Surface Josephson plasma waves in layered superconductors

We predict the existence of surface waves in layered superconductors in the THz frequency range, below the Josephson plasma frequency omega J. This wave propagates along the vacuum-superconductor interface and dampens in both transverse directions out of the surface (i.e., towards the superconductor and towards the vacuum). This is the first prediction of propagating surface waves in any superconductor. These predicted surface Josephson plasma waves are important for different phenomena, including the complete suppression of the specular reflection from a sample (Wood's anomalies) and a huge enhancement of the wave absorption (which can be used as a THz detector).     

Effect of spin-dependent phases of tunneling electrons on the conductance of a point ferromagnet/isolator/superconductor contact

The Andreev reflection probability for a ferromagnet/isolator/superconductor (FIS) contact at the arbitrary spin-dependent amplitudes of the electron waves transmitted through and reflected from the potential barrier is found. It is shown that the Andreev reflection probabilities of electron and hole excitations in the FIS contact are different. The energy levels of the Andreev bound states are found. The ballistic conductance of the point FIS contact is calculated. The text was submitted by the author in English.     

Magnetic polaritons at a superconductor-ferromagnet interface

The propagation of surface electromagnetic waves at the interface between a high-temperature superconductor and a ferromagnet is considered. Dispersion relations are derived for transverse electric and transverse magnetic surface eigenwaves in the case of various orientations of the crystallographic axes of the anisotropic superconductor with respect to the direction of the surface wave vector. A nonreciprocal character of the propagation of transverse electric polaritons is revealed, as well as a significant dependence of dispersion characteristics and the penetration depth on the external magnetic field.     

Influence of the pinning of Abrikosov vortices on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure

The influence of surface-layer vortex pinning in a type-II superconductor on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure is analyzed. The pinning is assumed to be strong enough to prevent vortex displacement under the influence of the Lorentz force generated by the surface magnetostatic waves, so that the ground state of the superconductor is determined by the elastic properties of the vortex lattice and by pinning. In the given model the problem reduces to the analysis of the wave spectrum in the scattered field created by the disordered vortex surface layer. A calculation shows that the influence of this field on the surface magnetostatic-wave spectrum is slight and, hence, degradation of the shielding properties of the superconductor does not take place in the presence of strong vortex pinning (as opposed to the ferromagnet-ideal superconductor structure). Fiz. Tverd. Tela (St. Petersburg) 40, 32–35 (January 1998)     

Surface electromagnetic waves in superconductors

Varying electromagnetic fields at the surface of a superconductor are studied by means of the boson method. It is found that the frequency of the surface electromagnetic waves satisfies a dispersion relation which is entirely controlled by the system itself.     

Surface electron scattering in d-wave superconductors

A theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger equations are derived at the interface between the impurity layer and the d-wave superconductor. The model is applied to the self-consistent calculation of the surface density of states and the critical current in d-wave Josephson junctions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 242–246 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the stability of capillary waves on the surface of a charged jet moving relative to the environment

A dispersion relation is derived for capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid moving relative to an ideal incompressible dielectric medium. It is shown that a tangential discontinuity in the velocity field on the surface of the jet leads to periodic instability of waves (similar to the Kelvin-Helmholtz instability) at the interface and destabilizes both axisymmetric and flexural waves. The wavenumber range for unstable waves and the instability growth rate increase with the field strength and relative speed of motion, varying as the square of these parameters. In the case of the neutral jet, the flexural instability is of the threshold character and sets in starting from a certain finite value of the speed rather than at an arbitrary small speed.     

Granular high-temperature superconductor film in a steady magnetic field

An electrodynamic model is constructed for a granular Josephson high-temperature superconductor film in a steady magnetic field. The field induces anisotropy and spatial inhomogeneity for a high-frequency field. The data can be used in boundary-value treatments for layered structures that include high-temperature superconductor films, and also in research on acoustoelectronic and magnetostatic interactions of surface acoustoelectronic and magnetostatic waves with the high-temperature superconductor medium.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 91–94, August, 1995.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.     

Interaction between gravity and moving superconductors

We propose a unified phenomenological theory to investigate the interaction between arbitrarily moving superconductors and gravitational fields including the Newtonian gravity, gravitational waves, vector transverse gravitoelectric fields, and vector gravitomagnetic fields. In the limit of weak field and low velocity, the expressions for the induced electromagnetic and gravitational fields in the interior of a moving superconductor are obtained. The Meissner effect, London moment, DeWitt effect, effects of gravitational wave on a superconductor, and induced electric fields in the interior of a freely vibrating superconductor are recovered from these two expressions. We demonstrate that the weak equivalence principle is valid in superconductivity, that Newtonian gravity and gravitational waves will penetrate either a moving superconductor or a superconductor at rest, and that a superconductor at rest cannot shield either vector gravitomagnetic fields or vector transverse gravitoelectric fields.     

Theory of elastic waves produced by a spherical source for generalized boundary conditions

Both fundamental boundary-value problems for elastic waves produced by a spherical source are solved on the assumption that the boundary conditions on the surface of the source apart from being an arbitrary function of the coordinates are also an arbitrary function of time.     

