Influence of Grain Properties on the Abrikosov Vortices Interaction with Josephson Junction

No Heading The problem of the displacement of an Abrikosov vortex is investigated when the magnetic field decreases to H^G_c1 in a grain of a type II superconductor. It is shown that near grain boundaries the vortex line generates an intergranular current which depends on the normalized grain size and the anisotropy ratio . These parameters strongly influence the conditions of the Josephson vortex generation as a result of the interaction of the Abrikosov vortex with the Josephson junction. We support our theory with calculations of the intergrain critical current taking into account two types of the vortex configuration, triangular and square, for different grain characteristics. The results are of interest for the charge transport in granular superconductors as well as the relaxation process in devices that contain Josephson junctions in micro- and nanoelectronics in magnetic field.PACS numbers: 74.25.Qt, 74.25Sv, 74.50.+r.     

Interplay Between Surface Effects and the Magnetic Properties in Polycrystalline Superconductors

The effects of the grain boundaries on the magnetic properties are studied in the polycrystalline superconductors. The interaction of the Abrikosov vortex with both the surface and Josephson junction as well as with other vortices and applied magnetic field are taken into account in this study by the London theory approach. It is shown that the magnetic behavior is strongly dependent of the anisotropy ratio as well as the normalized grain size and the coupling parameter between the grains. The first flux entry field H _p , the lower critical field H _{c 1} and the Gibbs free energy are computed. The vortex–vortex interaction and magnetization M(H) are also investigated.     

Quantum creep of Josephson intergrain vortices in Bi2Sr2Ca2Cu3O10

Magnetic relaxation caused by the creep of Josephson intergrain vortices is studied in Bi₂Sr₂Ca₂Cu₃O₁₀ high-T_c superconductor in the temperature interval 1.8–30 K for applied magnetic fields between 15 and 25 Oe. It is found that the magnetic moment M logarithmically decays with time t. At high enough temperatures the normalized logarithmic decay rate S=−(1/M_J0)(dM_J/dlnt) linearly increases with temperature, while at T<T₀(H), a temperature-independent relaxation rate S≈1.7·10⁻³ is found, manifesting the occurrence of quantum creep of the Josephson vortices. The “crossover” temperature T₀ from the quantum tunneling to the classical thermally activated regime of the vortex motion rapidly decreases from T₀=10 K to T₀<2 K when the field is increased from H=15 Oe to H=25 Oe. No thermal enhancement of the tunneling rate was found in contrast to the quantum creep behavior of Abrikosov intragrain vortices measured in the same sample (Physica C 222 (1994) 149).     

The role of intergrain junctions in transport critical current irreversibility

The magnetic field dependence of voltage at constant measuring currents of YBa₂Cu₃O_7– bulk ceramics and Bi(Pb)SrCaCuO screen printed films were studied at different temperatures so as to obtain information on critical current irreversibility. Two ranges of these curves were found to show sensitivity to magnetic field. They suggest that the two types of superconducting medium, i.e., the Josephson and Abrikosov medium, result in two different voltage generation mechanisms. It is shown that the Josephson medium plays a role in both low and high magnetic field critical current irreversibility.     

High-field Josephson magnetic resonance in high-temperature superconductors

The possibility of high-field Josephson magnetic resonance (HFJMR) in high-temperature super-conductors (HTSCs) is theoretically demonstrated. The HFJMR mechanism is related to the Josephson oscillations in intergranular junctions of a polycrystalline HTSC, which are caused by the penetration of Abrikosov vortices into the grains. In fields within H _c1 ≤ H < H _x (where H _c1 is the first critical field and H _x is the field corresponding to vortex separation from pinning centers in the grains), measurements of the microwave absorption spectra of a sample can be used for investigations of the HTSC macrostructure and the properties of vortex matter. In the latter aspect, the HFJMR method is analogous to the SQUID technique.     

