Investigation of stimulated dynamics in strongly anisotropic high-temperature superconductors system Bi-Pb-Sr-Ca-Cu-O

It is used the mechanical method of Abrikosov vortex stimulated dynamics investigation in superconductors. With its help it was studied relaxation phenomena in vortex matter of high-temperature superconductors. It established that pulsed magnetic fields change the course of relaxation processes taking place in vortex matter. The study of the influence of magnetic pulses differing by their durations and amplitudes on vortex system of strongly anisotropic high-temperature superconductors system Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ showed the presence of threshold phenomena. The small duration pulses do not change the course of relaxation processes taking place in vortex matter. When the duration of pulses exceeds some critical value (threshold), then their influence changes the course of relaxation process which is revealed by stepwise change of relaxing mechanical moment τrel. These investigations showed that the time for formatting of Abrikosov vortex lattice in Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ is of the order of 150 μs which on the order of value exceeds the time necessary for formation of a single vortex observed in isotropic high-temperature superconductor HoBa₂Cu₃O_7−δ and on two orders exceeds the creation time of a single vortex observed in classical type II superconductors.     

GINZBURG-LANDAU THEORY AND VORTEX LATTICE OF HIGH-TEMPERATURE SUPERCONDUCTORS

The thermodynamics of the vortex lattice of high-temperature superconductors has been studied by solving the generalized Ginzburg-Landau equations derived microscopically. Our numerical simulation indicates that the structure of the vortex lattice is oblique at the temperature far away from the transition temperature T_c, where the mixed s-d_x²-y² state is expected to have the lowest energy. Whereas, very close to T_c, the d_x²-y² wave is slightly lower energetically, and a triangular vortex lattice recovers. The coexistence and the coupling between the s and d waves would account for the unusual dynamic behaviours such as the upward curvature of the upper critical field curve H_C2(T), as observed in dc magnetization measurements on single-crystal YBa₂Cu₃O₇ samples.     

Vortex deformation and breaking in superconductors: a microscopic description

Vortex breaking has traditionally been studied for non-uniform critical current densities, although it may also appear due to non-uniform pinning force distributions. In this article we study the case of a high-pinning/low-pinning/high-pinning layered structure. We have developed an elastic model for describing the deformation of a vortex in these systems in the presence of a uniform transport current density J for any arbitrary orientation of the transport current and the magnetic field. If J is above a certain critical value, J_c , the vortex breaks and a finite effective resistance appears. Our model can be applied to some experimental configurations where vortex breaking naturally exists. This is the case for YBa₂Cu₃O_7?δ (YBCO) low-angle grain boundaries and films on vicinal substrates, where the breaking is experienced by Abrikosov–Josephson vortices (AJV) and Josephson string vortices (SV), respectively. With our model, we have experimentally extracted some intrinsic parameters of the AJV and SV, such as the line tension ? _l and compared it to existing predictions based on the vortex structure.     

Vortex phase diagram studies in the weakly pinned single crystals of YNi2B2C and LuNi2B2C

We present a study of magnetization measurements performed on the single crystals of YNi₂B₂C and LuNi₂B₂C. For both the compounds, we find flux jumps in magnetisation values in the respective field regions, where the structural transitions in the flux line lattice symmetry have been reported in these systems via the small angle neutron scattering experiments. The magnetisation hysteresis loops and the AC susceptibility measurements show pronounced peak effect as well as second magnetisation peak anomaly for both YNi₂B₂C and LuNi₂B₂C. Based on these results, a vortex phase diagram has been constructed for YNi₂B₂C forH∥c depicting different glassy phases of the vortex matter.     

Effects of sample size on the second magnetization peak in Bi2Sr2CaCuO8+δ at low temperatures

Effects of sample size on the second magnetization peak (SMP) in Bi₂Sr₂CaCuO₈+δ crystals are observed at low temperatures, above the temperature where the SMP totally disappears. In particular, the onset of the SMP shifts to lower fields as the sample size decreases —a result that could be interpreted as a size effect in the orderdisorder vortex matter phase transition. However, local magnetic measurements trace this effect to metastable disordered vortex states, revealing the same order-disorder transition induction in samples of different size.     

