Low-TT Phononic Thermal Conductivity in Superconductors with Line Nodes

The phonon contribution to the thermal conductivity at low temperature in superconductors with line nodes is calculated assuming that scattering by both nodal quasiparticles and the sample boundaries is significant. It is determined that, within the regime in which the quasiparticles are in the universal limit and the phonon attenuation is in the hydrodynamic limit, there exists a wide temperature range over which the phonon thermal conductivity varies as $T^2$. This behaviour comes from the fact that transverse phonons propagating along certain directions do not interact with nodal quasiparticles and is thus found to be required by the symmetry of the crystal and the superconducting gap, independent of the model used for the electron-phonon interaction. The $T^2$-dependence of the phonon thermal conductivity occurs over a well-defined intermediate temperature range: at higher $T$ the temperature-dependence is found to be linear while at lower $T$ the usual $T^3$ (boundary-limited) behaviour is recovered. Results are compared to recent measurements of the thermal conductivity of Tl2201, and are shown to be consistent with the data.Comment: 4 page

De Haas-van Alphen effect in two- and quasi two-dimensional metals and superconductors

An analytical form of the quantum magnetization oscillations (de Haas-van Alphen effect) is derived for two- and quasi two-dimensional metals in normal and superconducting mixed states. The theory is developed under condition that the chemical potential is much greater than the cyclotron frequency, which is proved to be valid for using grand canonical ensemble in the systems of low dimensionality. Effects of impurity, temperature, spin-splitting and vortex lattice - in the case of superconductors of type II -, are taken into account. Contrary to the three dimensional case, the oscillations in sufficiently pure systems of low dimensionality and at sufficiently low temperatures are characterized by a saw-tooth wave form, which smoothened with temperature and concentration of impurities growth. In the normal quasi two-dimensional systems, the expression for the magnetization oscillations includes an extra factor expressed through the transfer integral between the layers. The additional damping effect due to the vortex lattice is found. The criterion of proximity to the upper critical field for the observation of de Haas-van Alphen effect in the superconducting mixed state is established.Comment: 18 pages, Latex, revised versio

Self-similarity in Laplacian Growth

We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the integral equation for the conformal map. It is shown that solutions to the integral equation obey also a second order differential equation which is the one dimensional Schroedinger equation with the sinh inverse square potential. The solutions, which are expressed through the Gauss hypergeometric function, characterize the geometry of self-similar patterns in a wedge. We also find the potential for the Coulomb gas representation of the self-similar Laplacian growth in a wedge and calculate the corresponding free energy.Comment: 16 pages, 9 figure

Enhanced Coherence of Antinodal Quasiparticles in a Dirty d-wave Superconductor

Recent ARPES experiments show a narrow quasiparticle peak at the gap edge along the antinodal [1,0]-direction for the overdoped cuprate superconductors. We show that within weak coupling BCS theory for a d-wave superconductor the s-wave single-impurity scattering cross section vanishes for energies of the gap edge. This coherence effect occurs through multiple scattering off the impurity. For small impurity concentrations the spectral function has a pronounced increase of the (scattering) lifetime for antinodal quasiparticles but shows a very broad peak in the nodal direction, in qualitative agreement with experiment and in strong contrast to the behavior observed in underdoped cuprates.Comment: 4 pages, 3 figures, submitte

Classical phase fluctuations in d-wave superconductors

We study the effects of low-energy nodal quasiparticles on the classical phase fluctuations in a two-dimensional d-wave superconductor. The singularities of the phase-only action at T\to 0 are removed in the presence of disorder, which justifies using an extended classical XY-model to describe phase fluctuations at low temperatures.Comment: 14 pages, brief review for Mod. Phys. Lett.

Nonuniform mixed-parity superfluid state in Fermi gases

We study the effects of dipole interaction on the superfluidity in a homogeneous Fermi gas with population imbalance. We show that the Larkin-Ovchinnikov-Fulde-Ferrell phase is replaced by another nonuniform superfluid phase, in which the order parameter has a nonzero triplet component induced by the dipole interaction.Comment: 4 pages, 1 figur

The ground state of binary systems with a periodic modulation of the linear coupling

We consider a quasi-one-dimensional two-component systm, described by a pair of Nonlinear Schr\"{o}dinger/Gross-Pitaevskii Equations (NLSEs/GPEs), which are coupled by the linear mixing, with local strength $\Omega$, and by the nonlinear incoherent interaction. We assume the self-repulsive nonlinearity in both components, and include effects of a harmonic trapping potential. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics, and in Bose-Einstein condensates too. Depending on the strengths of the linear and nonlinear couplings between the components, the ground states (GSs) in such binary systems may be symmetric or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $\Omega$ an odd, or even function of the coordinate. The sign flips of $\Omega (x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $\Omega$. Using a systematic numerical analysis, and an analytical approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. Final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd/even modulation function giving rise to the odd/even number of the kinks. The modulation of $\Omega (x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.Comment: 8 pages, 3 figure