11B NMR Study of Pure and Lightly Carbon-Doped MgB2 Superconductors

We report a¹¹B NMR line shape and spin-lattice relaxation rate (1/(T ₁ T)) study of pure and lightly carbon-doped MgB_2−x C _x forx=0, 0.02, and 0.04, in the vortex state and in magnetic field of 23.5 kOe. We show that while pure MgB₂ exhibits the magnetic field distribution from superposition of the normal and the Abrikosov state, slight replacement of boron with carbon unveils the magnetic field distribution of the pure Abrikosov state. This indicates a considerable increase ofH _c ^2/c with carbon doping with respect to pure MgB₂. The spin-lattice relaxation rate 1/(T ₁ T) demonstrates clearly the presence of a coherence peak right belowT _c in pure MgB₂, followed by a typical BCS decrease on cooling. However, at temperatures lower than ≈10 K strong deviation from the BCS behavior is observed, probably from residual contribution of the vortex dynamics. In the carbon-doped systems both the coherence peak and the BCS temperature dependence of 1/(T ₁ T) weaken, an effect attributed to the gradual shrinking of the σ hole cylinders of the Fermi surface with electron doping.     

Josephson decoupling in single crystal Nd1.85Ce0.15CuO4?y superconductors

Magnetization as a function of temperature and field has been measured with field parallel or close to ab-plane geometry in single crystals of Nd_1.85Ce_0.15CuO_4–y . For fixed magnetic fields, anomalous temperature dependence of magnetization is observed. For fixed temperatures, the magnetization shows abrupt changes to almost zero value above some critical field, an indication of magnetic transparent state. The data deviates from the conventional Abrikosov theory for type-II superconductors. Instead, the results support the picture of Josephson decoupling between the superconducting layers.     

Vortex Matter in a Two-Band SQUID-Shaped Superconducting film

In the present work, we studied the magnetization, vorticity, Cooper pairs density, and the spatial distribution of the local magnetic field in a three-dimensional superconductor with a SQUID geometry (a square with a central hole connected to the outside vacuum through a very thin slit). Our investigation was carried out in both the Meissner-Ochsenfeld and the Abrikosov state solving the two-band Ginzburg-Landau equations considering a Josephson coupling between the bands. We found a non-monotonic vortex behavior and the respective generation of vortex clusters due to the Josephson coupling used between condensates.

     

The effect of the external magnetic field on the current-voltage characteristic of HTS Josephson junction arrays

The role of the external magnetic field in performance specialty of the high-temperature superconducting (HTS) Josephson junction array (JJA): HTS YBa₂Cu₃O_7−0.05 bicrystal JJA with 180 junctions, is considered. The junctions are created on the yttrium-stabilized zirconium (fianite) substrate with the bicrystal grain boundary. The experimental confirmation of the current density changes under the influence of the external DC magnetic field is obtained. The dependence of current density on the penetrated magnetic field is investigated. The optimal shielding factor needed to obtain high supercurrents in considered system is determined.     

Evidence for unpinned magnetic flux vortices above theIctransition in the 2223-phase high-Tcsuperconductor

A similarity in the dc voltage-current (V-I) curves for both direct and alternating transport currents is used to propose that unpinned flux vortices are generated above theI _ctransition for dc transport currents, when Abrikosov flux vortices begin to penetrate the superconductor. Two methods can be used to give a dc voltage drop for an ac transport current: (1) if there is a slight dc offset voltage in the ac current which favors vortex loop collapse as in a traditional dcI _ctest, or (2) if an asymmetric transverse magnetic field is present which favors vortex loop collapse for current in one direction over the reverse direction.     

Evidence for unpinned magnetic flux vortices above theI ctransition in the 2223-phase high-T csuperconductor

A similarity in the dc voltage-current (V-I) curves for both direct and alternating transport currents is used to propose that unpinned flux vortices are generated above theI _ctransition for dc transport currents, when Abrikosov flux vortices begin to penetrate the superconductor. Two methods can be used to give a dc voltage drop for an ac transport current: (1) if there is a slight dc offset voltage in the ac current which favors vortex loop collapse as in a traditional dcI _ctest, or (2) if an asymmetric transverse magnetic field is present which favors vortex loop collapse for current in one direction over the reverse direction.     

