Theory of pairing symmetry in the vortex states

We investigate pairing symmetry in an Abrikosov vortex and vortex lattice. It is shown that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has a different parity with respect to frequency from that in the bulk if m is an odd number, while it has the same parity if m is an even number. As a result, in a conventional vortex with m = 1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in an even (odd)-frequency superconductor. In the vortex lattice of s-wave superconductor, we find that only odd-frequency pairing is present at the core centers, while at the midpoint of the vortex lines, only even-frequency pairing exists. Thus, the odd and even-frequency pairings also form the lattice in the vortex lattice state. We also propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Noncollinear orientation of external magnetic field and flux lines penetrating an isotropic hard superconductor

Penetration by Abrikosov flux lines of an isotropic hard superconductor in the critical state induced by changes in the orientation of external magnetic field has been theoretically investigated. The analysis has been based on the microscopic nonlocal model taking into account forces of bulk and surface pinning, alongside magnetic forces of interaction of the row of penetrating vortices with existing flux lines, Meissner currents, and vortex images. New vortices penetrate a superconductor only when the angle through which the field is rotated is larger than a certain critical value. It has been determined that the alignment of entering vortices is essentially different from that of the applied magnetic field. The feasibility of detecting noncollinearity effects is discussed. Zh. éksp. Teor. Fiz. 114, 1804–1816 (November 1998)     

Shape of the magnetic resonance line in a thin film on the surface of an anisotropic superconductor

The shape of the EPR line in a thin (=λ/2, where λ is the London penetration depth of the magnetic field in the superconductor) paramagnetic film deposited on the surface of an anisotropic superconductor is calculated in an oblique magnetic field with allowance for the inhomogeneity of the local magnetic field of the Abrikosov vortex lattice. It is shown that, as the tilt angle of the external magnetic field is varied, the shape of the EPR line changes noticeably. This fact can give additional information about the superconductor parameters (the symmetry type of the vortex lattice and the anisotropy parameter of the superconductor). Fiz. Tverd. Tela (St. Petersburg) 41, 386–388 (March 1999)     

Distribution of the current density in the cylindrical sample of the type II superconductor

Deviation from a homogeneous distribution of the vortex line lattice and magnetic field induced by transport current near H_c2 in the cylindrical sample of type II superconductor in the mixed state without pinning is determined. The dependence of the critical current density on the position in the sample is calculated.     

Instability of Abrikosov vortices in a type-II superconductor-ferrite structure with a longitudinal electric field

The influence of the interaction of the Abrikosov vortices with the magnetization on the longitudinal vortex instability in a layered type-II superconductor-ferrite structure is analyzed. It is shown that in the vicinity of the orientational phase transition in the magnet, where the transverse susceptibility of the magnet is high, the longitudinal critical current in the structure can be almost 1.5 times smaller than the corresponding value in the isolated superconductor. Because of the influence of the nonlocality of the interaction between the vortices, such an effect can be observed only in structures with superconductors that have weak or moderate pinning. A structure is considered in which the thickness of the superconductor is significantly greater than the London magnetic-field penetration depth and the wavelength of the critical mode. Zh. Tekh. Fiz. 67, 28–34 (July 1997)     

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

We study the superconductor to insulator transition at zero temperature in aJosephson-junction array model on a honeycomb lattice with f flux quantum perplaquette. The path integral representation of the model corresponds to a (2 + 1)-dimensional classical model, which isused to investigate the critical behavior by extensive Monte Carlo simulations on largesystem sizes. In contrast to the model on a square lattice, the transition is found to befirst order for f = 1 /3 and continuous for f = 1 / 2 but in a different universality class.The correlation-length critical exponent is estimated from finite-size scaling of vortexcorrelations. The estimated universal conductivity at the transition is approximately fourtimes its value for f =0. The results are compared with experimental observations on ultrathinsuperconducting films with a triangular lattice of nanoholes in a transverse magneticfield.     

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (??SR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H _c2 ^P (T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn₅.     

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.     

Alumina nano-inclusions as effective flux pinning centers in Y–Ba–Cu–O superconductor fabricated by seeded infiltration and growth

The YBa₂Cu₃O_7?x (Y123) textured bulk superconductors with various amounts of nanometer alumina particles were fabricated by a seeded infiltration and growth process. The addition of nanometer alumina was found to be effective for an improvement of the superconducting properties. The critical current density (J_c) values were increased twice in self field with a slight addition amount of nanometer alumina particles (maximum J_c at 0.01 wt.% alumina addition). The present work suggests that the use of insulating inclusions in the nanometer sub-scale can stabilize the flux-line lattice and greatly enhance the pinning capabilities of the infiltrated samples. No refinement of Y211 particles was observed with alumina addition. The J_c improvement by nanometer alumina inclusions is likely rendered to the insulating nano-pinning centers that have been successfully embedded into superconducting Y123 matrix. On the other hand, we examined the effect of the pinning centers size on the superconducting properties of infiltrated YBCO bulk samples. To this effect insulating nano-pinning centers with two different size distributions has been successfully incorporated within YBCO matrix of bulk superconductor by slightly doping with nano-particle alumina dispersions. Two alumina nano-particle dispersions with mean size diameters of about 20 nm and 130 nm were used. It was shown that the size of the pinning centers can affect considerably the J_c performances and the pinning mechanism.     

