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We study the upper critical field of the A and B phases in the triplet superconductor PrOs_{4}Sb_{12} within the p+h-wave superconductivity proposed recently for this material. The present result is compared with H_{c2}(t) and H*(t), the boundary between the A and B phase in PrOs_{4}Sb_{12}, reported earlier and with more recent data of H$_{c2}(t)$ for the single phase crystal. We find H_{c2}(t)'s for both the two phase crystal and the single phase crystal are described by the model for the A phase. From this fitting one can deduce the Fermi velocity as v=2.5 x 10^6 cm/s. On the other hand H_{c2}(t) for the B phase is found to be somewhat smaller than H*(t), which is rather puzzling., Comment: 6 pages, 3 figures

Since the discovery of the high-T$_{c}$ cuprate superconductor La$_{2-x}$BaCuO$_{4}$ in 1986 by Bednorz and M\"{u}ller, controversy regarding the nature or origin of this remarkable superconductivity has continued. However, d-wave superconductivity in the hole-doped cuprates, arising due to the anti-paramagnon exchange, was established around 1994. More recently we have shown that the mean field theory, like the BCS theory of superconductivity and Landau's Fermi liquid theory are adequate to describe the cuprates. The keys for this development are the facts that a)the pseudogap phase is d-wave density wave (dDW) and that the high-T$_{c}$ cuprate superconductivity is gossamer (i.e. it exists in the presence of dDW)., Comment: 6 pages, 4 figures

In contrast to multigap superconductors (e.g. MgB$_{2}$), the low-temperature properties of nodal superconductors are dominated by nodal excitations. Here we extend for a variety of nodal superocnductors the earlier work by Simon and Lee and K\"ubert and Hirschfeld. The scaling relations seen in the thermodynamics and the thermal conductivity will provide an unequivocal test of nodal superconductivity., Comment: 9 pages, 3 figures

We shall review our recent works on d-wave density wave (dDW) and gossamer superconductivity (i.e. d-wave superconductivity in the presence of dDW) in high-T$_{c}$ cuprates and CeCoIn$_{5}$. a) We show that both the giant Nernst effect and the angle dependent magnetoresistance (ADMR) in the pseudogap phases of the cuprates and CeCoIn$_{5}$ are manifestations of dDW. b) The phase diagram of high-T$_{c}$ cuprates is understood in terms of mean field theory, which includes two order parameters $\Delta_{1}$ and $\Delta_{2}$, where one order parameter is from dDW and the other from d-wave superconductivity. c) In the optimally to the overdoped region we find the spatially periodic dDW, an analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, becomes more stable. d) In the underdoped region where $\Delta_{2}/\Delta_{1} \ll 1$ the Uemera relation is obtained within the present model. We speculate that the gossamer superconductivity is at the heart of high-T$_{c}$ cuprate superconductors, the heavy-fermion superconductor CeCoIn$_{5}$ and the organic superconductors $\kappa$- (ET)$_{2}$Cu(NCS)$_{2}$ and (TMTSF)$_2$PF$_{6}$.

After a brief introduction on nodal superconductors, we review the topological defects in triplet superconductors such as UPt$_{3}$, Sr$_{2}$RuO$_{4}$, etc. This is in part motivated by the surprising discovery of Ana Celia Mota and her colleagues that in some triplet superconductors the flux motion is completely impeded (the ideal pinning). Among topological defects the most prominent is Abrikosov's vortex with quantum flux $\phi_{0}= \frac{hc}{2e}$. Abrikosov's vortex is universal and ubiquitous and seen in both conventional and unconventional superconductors by the Bitter decoration technique, small angle neutron scattering (SANS), scanning tunneling microscopy (STM), micromagnetometer and more recently by Lorentz electron micrograph. In order to interpret the experiment by Mota et al a variety of textures are proposed. In particular, in analogy to superfluid $^{3}$He-A the $\hat{\ell}$-soliton and $\hat{d}$-soliton play the prominent role. We review these notions and point out possible detection of these domain walls and half-quantum vortices in some triplet superconductors., Comment: 6 pages, 4 figures

Scaling relations are one of the hallmarks of nodal superconductivity since they contain information characteristic for gapless order parameters. In this paper we derive the scaling relations for the thermodynamics and the thermal conductivity in the vortex state of the A and B phases of the skutterudite PrOs4Sb12. Experimental confirmation of these scaling relations can provide further support for anisotropic gap functions which were previously considered for this material., Comment: 11 pages, 3 figures

