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

Nematicity as a route to a magnetic field-induced spin density wave order; application to the high temperature cuprates

The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a critical magnetic field leading to a field-induced spin density wave order. Both commensurate and incommensurate orders are studied, and the experimental implications of our findings are discussed.Comment: 5 pages, 3 figure

A novel route to a finite center-of-mass momentum pairing state; current driven FFLO state

The previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is stabilized by a magnetic field via the Zeeman coupling in spin-singlet superconductors. Here we suggest a novel route to achieve non-zero center-of-mass momentum pairing states in superconductors with Fermi surface nesting. We investigate two-dimensional superconductors under a uniform external current, which leads to a finite pair-momentum of ${\bf q}_{e}$. We find that an FFLO state with a spontaneous pair-momentum of ${\bf q}_{s}$ is stabilized above a certain critical current which depends on the direction of the external current. A finite ${\bf q}_s$ arises in order to make the total pair-momentum of ${\bf q}_t(={\bf q}_s + {\bf q}_e)$ perpendicular to the nesting vector, which lowers the free energy of the FFLO state, as compared to the superconducting and normal states. We also suggest experimental signatures of the FFLO state.Comment: 4 pages, 5 figure

Critical Current of the Spin-Triplet Superconducting Phase in Sr2_2RuO4_4

There have been two different proposals for the spin-triplet order parameter of the superconducting phase in Sr$_2$RuO$_4$; an $f$-wave order parameter and the multigap model where some of the bands have the line node. In an effort to propose an experiment that can distinguish two cases, we study the behavior of the supercurrent and compute the critical current for these order parameters when the sample is a thin film with the thickness $d \ll \xi$ where $\xi$ is the coherence length. It is found that the supercurrent behaves very differently in two models. This will serve as a sharp test for the identification of the correct order parameter.Comment: 4 pages, 1 figur

The Trinidad and Tobago/Venezuela Fishing Agreement

The twin-island Republic of Trinidad and Tobago is situated adjacent to the Republic Of Venezuela such that at one point Trinidad is merely seven miles off the northeast coast of Venezuela. Fishing activities of nationals of each country in the waters of the other are therefore common and often lead to conflict. In an attempt to solve the fishing problem a fishing agreement was negotiated. It came into force in 1978 and expired in 1984 whereupon negotiations commenced once more in an attempt to achieve new accord. The fishing industries of both countries and the conflicts which led to the agreement are described. Fishing activities by nationals of each state in the waters of the other are detailed and values of these catches are estimate and compared. Conflicts and problems related to treaty implementation are discussed and proposals for a new agreement suggested. Indications are that Venezuela was the greater beneficiary of the agreement in terms of quality and value of catch; number of boats fishing and number of men employed; diversity of species landed. Four proposals which could lead to a more equitable agreement than the last are suggested. These proposals include options outside of the terms of the last agreement but which, if implemented, would be of benefit to both parties while simultaneously establishing closer relations over a wider sphere of activities

Ecogeographical variations of chromosomal polymorphism in Hawaiian populations of Drosophila immigrans

Reports were scanned in black and white at a resolution of 600 dots per inch and were converted to text using Adobe Paper Capture Plug-in.Eighteen samples from twelve populations of Drosophila immigrans in the islands of Kauai, Oahu and Hawaii in the Hawaiian archipelago were analyzed for inversion polymorphism in 1125 females and 206 males. Three kinds of second chromosome inversions, which appear to be identical with those previously reported by other workers, were present in all of our populations; two other new inversions of the same autosome were detected from the Hawaii collections, but their origin, whether natural or laboratory, could not be assured. The average proportion of inversion heterozygosity per individual of the populations from Kauai, Oahu and Hawaii was about 34%, 32% and 65% respectively. The frequencies of heterozygous inversions Here similar between different populations within islands (with one notable exception on Hawaii). In contrast, the frequencies were significantly heterogeneous from one island to the next. The results of gene arrangement frequency analysis consolidated the above findings. It is suggested that the inter-island differentiations are due to natural selection and probably maintained by the isolation by oceanic channels. Two near-by localities on Hawaii were inhabited with significantly heterogeneous populations. Such a microgeographic differentiation has been interpreted as being due to the presence of highly localized, differential selection forces in the two localities, and the difference seems to be maintained due to isolation by the lava flows. Our data suggest that the breeding units of Hawaiian populations of D. immigrans are not so small as to allow for genetic drift to significantly affect the populations. Inversion polymorphism was similar between females and males taken at the same time in the same localities

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

Supercurrent in Nodal Superconductors

In recent years, a number of nodal superconductors have been identified; d-wave superconductors in high T_c cuprates, CeCoIn$_5$, and \kappa-(ET)_2Cu(NCS)_2, 2D f-wave superconductor in Sr_2RuO_4 and hybrid s+g-wave superconductor in YNi_2B_2C. In this work we conduct a theoretical study of nodal superconductors in the presence of supercurrent. For simplicity, we limit ourselves to d-wave and 2D f-wave superconductors. We compute the quasiparticle density of states and the temperature dependence of the depairing critical current in nodal superconductors, both of which are accessible experimentally.Comment: revtex4, 6 pages, 7 figures; fixed typos, updated references, trimmed introductio