Effect of deoxygenation on the weak-link behavior of YBa2Cu3O7−δ superconductors

A systematic study of the weak-link behavior for YBa₂Cu₃O_7−δ polycrystalline samples has been done using the electrical resistivity and AC susceptibility techniques. The experiments were performed with two samples of similar grain, a sample of well-coupled grains, and a deoxygenated sample in such a way that the oxygen mostly comes from the intergrain region. Analysis of the temperature dependence of the AC susceptibility near the transition temperature (T_c) has been done employing Bean's critical state model. The observed variation of intergranular critical current densities (J_c) with temperature indicates that the weak links are changed from superconductor normal–metal superconductor (SNS) for well-coupled samples to superconductor insulator normal–metal–superconductor (SINS) type of junctions for the deoxygenated sample. These results are interpreted in terms of oxygen depletion from grain boundaries, which in turn decreases the intergranular Josephson coupling energy with a concomitant decrease of pinning of the intergranular vortices.     

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)     

Resistive state of superconducting structures with fractal clusters of a normal phase

The effect of morphologic factors on magnetic flux trapping and critical currents in a superconducting structure, which presents a type II percolation superconductor with pinning centers, is considered. The role of pinning centers is played by fractal clusters of the normal phase. The properties of these clusters are analyzed in detail: their statistics is studied, the distribution of critical currents of depinning is found, and the depen-dences of the main statistical parameters on the fractal dimension are obtained. The effect of fractal clusters of the normal phase on the electric field caused by the motion of the magnetic flux after the vortices have been broken away from pinning centers is considered. The current-voltage characteristics of superconducting structures in a resistive state are obtained for an arbitrary fractal dimension. It is found that the fractality of the boundaries of normal-phase clusters forces magnetic flux trapping, thereby increasing the critical current.     

Intrinsic behavior of flux lines in pure niobium near the upper critical field

We report small-angle neutron-scattering (SANS) measurements of flux line properties near H(c2) in an ultrapure sample of niobium with weak pinning of flux in the bulk. These confirm in detail the Abrikosov picture of the flux line lattice to within 20 mK of the upper critical field line. However, it has recently been claimed [X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001)], on the basis of SANS observations of a disordering of flux lines in niobium, that the flux lattice melts at temperatures clearly separated from the upper critical field line. This discrepancy may possibly arise from differences in sample purity and pinning.     

Critical vortex line length near a zigzag of pinning centers

A vortex line passes through as many pinning centers as possible on its way from one extremety of the superconductor to the other at the expense of increasing its self-energy. In the framework of the Ginzburg-Landau theory we study the relative growth in length, with respect to the straight line, of a vortex near a zigzag of defects. The defects are insulating pinning spheres that form a three-dimensional cubic array embedded in the superconductor. We determine the depinning transition beyond which the vortex line no longer follows the critical zigzag path of defects.Received: 23 July 2004, Published online: 26 November 2004PACS: 74.80.-g Spatially inhomogeneous structures - 74.25.-q General properties; correlations between physical properties in normal and superconducting states - 74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.)     

Electric field induced by magnetic flux motion in superconductor containing fractal clusters of a normal phase

The influence of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The voltage–current characteristics of such a superconductor are obtained taking into account the effect of fractal properties of cluster boundaries on the magnetic flux trapping. It is revealed that the fractality reduces the electric field arising from magnetic flux motion and thereby raises the critical current of a superconductor.     

Distribution of the local magnetic field of the vortex lattice near the surface of an anisotropic superconductor in oblique external magnetic fields

The distribution of the magnetic field in the unit cell of the Abrikosov vortex lattice near the surface of a uniaxial, anisotropic, type-II superconductor in an oblique external magnetic field is determined on the basis of the London model for the cases in which the symmetry axis is perpendicular and parallel to the boundary of the superconductor. The distribution of the local magnetic field is obtained as a function of the distance from the surface of the superconductor and the inclination angle of the external field. It is shown for an YBaCuO high-T _c superconductor that the investigation of the distribution function of the local magnetic field as a function of the angle of the external magnetic field relative to the symmetry axis and to the surface of the superconductor can yield important information about the anisotropic properties of the superconductor. Fiz. Tverd. Tela (St. Petersburg) 39, 1935–1939 (November 1997)     

Distribution of a local magnetic field in superconductors with an uncorrelated random lattice of abrikosov vortices

The distribution of a local magnetic field near the surface of a uniaxial anisotropic type-II superconductor is determined in the framework of the London model in the case when the Abrikosov vortices are randomly distributed in the superconductor. The distribution of a local magnetic field is obtained as a function of the distance from the surface of the superconductor. It is demonstrated that the shape of the distribution of the local magnetic field near the surface differs substantially from that in the bulk of the superconductor. This difference should be taken into account in interpreting experimental data on the local magnetic field in the surface region of the superconductor and in thin superconducting films (with a thickness of less than or equal to λ, where λ is the depth of penetration of the magnetic field into the superconductor). It is shown that, as in the case of a regular lattice of vortices, the value of λ can be determined from observations of the distribution of the local magnetic field in type-II superconductors with an uncorrelated random lattice of vortices.     

Effects of surface damage on critical current density in MgB2 thin films

We investigated the influence of surface damage on the critical current density (J_c) of MgB₂ thin films via 140-keV Co-ion irradiation. The J_c(H) of the surface-damaged MgB₂ films was remarkably improved in comparison with that of pristine films. The strong enhancement of J_c(H) caused by a surface damage in MgB₂ films can be ascribed to additional point defects along with an atomic lattice displacement introduced through low-energy Co-ion irradiation, which is consistent with the change in the pinning mechanism, from weak collective pinning to strong plastic pinning. The irreversible magnetic field (H_irr) at 5 K for surface-damaged MgB₂ films with a thickness of 850 and 1300 nm was increased by a factor of approximately 2 compared with that of a pristine film. These results show that the surface damage produced by low energy ion irradiation can serve as an effective pinning source to improve J_c(H) in a MgB₂ superconductor.