Vortex with Fractional Quantum Numbers in Chiral p-Wave Superconductor

We show that a vortex in a chiral p-wave superconductor, which has the p_{x}+ i p_{y}-wave pairing state and breaks U(1), parity and time reversal symmetry simultaneously, has fractional charge -{n e}/{4} and fractional angular momentum -n^{2}/{16} (n; vorticity). This suggests that the vortex could be anyon and could obey fractional statistics. Electromagnetic property of the vortex is also discussed and we find that an electric field is induced near the vortex core.Comment: 10 pages, 3 figures, accepted for publication in Phys. Rev.

Thermal Conductivity near H_c2 for spin-triplet superconducting States with line nodes in Sr_2RuO_4

We calculate the thermal conductivity kappa in magnetic fields near H_c2 for spin-triplet superconducting states with line nodes vertical and horizontal relative to the RuO_2-planes. The method for calculating the Green's functions takes into account the spatial variation of the order parameter and superconducting flow for the Abrikosov vortex lattice. For in-plane magnetic field we obtain variations of the in-plane kappa with two-fold symmetry as a function of rotation angle where the minima and maxima occur for field directions parallel and perpendicular to the heat flow. The amplitude of the variation decreases with increasing impurity scattering and temperature. At higher temperatures the minima and maxima of the variation are interchanged. Since the results for vertical and horizontal line nodes are almost the same we cannot say which of the two pairing models is more compatible with recent measurements of kappa in Sr_2RuO_4. The observed four-fold modulation of kappa in YBa_2Cu_3O_(7-\delta) is obtained for d-wave pairing by taking into account the particular shape of the Fermi surface and the finite temperature effect. The results for kappa for the f-wave pairing state with horizontal line nodes disagree in some respects with the measurements on UPt_3.Comment: 8 pages, 6 figures. To be published in Phys. Rev.

Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

Spin Ordering and Quasiparticles in Spin Triplet Superconducting Liquids

Spin ordering and its effect on low energy quasiparticles in a p-wave superconducting liquid are investigated. We show that there is a new 2D p-wave superconducting liquid where the ground state is rotation invariant. In quantum spin disordered liquids, the low energy quasiparticles are bound states of the bare Bogolubov- De Gennes ({\em BdeG}) quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low energy limit. Further more, spin collective excitations are fractionalized ones carrying a half spin and obeying fermionic statistics. In thermally spin disordered limits, the quasi-particles are bound states of bare {\em BdeG} quasi-particles. The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.Comment: 5 pages, no figures; published versio

Theory of NMR as a local probe for the electronic structure in the mixed state of the high-TcT_c cuprates

We argue that nuclear magnetic resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin-susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} a temperature dependence of $T_1$ which varies with frequency. We propose a nuclear quadrupole experiment to study the effects of a uniform supercurrent on the electronic structure and predict that $T_1$ varies with the direction of the supercurrent.Comment: RevTex, 5 pages, 3 figures embedded in the tex

Atomistic Studies of Defect Nucleation during Nanoindentation of Au (001)

Atomistic studies are carried out to investigate the formation and evolution of defects during nanoindentation of a gold crystal. The results in this theoretical study complement the experimental investigations [J. D. Kiely and J. E. Houston, Phys. Rev. B, v57, 12588 (1998)] extremely well. The defects are produced by a three step mechanism involving nucleation, glide and reaction of Shockley partials on the {111} slip planes noncoplanar with the indented surface. We have observed that slip is in the directions along which the resolved shear stress has reached the critical value of approximately 2 GPa. The first yield occurs when the shear stresses reach this critical value on all the {111} planes involved in the formation of the defect. The phenomenon of strain hardening is observed due to the sessile stair-rods produced by the zipping of the partials. The dislocation locks produced during the second yield give rise to permanent deformation after retraction.Comment: 11 pages, 13 figures, submitted to Physical Review

Low temperature electronic properties of Sr_2RuO_4 II: Superconductivity

The body centered tetragonal structure of Sr_2RuO_4 gives rise to umklapp scattering enhanced inter-plane pair correlations in the d_{yz} and d_{zx} orbitals. Based on symmetry arguments, Hund's rule coupling, and a bosonized description of the in-plane electron correlations the superconducting order parameter is found to be a orbital-singlet spin-triplet with two spatial components. The spatial anisotropy is 7%. The different components of the order parameter give rise to two-dimensional gapless fluctuations. The phase transition is of third order. The temperature dependence of the pair density, specific heat, NQR, Knight shift, and susceptibility are in agreement with experimental results.Comment: 20 pages REVTEX, 3 figure

Low temperature electronic properties of Sr_2RuO_4 III: Magnetic fields

Based on the microscopic model introduced previously the observed specific heat and ac-susceptibility data in the superconducting phase in Sr_2RuO_4 with applied magnetic fields are described consistently within a phenomenological approach. Discussed in detail are the temperature dependence of the upper critical fields H_{c2} and H_2, the dependence of the upper critical fields on the field direction, the linear specific heat below the superconducting phase transition as a function of field or temperature, the anisotropy of the two spatial components of the order parameter, and the fluctuation field H_p.Comment: 8 pages REVTEX, 4 figure

Recent developments in unconventional superconductivity theory

The review of recent developments in the unconventional superconductivity theory is given. In the fist part I consider the physical origin of the Kerr rotation polarization of light reflected from the surface of superconducting $Sr_2RuO_4$. Then the comparison of magneto-optical responses in superconductors with orbital and spin spontaneous magnetization is presented. The latter result is applied to the estimation of the magneto-optical properties of neutral superfluids with spontaneous magnetization. The second part is devoted to the natural optical activity or gyrotropy properties of noncentrosymmetric metals in their normal and superconducting states. The temperature behavior of the gyrotropy coefficient is compared with the temperature behavior of paramagnetic susceptibility determining the noticeable increase of the paramagnetic limiting field in noncentrosymmetric superconductors. In the last chapter I describe the order parameter and the symmetry of superconducting state in the itinerant ferromagnet with orthorhombic symmetry. Finally the Josephson coupling between two adjacent ferromagnet superconducting domains is discussed.Comment: 15 page

Field dependence of the vortex structure in chiral p-wave superconductors

To investigate the different vortex structure between two chiral pairing p_x +(-) i p_y, we calculate the pair potential, the internal field, the local density of states, and free energy in the vortex lattice state based on the quasiclassical Eilenberger theory, and analyze the magnetic field dependence. The induced opposite chiral component of the pair potential plays an important role in the vortex structure. It also produces H^{1/2}-behavior of the zero-energy density of states at higher field. These results are helpful when we understand the vortex states in Sr2RuO4.Comment: 11 pages, 10 figures, to be published in Phys. Rev.