Noise spectral power and non-equilibrium dynamics of vortices in the mixed state of Bi2Sr2CaCu2Oy

A model is proposed to explain the observed noise spectral power generated by the moving vortex lattice in Bi₂Sr₂CaCu₂O_y single crystals. The analysis is based on the observations that the noise generated is due to the vortex velocity rather than the thermodynamic phase of the material. The motion of vortices induces a gradual transition of the vortex lattice from the plastic flow to the uniform flow with increasing magnetic field. The influence of the disorder on the dynamics of vortices is such that a uniform distribution in the activation barrier width will exist. This distribution will affect the attempt frequency of the flux line hopping and consequently the spectral shape of the noise generated. The model provides physical basis to the fact that the observed 1/f-noise power corresponds to the smaller velocity of the vortex lattice, while the deviation from the 1/f-spectrum corresponds to the larger velocity region. The results of the simulation are compared to recent experimental measurements where good agreement has been achieved.     

Vortex lattice transitions in YNi2B2C

We have performed extensive small-angle neutron scattering (SANS) diffraction studies of the vortex lattice in single crystal YNi₂B₂C for B‖c. High-resolution SANS, combined with a field-oscillation vortex lattice preparation technique, allows us to separate Bragg scattered intensities from two orthogonal domains and accurately determine the unit cell angle, β. The data suggest that upon increasing field there is a finite transition width where both low- and high-field distorted hexagonal vortex lattice phases, mutually rotated by 45°, coexist. The smooth variation of diffracted intensity from each phase through the transition corresponds to a redistribution of populations between the two types of domains.     

Structure of the Abrikosov vortex lattice in a thin superconducting film in a parallel magnetic field

The structure of a vortex lattice in thin (d<λ, where d is the film thickness and λ is the London penetration depth) superconducting films is investigated in a magnetic field parallel to the film surface. It is shown that the stable configuration has the form of discrete vortex rows whose number changes discretely with an increase in the applied magnetic field. The entry fields H _c1 ^(N) (d) for vortex rows are calculated for N=1, 2. It is shown that the structural transition in the vortex ensemble is a second-order phase transition. A simpler method (as compared to the Monte Carlo technique) is proposed for calculating the vortex lattice parameters.     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.     

Direct visualization of the vortex distributions in a superconducting film with a Penrose array of magnetic pinning centers: Symmetry induced giant vortex state

Using scanning Hall probe microscopy a direct visualization of the flux distribution in a Pb film covering a fivefold Penrose array of Co dots is obtained. We demonstrate that stable vortex configurations can be found for fields H ∼ 0.8H₁, H₁ and 1.6H₁, where H₁ corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H₁ corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H₁ the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H = 1.6H₁ interstitial and pinned vortices arrange themselves in ring-like structures (“vortex corrals”) which favor the formation of a giant vortex state at their center.     

Dynamic behavior of diffusion flame interacting with a large-scale vortex by laser imaging techniques

Instantaneous and simultaneous measurements of two-dimensional temperature and OH-LIF profiles by combining Rayleigh scattering with laser induced fluorescence (LIF) were demonstrated in a nitrogen-diluted hydrogen (H₂ 30% + N₂ 70%) laminar normal diffusion flame interacting with a large-scale vortex by oscillating central fuel flow or in an inverse diffusion flame by oscillating central airflow. The dynamic behavior of the diffusion flame extinction and reignition during the flame–vortex interaction processes was investigated. The results obtained are described as follows. (1) The width of the reaction zone decreases remarkably, and a decrease in flame temperature and OH-LIF is seen with increasing central airflow in an inverse diffusion flame. OH-LIF increases, and temperature does not change with increasing central fuel flow in a normal diffusion flame. The computations predict the experimental results well, and it is revealed that flame temperature characteristics result from the preferential diffusion of heat and species, which induces excess enthalpy or on enthalpy deficit, and an increase or decrease in H₂ mole fraction in the flame. (2) When a large velocity fluctuation is given to the central flow, the temperature and the OH-LIF at the reaction zone become thin at the convex and circumferential part of the vortex where a high temperature layer exists, and the temperature at the reaction zone is lowered in the inverse flame and the normal flame. (3) The width and temperature of the reaction zone interacting with the vortex recover quickly to that of the laminar steady flame after the vortex passing in the normal flame, but the recovery to that of the steady flame after the vortex passing is delayed in the inverse flame. (4) When a remarkably large velocity fluctuation is given to the central airflow in the inverse flame, thinning of temperature and reaction zone starts at the convex and circumferential part of the vortex, resulting in a and flame extinction completely occurs at the tail part of the vortex and makes the pair of edge flames. The outside edge flame reignites and connects with the upstream reaction zone. The inside edge flame finally extinguishes as the supply of fuel is interrupted by the outside edge flame.     

