Star-shaped Local Density of States around Vortices in a Type II Superconductor

The electronic structure of vortices in a type II superconductor is analyzed within the quasi-classical Eilenberger framework. The possible origin of a sixfold ``star'' shape of the local density of states, observed by scanning tunneling microscope experiments on NbSe$_2$, is examined in the light of the three effects; the anisotropic pairing, the vortex lattice, and the anisotropic density of states at the Fermi surface. Outstanding features of split parallel rays of this star are well explained in terms of an anisotropic $s$-wave pairing. This reveals a rich internal electronic structure associated with a vortex core.Comment: 4 pages, REVTeX, 3 figures available upon reques

Antivortices due to competing orbital and paramagnetic pair-breaking effects

Thermodynamically stable vortex-antivortex structures in a quasi-two-dimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle \Theta. The spectrum of possible states contains as limits the ordinary vortex state (for large \Theta) and the Fulde-Ferrell-Larkin-Ovchinnikov state (for \Theta=0). The quasiclassical equations are solved near H_{c2} for arbitrary \Theta and it is shown that stable states with coexisting vortices and antivortices exist in a small interval close to \Theta=0. The results are compared with recent predictions of antivortices in mesoscopic samples.Comment: 11 pages, 3 figure

Gravity waves, scale asymptotics, and the pseudo-incompressible equations

Multiple-scale asymptotics is used to analyze the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As small expansion parameter the ratio of inverse of the vertical wave number and potentialtemperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic gravity waves, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak stratication is adopted. To describe vertical propagation of wave packets over several atmospheric scale heights, WKB theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justication for the use of the pseudo-incompressible equations for studies of gravity-wave breaking in the atmosphere for arbitrary background stratication. The WKB theory interestingly also holds at wave amplitudes close to static instability. In the mean-flow equations we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical-momentum equation which cannot be obtained from Boussinesq or anelastic dynamics

Diffuse radio emission in the complex merging galaxy cluster Abell 2069

Galaxy clusters with signs for a recent merger show in many cases extended diffuse radio features. This emission originates from relativistic electrons which suffer synchrotron losses due to the intra-cluster magnetic field. The mechanisms of the particle acceleration and the properties of the magnetic field are still poorly understood. We search for diffuse radio emission in galaxy clusters. Here, we study the complex galaxy cluster Abell 2069, for which X-ray observations indicate a recent merger. We investigate the cluster's radio continuum emission by deep Westerbork Synthesis Radio Telescope (WSRT) observations at 346 MHz and a Giant Metrewave Radio Telescope (GMRT) observation at 322 MHz. We find an extended diffuse radio feature roughly coinciding with the main component of the cluster. We classify this emission as a radio halo and estimate its lower limit flux density to 25 +/- 9 mJy. Moreover, we find a second extended diffuse source located at the cluster's companion and estimate its flux density to 15 +/- 2 mJy. We speculate that this is a small halo or a mini-halo. If true, this cluster is the first example of a double-halo in a single galaxy cluster.Comment: 6 pages, 3 figures, accepted for publication in A&

Local density of states in the vortex lattice in a type II superconductor

Local density of states (LDOS) in the triangular vortex lattice is investigated based on the quasi-classical Eilenberger theory. We consider the case of an isotropic s-wave superconductor with the material parameter appropriate to NbSe_2. At a weak magnetic field, the spatial variation of the LDOS shows cylindrical structure around a vortex core. On the other hand, at a high field where the core regions substantially overlap each other, the LDOS is sixfold star-shaped structure due to the vortex lattice effect. The orientation of the star coincides with the experimental data of the scanning tunneling microscopy. That is, the ray of the star extends toward the nearest-neighbor (next nearest-neighbor) vortex direction at higher (lower) energy.Comment: 10 pages, RevTex, 32 figure

A Two-dimensional Superconductor in a Tilted Magnetic Field - new states with finite Cooper-pair momentum

Varying the angle Theta between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers 0<n<\infty. The stable order parameter structure and magnetic field distribution for these states is found by minimizing the quasiclassical free energy near H_{c2} including nonlinear terms. One finds states with coexisting line-like and point-like order parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at Theta=0 is reconsidered. The transition n->\infty of the paramagnetic vortex states to the FFLO-limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.Comment: 24 pages, 11 figure

Absence of Dipole Transitions in Vortices of Type II Superconductors

The response of a single vortex to a time dependent field is examined microscopically and an equation of motion for vortex motion at non-zero frequencies is derived. Of interest are frequencies near $\Delta^{2}/E_{F}$, where $\Delta$ is the bulk energy gap and $E_{F}$ is the fermi energy. The low temperature, clean, extreme type II limit and maintaining of equilibrium with the lattice are assumed. A simplification occurs for large planar mass anisotropy. Thus the results may be pertinent to materials such as $NbSe_2$ and high temperature superconductors. The expected dipole transition between core states is hidden because of the self consistent nature of the vortex potential. Instead the vortex itself moves and has a resonance at the frequency of the transition.Comment: 12 pages, no figure