Vortex Molecules in Thin Films of Layered Superconductors

Both the equilibrium and transport properties of the vortex matter are essentially affected by the behavior of the intervortex interaction potential. In isotropic bulk superconductors this potential is well known to be repulsive and is screened at intervortex distances R greater than the London penetration depth λ. As a result, in perfect crystals quantized Abrikosov vortices form a triangular lattice. In thin films of anisotropic superconductors this standard interaction potential behavior appears to be strongly modified because of the interplay between the long-ranged repulsion predicted in the pioneering work by J. Pearl and the attraction caused by the tilt of the vortex lines with respect to the anisotropy axes. This interplay results in a new type of vortex arrangement formed by finite-size vortex chains, i.e., vortex molecules. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number N of flux quanta. Thus, the increase in the field tilting (or varying temperature) should be accompanied by the series of the phase transitions between the vortex lattices with different N. A similar scenario should be realized in strongly anisotropic BSCCO high-T _c superconductors where in tilted field a crossing lattice of Abrikosov vortices (the stacks of pancakes in this case) and Josephson vortices appears. This crossing leads to the zigzag deformation of the pancakes stacks which is responsible for the attraction interaction competing with the long-ranged Pearl’s repulsion.     

Nucleation of normal phase in the dynamic resistive state in submicron Bi2212 bridges

The resistive state above the Larkin-Ovchinnikov (LO) instability current has been experimentally studied. Analysis of the stepwise I–V curves of thin superconducting bridges ≤1 μm wide, etched from the Bi₂Sr₂Ca₁Cu₂O_y (Bi2212) whiskers, reveals the following scenario of vortex dynamics: first, a pair of current-induced Abrikosov vortices enter the bridge, then they are accelerated by the current above the critical velocity of the LO instability and approach the limiting velocity of the normal phase propagation, of the order of 10⁷ cm/s. Each vortex leaves a tail of normal phase behind itself, which is equivalent to a phase slip line. At low temperatures the tails cover the whole width of the bridge—the I–V curves between the steps become Ohmic.     

11B NMR Study of Pure and Lightly Carbon-Doped MgB2 Superconductors

We report a ¹¹B NMR line shape and spin-lattice relaxation rate (1/(T₁T))(1/(T_1T)) study of pure and lightly carbon-doped MgB_2-xC_x_{2-x}{\rm C}_x for x = 0,0.02x = 0,0.02, and 0.04, in the vortex state and in magnetic field of 23.5 kOe. We show that while pure MgB₂_2 exhibits the magnetic field distribution from superposition of the normal and the Abrikosov state, slight replacement of boron with carbon unveils the magnetic field distribution of the pure Abrikosov state. This indicates a considerable increase of H^c_c2H^c_{c2} with carbon doping with respect to pure MgB₂_2. The spin-lattice relaxation rate 1/(T₁T)1/(T_1T) demonstrates clearly the presence of a coherence peak right below T_cT_{\rm c} in pure MgB₂_2, followed by a typical BCS decrease on cooling. However, at temperatures lower than ?\approx 10 K strong deviation from the BCS behavior is observed, probably from residual contribution of the vortex dynamics. In the carbon-doped systems both the coherence peak and the BCS temperature dependence of 1/(T₁T)1/(T_1T) weaken, an effect attributed to the gradual shrinking of the σ hole cylinders of the Fermi surface with electron doping.     

Magnetic Field Dependence of Intergrain Pinning Potential in Bulk Granular Composites YBCO + CuO Demonstrating Large Magneto-Resistive Effect

The broadening of the resistive transition in magnetic field and isotherms of magnetoresistance of bulk composites Y–Ba–Cu–O + CuO have been studied. These composites exhibit large magneto-resistive effect in a wide temperature range below T _C due to weakening of Josephson coupling in this system. The broadening of the resistive transition and magnetoresistance are explained well by the Ambegaokar–Halperin (AH) model for phase slip in Josephson junctions. The magnetic field dependence of pinning potential in the intergrain boundaries deduced from AH model found out to be similar to that of critical current of an array of Josephson junctions. The values of pinning energy point out that the large magneto-resistive effect observed in the composites results from flux flow-like processes at the intergrain boundaries.     