This course has a dual purpose. First we review the successes of the weak-coupling BCS theory in describing new classes of superconductors discovered since 1979. They include the heavy-fermion superconductors, high-Tc cuprate superconductors, organic superconductors, Sr2RuO4, etc. Second, we present the quasiclassical approximation introduced by Volovik, which we extend to describe the thermodynamics and the thermal conductivity of the vortex state in nodal superconductors. This approach provides the most powerful tool to identify the symmetry of the energy gap function Delta(k) in these new superconductors., Comment: 31 pages, 33 figures

Here we consider the universal heat conduction and the angular dependent thermal conductivity in the vortex state for a few nodal superconductors. We present the thermal conductivity as a function of impurity concentration and the angular dependent thermal conductivity in a few nodal superconductors. This provides further insight in the gap symmetry of superconductivity in Sr$_2$RuO$_4$ and UPd$_2$Al$_3$., Comment: 2 pages, proceedings of SCES '04

The angle dependent thermal conductivity of the heavy-fermion superconductor UPd$_2$Al$_3$ in the vortex state was recently measured by Watanabe et al. Here we analyze this data from two perspectives: universal heat conduction and the angle-dependence. We conclude that the superconducting gap function $\Delta({\bf k})$ in UPd$_2$Al$_3$ has horizontal nodes and is given by $\Delta({\bf k}) =\Delta\cos(2\chi)$, with $\chi = ck_{z}$., Comment: 8 pages, 4 figures, improved figures in replacement

Since 1979, many new classes of superconductors have been discovered, including heavy-fermion compounds, organic conductors, high-Tc cuprates, and Sr2RuO4. Most of these superconductors are unconventional and/or nodal. Therefore it is of central importance to determine the symmetry of the order parameter in each of these superconductors. In particular, the angular-controlled thermal conductivity in the vortex state provides a unique means of investigating the nodal structure of the superconducting energy gap when high-quality single crystals in the extremely clean limit are available. Using this method, Izawa et al have recently succeeded in identifying the energy gap symmetry of superconductivity in Sr2RuO4, CeCoIn5, kappa-(ET)2Cu(NCS)2, YNi2B2C, and PrOs4Sb12., Comment: 23 pages, 11 figures

Recently a hybrid s+g-wave pairing is proposed to describe the experimental observation for a nodal structure of the superconducting gap in borocarbide YNi$_2$B$_2$C and possibly LuNi$_2$B$_2$C. In this paper the impurity effects on the s+g-wave superconductivity are studied in both Born and unitarity limit. The quasiparticle density of states and thermodynamics are calculated. It is found that the nodal excitations in the clean system are immediately prohibited by impurity scattering and a finite energy gap increases quickly with the impurity scattering rate. This leads to an activated behavior in the temperature dependence of the specific heat. Qualitative agreement with the experimental results is shown. Comparison with d-wave and some anisotropic s-wave studied previously is also made., Comment: 6 pages, 6 eps figures

How to determine the symmetry of the superconducting order parameter is one of the important issues in novel superconductors, which include charge conjugated organic superconductors. We have proposed that the angular dependence of the thermal conductivity in a planar magnetic field provides a new window to look at the symmetry of the order parameter. After a brief summary of the quasiclassical approach we describe how the symmetry of the superconducting order parameter in Sr$_2$RuO$_4$, CeCoIn$_5$ and $\kappa$-(ET)$_2$Cu(NCS)$_2$ is determined. Also in some of experiments the phononic thermal conductivity plays the crucial role., Comment: 5 pages, 3 figures. to be published in Synthetic Metals

Recently we have proposed a s+g-wave model for the superconductivity in borocarbides, YNi2B2C and LuNi2B2C. In the present paper we first summarize thermodynamic properties of s+g-wave model. Then we shall analyse the recent Raman spectra data of RNi2B2C (with R=Lu and Y) by Yang et al. The present model appears to describe salient features of the Raman spectra., Comment: 7pages, 5figures

We propose a model of nodal order parameters for the superconducting A and B - phase of skutterudite PrOs_4Sb_{12} and discuss the associated angular dependent magnetothermal conductivity at low temperatures. The model for the hybrid gap functions \De(k) containing an s- and g- wave parts is consistent with recent thermal conductivity experiments in PrOs_4Sb_12. In particular the model accounts for the data on polar an azimuthal field angle dependence of \kappa_zz(\theta,\phi). The low temperature behaviour of thermodynamic properties in zero field is also presented. We show that the effect of impurity scattering on a nodal hybrid gap function immediately leads the opening of a gap and related exponential behaviour of low temperature specific heat and thermal conductivity which is very different from d- wave superconductors., Comment: 7 pages, 3 figures

