Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

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 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)     

On the origin of quantum oscillations in the mixed state of an anisotropic superconductor

For the vortex lattice in an anisotropic superconductor with well-separated cores (H _c1≪ B≪H _c2) it is shown that sizable de Haas-van Alphen oscillations are caused by the levels’ crossing of the energy threshold separating localized and extended states of excitations moving in the average magnetic field B. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 705–710 (10 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Anisotropic distributions of electrical currents in high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> grain-boundary junctions

We developed a self-consistent method for the calculation of spatial current distributions in high-T _c grain-boundary junctions. It is found that crystallographic anisotropy of high-T _c superconducting electrodes results in the effects, which previously were not taken into account for interpretations of experimental data. Among them is a significant redistribution of electrical currents in superconducting electrodes in the vicinity of a grain boundary. In particular in the case of [100]-tilt bicrystal junctions, this current redistribution results in a substantial focusing to the top or bottom part of a thickness of the grain boundary, depending on “roof”- or “valley”-type of the grain boundary. This redistribution is accompanied by generation of vortex currents around the grain boundary, which leads to self-biasing of grain-boundary junctions by magnetic field nucleated by these vortex currents. It is shown that twinning or variation of geometrical shape of the high-T _c electrode may also result in intensive redistribution of electrical currents and nucleation of local magnetic fields inside a high-T _c superconducting electrodes.     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)     

Vortex lattice in Bi2Sr2CaCu2O8+δ well above the first-order phase-transition boundary

Measurements of non-local in-plane resistance originating from transverse vortex-vortex correlations have been performed on a Bi₂Sr₂CaCu₂O_8+δ high-T_c superconductor in a magnetic field up to 9 T applied along the crystal c-axis. Our results demonstrate that a rigid vortex lattice does exist over a broad portion of the magnetic field-temperature (H-T) phase diagram, well above the first-order transition (FOT) boundary H_FOT(T). The results also provide evidence for the vortex lattice melting and vortex liquid decoupling phase transitions, occurring above the H_FOT(T).     

Study of the magnetic state of a highly dispersed BaO · 6Fe2O3 system with near-critical particle size

An investigation was made of the magnetic state of a system of highly anisotropic BaO · 6Fe₂O₃ nanocrystals several lattice parameters thick and having a near-critical volume (∼10⁻¹⁸ cm³), obtained using cryochemical technology. It is observed that the particles are transformed to the superparamagnetic state and it is shown that the external magnetic field plays a role in its formation. An H-T diagram was obtained for the temperature range 300 K-T _c, which shows various regions uncharacteristic of the macro-object, which are specifically attributed to the distribution over the anisotropy fields in the system and the impaired magnetic structure in the surface zone of the particles. Relatively large regions of magnetic fields and temperatures were observed where reversible rotation of the magnetization vector of particles with near-critical volume plays an important role. Fiz. Tverd. Tela (St. Petersburg) 40, 1294–1297 (July 1998)     

Statistical mechanics of flux lines in high-T c superconductors

A theory of the entangled flux liquids which arise in the new high-T _c superconductors is reviewed. New physics appears because of the weak interplanar couplings and high critical temperatures in these materials. Flux line wandering melts the conventional Abrikosov flux lattice, and leads to an entangled vortex state whose statistical mechanics is closely related to the physics of interacting bosons in two dimensions. The phase diagram as a function of magnetic field and temperature is discussed, and it is argued that an entangled vortex liquid appears just aboveH _c1 at all nonzero temperatures. The decay of vortex line correlations in the entangled liquid state is controlled by the superfluid excitation spectrum of the bosons. Line wandering produces drastic changes in theB(H) constitutive relation nearH _c1.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

On the role of the Coulomb interaction in the mechanism of d-wave Cooper pairing of charge carriers in high-T c superconductors

The question of the effect of the structure of the anisotropic quasi-two-dimensional electron spectrum of high-T _c superconductors on the character of the screening of the Coulomb interaction and the symmetry of the superconducting order parameter is studied. Calculations of the polarization operator of electrons are performed on the basis of the single-particle band spectrum extracted from angle-resolved photoemission spectroscopy data. It is shown that the static screened Coulomb repulsion has a minimum at small momentum transfers. This corresponds to an effective electron-electron attraction in the -wave channel of Cooper pairing of the charge carriers on account of their interaction with the long-wavelength charge-density fluctuations. This attraction together with the anisotropic electron-phonon interaction increase the critical superconducting transition temperature T _c with increasing hole density and can give quite high values of T _c while at the same time suppressing the isotope effect, in qualitative agreement with the experimental data for underdoped hole-type cuprate metal-oxide compounds. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 703–710 (25 May 1999)     