Vortex Dynamics in Bi2Sr2CaCu2O8 Single Crystal with Low Density Columnar Defects Studied by Magnetic Force Microscope

We have studied vortex dynamics in Bi₂Sr₂CaCu₂O₈ single crystal with low density columnar defects by using a magnetic force microscope. Single crystal Bi₂Sr₂CaCu₂O₈ sample was irradiated by 1.3 GeV uranium ion to form artificial pinning centers along the crystalline c-axis. The irradiation dose corresponded to a matching field of 20 gauss. The radius of an individual vortex is approximately 140 nm, which is close to the penetration depth of this material. Magnetic force microscope (MFM) images show that intrinsic crystalline defects such as stacking fault dislocations are very effective pinning centers for vortices in addition to the pinning centers due to ion bombardment. By counting the number of vortex, we found that the flux trapped at each pinning center is a single flux quantum. At higher magnetic field, the vortex structure showed an Abrikosov lattice disturbed only by immobile vortices located at pinning centers. When increasing or decreasing the external magnetic field, the spatial distribution of vortices showed a Bean model like behavior.     

Tilted and crossing vortex chains in layered superconductors

In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [λ] and Josephson [λ _J ] lengths, α=λ/λ _J . The chain is composed of tilted vortices at large α's (tilted chain) and at small α's it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate α's and found two types of phase transitions. For α≲0.6 the groud state is given by the crossing chain in a wide range of pancake separationsa≳[2−3]λ _J . However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and α. The first phase transition takes place with decreasing pancake-stack separation a ata≳[1−2]λ _J , and rather wide range of the ratio α, 0.4≲α≲0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices,a ~ [20−30]λ _J , and only when α exceeds a certain critical value ∼0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.     

On the limiting factors of the critical current density in high-Tc superconducting ceramics

The temperature dependence of the critical current density at high temperatures and in weak applied magnetic field for YBa₂Cu₃O_7–y ceramic samples with a pronounced granular character is analyzed. The experimental results can be explained in terms of thermally activated motion of the intergrain Josephson vortices at grain boundaries, which may be an indication that the actual limiting factor for the critical current density in ceramic samples results from a weak pinning force density for the intergrain vortices rather than from the weak-link quenching.     

Collective Motion of Vortices Induced by A.C. Magnetic Field in the High Anisotropy BSCCO

The microwave dissipation induced by an ac magnetic field collinear to the dc magnetic field in the highly anisotropic BSCCO shows two signals. One, that occurs just below T _c in all superconductors, corresponds to changes in the microwave dissipation of the TAFF resistivity caused by a magnetic modulation. The other signal arises from a double frequency process, where the ac field prepares the vortex system to enable its interaction with the microwave. This signal whose response to the ac field is non-linear (NL) is studied in this work, mostly for the configuration where the dc and the ac magnetic field are parallel the a–b plane. We demonstrate that below B _dc=0.0025 T the ac field interacts with individual non-interacting vortices. Above B _dc=0.005 T, the ac induces simultaneously, collective motions of pinned vortices and Josephson unpinned vortices. The latter has a bell-shaped form and therefore can be identified as an oscillation mode induced by the magnetic microwave field. This oscillation mode is excited by the microwave magnetic field and therefore it differs from the Josephson plasma excitation mode or the vortex excitation mode where both are excited by the microwave electric field. Defects, high temperatures and high ac fields impedes the excitation of this mode. The results are discussed with respect to the vortex shaking effect and other experimental and theoretical results.     

Magnetic field dependence of the Josephson coupling energy along the c-axis in Bi2Sr2CaCu2O8+y

The magnetic field dependent c-axis dissipation in Bi₂Sr₂CaCu₂O_8+y single crystals is shown to agree with that of a series stack of Josephson tunnel junctions. We extract the Josephson coupling energy E_j from the measured the c-axis resistance as a function of the angle between the c-axis and the magnetic field B using an extended Ambegaokar-Halperin model. For B > 0.5T, E_j increases continuously with both decreasing temperature and decreasing magnetic field. At T = 78K, E_j exhibits a B^–0.5 behavior.