Attraction-repulsion transition between abrikosov vortices and Josephson vortices in the strongly layered superconductor Bi2Sr2CaCu2O8

A change in the effect of a frozen magnetic field parallel to the c-axis on rf power absorption, which is associated with the motion of Josephson vortices, is observed in the layered superconductor Bi₂Sr₂CaCu₂O₈ at a low temperature (～15 K). The effect is interpreted as a change in the interaction between an Abrikosov vortex and a Josephson vortex from attraction (at high temperatures) to repulsion (at low temperatures). It is found that the dynamics of the magnetic flux parallel to the ab plane of the single crystal becomes irreversible upon a transition of the superconductor to the layered state. Possible reasons behind the observed effect are considered, one of them being a manifestation of the second superconducting transition in the elementary-excitation spectrum of a d-type superconductor near the core of Abrikosov vortices.     

Vortex motion in high-Tc films and a micropattern-induced phase transition

A micropattern-induced transition in the mechanism of vortex motion and vortex mobility is observed in high-T_c thin films. The competition between the anomalous Hall effect and the guidance of vortices by rows of microholes (antidots) lead to a sudden change in the direction of vortex motion that is accompanied by a change in the critical current density and microwave losses. The latter effect demonstrates the difference in vortex mobility in different phases of vortex motion in between and within the rows of antidots.     

Inhomogeneous superconducting state in the overdoped regime of La2−xSrxCuO4: Comparison with the superconducting state of NbSe2

We have measured the temperature dependence of the magnetic susceptibility, χ vs. T, and the magnetization curve, M vs. H, for NbSe₂ single crystals, in order to compare the superconducting (SC) state in the overdoped regime of La_2−xSr_xCuO₄ (LSCO) with the SC state of the layered conventional superconductor NbSe₂. While a plateau in χ vs. T in a moderate magnetic field and a so-called second peak in M vs. H, which is due to the marked enhancement of vortex pinning, have been observed in the overdoped regime of LSCO, these behaviors have not been observed in NbSe₂. The present results indicate that the anomalously marked enhancement of vortex pinning is a characteristic feature in the overdoped LSCO where a microscopic phase separation into SC and normal-state regions takes place.     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Non-Abelian vortex in four dimensions as a critical superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional supersymmetric QCD with the gauge group, N _f = 4 quark flavors and the Fayet–Iliopoulos term. Under certain conditions, the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli, the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space ?⁴ × Y ₆, where Y ₆ is a non-compact Calabi–Yau conifold. The closed string states that emerge in four dimensions (4D) are identified with hadrons of 4D bulk N= 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole–monopole baryon of the 4D theory (at strong coupling).     

Vortex structure in superconducting iron pnictide single crystals

The vortex structure in the iron pnictide single crystals Ba_1?x K _x Fe₂As₂ and Sr_1?x K _x Fe₂As₂ of the 122 type and SmFeAsO_1?x F _x of the 1111 type has been investigated using the decoration method. In all of the crystals under investigation, no regular vortex lattice has been revealed in the magnetic field range up to 200 Oe. The disordered vortex structure is discussed in view of the vortex pinning in single crystals.     

A nonlinear scenario for development of vortex layer instability in gravity field

A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t ₀ ? t)^?1, where t ₀ is the collapse time.     

Anomalous vortex dynamics in

We report on measurements of current–voltage (I–V) characteristics for YNi₂B₂C single crystals with weak pinning in various fields at 7.6 K. We find nonmonotonic, N-shaped I–V curves in a certain field region deep in the vortex solid phase. This behavior is anomalous, since there exists an intermediate I region where flow voltage V shows a decrease with increasing I (a driving force). While the exact nature remains unknown, this phenomenon suggests vortex motion (driving I) induced pinning.     

A disorder parameter that test for confinement in gauge theories with quark fields

We propose to use a suitably defined vortex free energy as a disorder parameter in gauge field theories with matter fields. It is supposed to distinguish between the confinement phase, massless phase(s) and Higgs phase where they exist. The matter fields may transform according to an arbitrary representation of the gauge group. We compute the vortex free energy by series expansion for a Z₂ Higgs model and for SU(2) lattice models with quark or Higgs fields in the fundamental representation at strong coupling (confinement phase), and for the Z₂ Higgs model in the range of validity of low-temperature expansions (Higgs phase). The results are in agreement with the expected behavior.