Characteristic features of vortex depinning in a layered superconductor

The field H*(T) for the onset of dissipation is estimated self-consistently from the results of an investigation of the transverse resistance and current-voltage characteristics of a Bi₂Sr₂CaCu₂O₈ (BSCCO-2212) single crystal in a mixed state. It is established that H* is close to H _c1 in the interval T _c/2⩽T⩽T _c. Rapid growth of H*(T), accompanied by a transformation of the current-voltage characteristics, as the temperature decreases below ≈ 40 K attests to the formation of a nonvanishing region of stability of an ordered state of the vortex system, possibly as a result of a change in the effective dimensionality of the fluxoid. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 629–634 (25 April 1997)     

Structure and transport properties of ultrathin YBa2Cu3O7−x films

The crystal structure and transport properties of epitaxial c-oriented YBa₂Cu₃O_7−x films are investigated for high-T _c layer thicknesses from 5 to 300 nm. The films were prepared by laser deposition. Films less than 30 nm thick become predominantly single-domain in the direction of the c axis. As the thickness decreases, the orthorhombicity parameter of the YBaCuO lattice decreases, which correlates with the critical temperature degradation observed in films less than 9 nm thick. The obtained thickness dependence of the effective microwave surface resistance of a YBaCuO film agrees well with the computational result obtained in the framework of local electrodynamics for samples with a constant microwave conductance. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 608–613 (25 April 1996)     

Short-circuit current limiter utilizing a high-Tc superconductor

Experimental data are given on a prototype short-circuit current limiter utilizing a polycrystalline high-T _c superconductor of composition Y₁Ba₂Cu₃O_7−δ . The limiter comprises a seriesconnected dc circuit element immersed in liquid nitrogen. To improve the efficiency, a polycrystalline high-T _c superconductor having an S-shaped current-voltage characteristic is used as the current limiter. Zh. Tekh. Fiz. 68, 129–130 (October 1998)     

Different types of vortex pinning contribution to critical current density in YBa2Cu3O7−δ /YSZ quasi-multilayer

The quasi-multilayer films of YBa₂Cu₃O_7−δ /YSZ (YSZ denotes Yttria Stabilized Zirconia) are prepared by means of pulsed laser deposition (PLD), and a systematic study of the magnetic-field and temperature dependence of the critical current density J _c(H,T) for the YBCO/YSZ quasi-multilayer film is presented. Angular-dependent J _c(H,T) measurements have demonstrated that the growth control strategy is very effective in preventing the vortex motion at high fields and high temperatures. The temperature dependence of isotropic and anisotropic contribution to J _c is investigated in order to evaluate the strength of the defects. It is suggested that at high applied fields (such as 7 T), the pinning contribution of the YBCO/YSZ quasi-multilayer is dominated by the anisotropic disorders, while at intermediate-low fields (such as 1 and 3 T) the pinning contribution is determined by both isotropic and anisotropic disorders.     

On the lower critical field and phase diagram of a thin cylindrical type-II superconductor

The lower critical field H _c1 ^cyl (T) of a superconducting cylinder with radius r ₀∼ξ(T)≪λ(T) is found on the basis of the Ginzburg-Landau theory with various boundary conditions. These results together with the well-known results for the upper critical field are used to construct phase diagrams in terms of the field versus the reduced radius r ₀∼ξ(T) variables. The jump in the average magnetization at H _c1 ^cyl (T) is calculated as a function of the reduced radius. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 537–542 (25 April 1999)     

Measurements of the London penetration depth in Bi-based high-T c compounds

The muon spin relaxation was measured in the high-T _c superconductors Bi₂Sr_1.3Ca_0.7 CuO_6.15, Bi₂Sr₂CaCu₂O₈ and Bi₂Pb _x Sr₂Ca₂Cu₃O₁₀. We present our method to determine the London penetration depth perpendicular toc-axis λ_⊥ (0) taking also contributions from the anisotropic magnetization and nuclear dipoles to the muon frequency spectrum into account.