru interface may be responsible for this suppression. In addition, we observed unusual hysteresis in the out-of-plane resistivity, ρ _c , at low temperatures and near H _c2, only when the field was applied parallel to the RuO₂ plane.     

Superconductivity in Cuprates, the van Hove Scenario

We review the consequences of the presence of van Hove singularities close to the Fermi level in the HTCS cuprates. We show that it may explain the properties of these materials such as the high T _c, anomalous isotope effect, marginal Fermi liquid properties, gap anisotropy, etc. We show that the pseudogap observed in the normal state can be attributed to the Coulomb interaction between carriers in these disordered compounds.