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered d-wave superconductors such as high $T_c$ cuprates and $\kappa$-(ET)$_2$ salts in a planar magnetic field. We show the superconducting order parameter forms two dimensional crystalline lattice in the FFLO state for d-wave superconductors. Also the quasiparticle density of states and the thermodynamics of FFLO state are constructed. Therefore STM or NMR will provide a definitive test for the existence of the FFLO state., Comment: 5 pages including 2 figures

The symmetry of superconductivity in borocarbides LuNi2B2C and YNi2B2C is an outstanding issue. Here an anisotropic s- wave order parameter (or s+g model) is proposed for these borocarbides. In spite of the dominant s- wave component the proposed superconducting order parameter has nodes and gives rise to the H^(1/2) dependent specific heat in the vortex state (the Volovik effect). This model predicts the fourfold symmetry both in the angular dependent thermal conductivity and in the excess Dingle temperature in the vortex state, which should be readily accessible experimentally., Comment: 4 pages, 3 figures

We study the field dependence of the quasi-particle density of states, the thermodynamics and the transport properties in the vortex state of d-wave superconductors when a magnetic field is applied perpendicular to the conducting plane, specially for the low field and the low temperature compared to the upper critical field and transition temperature, respectively, $H/H_{c2} \ll 1$ and $T/T_c \ll 1$. Both the superfluid density and the spin susceptibility exhibit the characteristic $\sqrt{H}$-field dependence, while the nuclear spin lattice relaxation rate T$_1^{-1}$ and the thermal conductivity are linear in field $H$. With increasing temperature, these quantities exhibit the scaling behavior in $T/\sqrt{H}$. The present theory applies to 2D $f$-wave superconductor as well; a possible candidate of the superconductivity in Sr$_2$RuO$_4$., Comment: 11 pages, 4 figures

Recent experimental data on purest Sr_2RuO_4 single crystals clearly indicate the presence of nodes in the superconducting order parameter. Here, we consider one special p-wave order parameter symmetry and two two-dimensional f-wave order parameter symmetries having nodes within the RuO_2 plane. These states reasonably describe both specific heat and penetration depth data. We calculate the thermal conductivity tensor for these three states and compare the results with recent thermal conductivity data. This allows us to single out one of these states being consistent with both thermodynamic and thermal conductivity data: the planar f-wave state having B_{1g} x E_u symmetry., Comment: 4 pages, 4 figures

Until recently it has been believed that the superconductivity in Sr$_2$RuO$_4$ is described by p-wave pairing. However, both the recent specific heat and the magnetic penetration depth measurements on the purest single crystals of Sr$_2$RuO$_4$ appear to be explained more consistently in terms of f-wave superconductivity. In order to further this hypothesis, we study theoretically the thermodynamics and thermal conductivity of f-wave superconductors in a planar magnetic field. We find the simple expressions for these quantities when $H \ll H_{c2} $ and $T \ll T_{c}$, which should be readily accessible experimentally., Comment: 6 pages, 2 figures

Quasiparticle spectrum associated with the nodal structure in d-wave superconductors is of great interest. We study theoretically the quasi-particle spectrum in a planar magnetic field, where the effect of the magnetic field is treated in terms of the Doppler shift. We obtain the angular dependent specific heat in the presence of a planar magnetic field and impurities, both in the superclean limit (Gamma/Delta << H/H_{c2}<< 1) and in the clean limit (H/H_{c2} << Gamma/Delta <<1). Also a similar analysis is used for the thermal conductivity tensor within the a-b plane. In particular, in contrast to the earlier works, we find a fourfold symmetry term in \kappa_{\parallel} and \kappa_{\perp} \sim -H \sin(2\theta) where kappa_{perp} are the diagonal- and the off-diagonal components of the thermal conductivity tensor and \theta is the angle between the heat current and the magnetic field., Comment: RevTex, 5 pages, 5 postscript figures

We study theoretically the paramagnetic state in d-wave superconductors. We present the specific heat, the magnetization, superfluid density obtained within the weak-coupling model. At low temperatures and for small magnetic fields they exhibit simple power law behaviors, which should be accessible experimentally in hole-doped high-T_c cuprates and \kappa-(ET)_2 salts in a magnetic field within the conducting plane., Comment: 5 pages(EuroTeX), 13 figures, submitted to Europhysics Letters