Stability of the viscous fluid film flow on a uniformly heated substrate

The linear stability is investigated of a viscous fluid film on a uniformly heated substrate under an arbitrary angle of inclination against the horizon. At the substrate, the heat flux is set; at the film surface, the fluid-gas heat transfer coefficient is specified. The waves are considered in the film propagating in an arbitrary direction. Within the frame of the integral model, the dispersion ratios are obtained for the wave increment and phase velocity. The analysis is performed of the dispersion ratios, and the flow instability range is determined. At the Marangoni numbers above a certain threshold, standing wave or traveling wave type disturbances take place; the waves increase in the horizontal direction. For the traveling waves, the Marangoni number threshold value is significantly lower than the same for the standing waves.     

On the stability of a cylindrical jet moving in a material medium along an external electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a jet of an ideal incompressible dielectric liquid moving in an ideal incompressible dielectric medium along an external uniform electrostatic field. A tangential discontinuity in the velocity field on the jet surface is shown to cause Kelvin-Helmholtz periodical instability at the interface and destabilize axisymmetric, flexural, and flexural-deformational waves. Both the flexural and flexural-deformational instabilities have a threshold and are observed not at an arbitrarily small velocity of the jet but starting from a certain finite value. It is shown that the instability of waves generated by the tangential discontinuity of the velocity field is periodic only formally (from the pure mathematical point of view). Actually, the jet disintegrates within the time of instability development, which is shorter than the half-cycle of the wave.     

Electromagnetic waves in uniaxial crystals with metallized boundaries: Mode conversion,pure reflections,and bulk polaritons

A theory is constructed for the reflection of plane electromagnetic waves in uniaxial crystals with a positive definite permittivity tensor and an arbitrarily oriented metallized boundary. The problem is solved both for general-position orientations corresponding to three-partial reflection and for special conditions allowing two-partial reflections: mode conversions when the incident and reflected waves belong to different sheets of the refraction surface and “pure” reflections when both waves belong to the same sheet. The space of pure reflections is shown to be formed by two types of optical-axis orientations: arbitrary directions in the plane of the crystal surface and in the plane of incidence. The configurations of the conversion surface for optically positive and negative crystals are investigated. A subspace of pure reflections that transform into one-partial bulk polaritons with the energy flux parallel to the surface at grazing incidence has been found. The domain of existence of such bulk eigenmodes is bounded by two “lines” of solutions. These are any directions along the boundary containing the optical axis for ordinary polaritons and the direction along the projection of the optical axis onto the surface at an arbitrary orientation of the axis with respect to the boundary for extraordinary polaritons.     

Topological vortices in a two-gap superconductor

Based on the ϕ-mapping theory, we derive a new rigorous equation describing the distribution of the magnetic field for vortices in a two-gap superconductor, of which the so-called modified London equation is just a special case in a one-flavor limit. We explicitly investigate the London penetration depth, the Meissner and mixed states and Josephson effect. A magnetic flux quantization condition for vortices in a two-gap superconductor is also derived, from which it follows that in a two-gap superconductor there exist vortices which carry an arbitrary fraction of magnetic flux quantum. The branch processes during the evolution of the vortices in a two-gap superconductor are discussed.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

Surface reverberation spectrum of underwater sound

A general formulation is derived for the power spectrum of fluctuations in the signal received by way of reflection from a rough sea surface, in terms of an arbitrary wavenumber-frequency spectrum of the surface waves and an arbitrary source directivity function. The formulation is then applied to the specific case of backscatter for which the extreme cases of acoustically slightly rough and very rough sea surfaces are examined in detail. The results of the analysis are compared with experiments, and with the somewhat more restricted results of other theoretical work.     

Specific features of the propagation of electromagnetic waves in a waveguiding structure with superconducting film and metamaterial

The propagation of electromagnetic waves in a rectangular waveguide containing layers of common dielectric and metamaterial with a negative refractive index separated by a thin film of a superconductor of the second type in the mixed state is considered. The possibility of amplifiying waves at frequencies lower than the cutoff energy due to the energy of an Abrikosov vortex lattice moving in the superconductor is demonstrated.     

On a theory of surface waves in a smoothly inhomogeneous plasma in an external magnetic field

A theory of surface waves in a magnetoactive plasma with smooth boundaries has been developed. A dispersion equation for surface waves has been derived for a linear law of density change at the plasma boundary. The frequencies of surface waves and their collisionless damping rates have been determined. A generalization to an arbitrary density profile at the plasma boundary is given. The collisions have been taken into account, and the application of the Landau rule in the theory of surface wave damping in a spatially inhomogeneous magnetoactive collisional plasma has been clarified.     

Josephson and quasiparticle currents in tunneling junctions between partially dielectrized (partially gapped) superconductors with spin density waves

The current-voltage characteristics (CVC) are calculated for the Josephson, interference, and quasiparticle components of the current through a tunneling junction formed by two superconductors with spin density waves (SDW). The treatment is based on the model of partial dielectrization (gapping) of the Fermi surface and the assumption of pinning of the spin density waves. The following particular cases are studied in detail: asymmetric SDW superconductor-ordinary superconductor junctions and symmetric junctions between two identical SDW superconductors. The positions and nature of the singularities in the CVC are determined. For a symmetric contact the possibility of the existence of asymmetric CVC’s is predicted. The calculations are in qualitative agreement with the experimentally observed behavior of the CVC’s of tunneling junctions and microcontacts containing the SDW superconductor with heavy fermions URu₂Si₂. Fiz. Tverd. Tela (St. Petersburg) 41, 1743–1749 (October 1999)