Out of plane optical conductivity in d-wave superconductors

We study theoretically the out of plane optical conductivity of d-wave superconductors in the presence of impurities at T=0K. Unlike the usual approach, we assume that the interlayer quasi-particle transport is due to coherent tunneling. The present model describes the T^2 dependence of the out of plane superfluid density observed in YBCO and Tl2201 for example. In the optical conductivity there is no Drude peak in agreement with experiment, and the interlayer Josephson tunneling is also assured in this model. In the unitary limit we predict a step like behaviour around omega=Delta in both the real and imaginary part of the optical conductivity.Comment: 7 pages, 7 figure

Nonlinear response and scaling law in the vortex state of d-wave superconductors

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 figure

Low-lying excitations around a single vortex in a d-wave superconductor

A full quantum-mechanical treatment of the Bogoliubov-de Gennes equation for a single vortex in a d-wave superconductor is presented. First, we find low-energy states extended in four diagonal directions, which have no counterpart in a vortex of s-wave superconductors. The four-fold symmetry is due to 'quantum effect', which is enhanced when $p_{F}\xi$ is small. Second, for $p_{F}\xi \sim 1$, a peak with a large energy gap $E_{0}\sim \Delta$ is found in the density of states, which is due to the formation of the lowest bound states.Comment: 7pages, Revte

Superconducting Gap Function in Antiferromagnetic Heavy-Fermion UPd_2Al_3 Probed by Angle Resolved Magnetothermal Transport Measurements

The superconducting gap structure of heavy fermion UPd_2Al_3, in which unconventional superconductivity coexists with antiferromagnetic (AF) order with atomic size local moments, was investigated by the thermal conductivity measurements in a magnetic field rotating in various directions relative to the crystal axes. The results provide strong evidence that the gap function \Delta(k) has a single line node orthogonal to the c-axis located at the AF Brillouin zone boundary, while \Delta(k) is isotropic within the basal plane. The determined nodal structure is compatible with the resonance peak in the dynamical susceptibility observed in neutron inelastic scattering experiments. Based on these results, we conclude that the superconducting pairing function of UPd_2Al_3 is most likely to be d-wave with a form \Delta(k)=\Delta_0 cos(k_zc)Comment: 10 pages, 9 figure

Collective modes and sound propagation in a p-wave superconductor: Sr2_2RuO4_4

There are five distinct collective modes in the recently discovered p-wave superconductor Sr$_2$RuO$_4$; phase and amplitude modes of the order parameter, clapping mode (real and imaginary), and spin wave. The first two modes also exist in the ordinary s-wave superconductors, while the clapping mode with the energy $\sqrt{2} \Delta(T)$ is unique to Sr$_2$RuO$_4$ and couples to the sound wave. Here we report a theoretical study of the sound propagation in a two dimensional p-wave superconductor. We identified the clapping mode and study its effects on the longitudinal and transverse sound velocities in the superconducting state. In contrast to the case of $^3$He, there is no resonance absorption associated with the collective mode, since in metals $\omega/(v_F |{\bf q}|) \ll 1$, where $v_F$ is the Fermi velocity, {\bf q} is the wave vector, and $\omega$ is the frequency of the sound wave. However, the velocity change in the collisionless limit gets modified by the contribution from the coupling to the clapping mode. We compute this contribution and comment on the visibility of the effect. In the diffusive limit, the contribution from the collective mode turns out to be negligible. The behaviors of the sound velocity change and the attenuation coefficient near $T_c$ in the diffusive limit are calculated and compared with the existing experimental data wherever it is possible. We also present the results for the attenuation coefficients in both of the collisionless and diffusive limits at finite temperatures.Comment: RevTex, 12 pages, 2 figures, Replaced by the published versio

Novel vortex lattice transition in d-wave superconductors

We study the vortex state in a magnetic field parallel to the $c$ axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to $\cos(4\phi)$ where $\phi$ is the angle ${\bf r}$ makes with the $a$-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to $(1,1,0)$ or $(1,-1,0)$. We predict the first order vortex lattice transition at $B=H_{cr}\sim \kappa^{-1} H_{c2}(t)$ from triangular into the square lattice tilted by $45^\circ$ from the $a$ axis. This gives the critical field $H_{cr}$ a few Tesla for YBCO and Bi2212 monocrystals at low temperatures ($T\leq 10 K$).Comment: 6 pages, 4 figure

Gap Symmetry of Superconductivity in UPd2Al3

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 replacemen

Half quantum vortex in superfluid 3^3He-A phase in parallel plate geometry

The half quantum vortex(HQV) in condensate has been studied, since it was predicted by Salomaa and Volovik in superfluid $^3$He-A phase. However, an experimental evidence for its existence has not been reported so far. Motivated by a recent experimental report by Yamashita et al\cite{yamashita}, we study the HQVs in superfluid $^3$He confined between two parallel plates with a gap D $\sim$ 10 $\mu$m in the presence of a magnetic field H $\sim$ 26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, $\Omega_c \sim$ 2 rad/s. The bound pair of HQVs accompanies the tilting of ${\hat d}$-vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in $^3$He.Comment: 5 pages, 5 figure

Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?

We investigate whether the lepton flavor mixing angles in the so-called democratic type of mass matrix are stable against quantum corrections or not in the minimal supersymmetric standard model with dimension five operator which induces neutrino mass matrix. By taking simple breaking patterns of $S_3{}_L \times S_3{}_R$ or $O(3)_L \times O(3)_R$ flavor symmetries and the scale where democratic textures are induced as $O(10^{13})$ GeV, we find that the stability of the lepton flavor mixing angles in the democratic type of mass matrix against quantum corrections depends on the solar neutrino solutions. The maximal flavor mixing of the vacuum oscillation solution is spoiled by the quantum corrections in the experimental allowed region of $\tan \beta$. The large angle MSW solution is spoiled by the quantum corrections in the region of $\tan \beta > 10$. The condition of $\tan \beta \leq 10$ is needed in order to obtain the suitable mass squared difference of the small angle MSW solution. These strong constraints must be regarded for the model building of the democratic type of mass matrixComment: 12pages,LaTe

Impurity scattering in unconventional density waves

We have investigated the effect of nonmagnetic impurities on the quasi-one-dimensional unconventional density wave (UDW) ground state. The thermodynamics were found to be close to those of a d-wave superconductor in the Born limit. Four different optical conductivity curves were found depending on the direction of the applied electric field and on the wavevector dependence of the gap.Comment: 14 pages, 9 figure