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To study the influence of artificial periodic pinning centers on the vortex matter in high- T c superconductors, we have measured the local magnetization and the electrical resistance of Bi 2 Sr 2 CaCu 2 O 8+ y single crystals with sub-micron holes, which are distributed as a triangular lattice. Both measurements show matching effects in multiples of the matching field calculated from the lattice spacing of the defect array. The maximum field in which the matching effect is observed is larger than the field of the vortex-lattice melting transition in samples without artificial defects. The results suggest the existence of a kind of vortex liquid phase which has an in-plane order.

The melting transition of vortex lattice in type-II superconductors with magnetic field perpendicular to the anisotropy axis is studied in the framework of the elastic theory. It is found that the thermal fluctuations in the two directions transverse to the magnetic field are approximately proportional to each other with the constant, different from the anisotropy parameter, in a wide portion of phase diagram. One can introduce two Lindemann numbers with the ratio determined by the thermal fluctuations to draw a single melting line. The melting line thus obtained fits the experimental phase boundary quite well.

Some properties of the flux-line lattice in conventional and high-Tc supperconductors are reviewed, with particular stress on phenomenological theories, magnetization curves, vortex lattice in films, nonlocal elasticity, phase diagram of vortex arrangements, vortex dynamics, and geometry effects.

In this study, we report on the current–voltage characteristics of a bridge cut out from YBCO single crystal. The de-pinning critical current and the flux flow resistance dependencies on temperature have been investigated for samples placed in a zero magnetic field and in a magnetic field of 1.5 T applied parallel to the c-axis of the crystal (H∥c). The overall observed general behavior is similar to the flux creep and flux flow behaviors that have been observed in “cold” superconductors. Down to 78 K, the glass-like behavior of used crystals is absent. Between the irreversible and the shoulder temperatures, the existence of spatially inhomogeneous vortex phase is very plausible: solid phase––in the vicinity of twins and liquid––far from twin planes. Direct measurements of the shear modulus and plastic flow of vortex lattice were performed and included.

It is known that the quantized vortices in a superfluid can be described by a dual electromagnetic model through the duality transformation. Recently a new technique, which can selectively remove atoms from a Bose-Einstein condensate, was applied to the vortex lattice state of the rapid rotating Boson gases. The increase of vortex number, dynamical formation of giant vortex, the oscillation and damping of vortex motion were observed in these experiments. In this paper we will discuss these observations in the framework of dual description and show how to understood these observations naturally., 10 pages, 3 figures, published version

arXiv:1410.7782v1, Long-range correlations in two-dimensional (2D) systems are significantly altered by disorder potentials. Theory has predicted the existence of disorder-induced phenomena, such as Anderson localization or the emergence of a Bose glass. More recently, it has been shown that when disorder breaks 2D continuous symmetry, long-range correlations can be enhanced. Experimentally, developments in quantum gases have allowed the observation of the effects of competition between interaction and disorder. However, experiments exploring the effect of symmetry-breaking disorder are lacking. Here, we create a 2D vortex lattice at 0.1 K in a superconducting thin film with a well-defined 1D thickness modulation - the symmetry-breaking disorder - and track the field-induced modification using scanning tunnelling microscopy. We find that the 1D modulation becomes incommensurate with the vortex lattice and drives an order-disorder transition, behaving as a scale-invariant disorder potential. We show that the transition occurs in two steps and is mediated by the proliferation of topological defects. The resulting critical exponents determining the loss of positional and orientational order are far above theoretical expectations for scale-invariant disorder and follow instead the critical behaviour describing dislocation unbinding melting. Our data show that randomness disorders a 2D crystal, with enhanced long-range correlations due to the presence of a 1D modulation., This work was supported by the Spanish MINECO (FIS2011-23488, MAT2011-27553-C02, MAT 2012-38318-C03, Consolider Ingenio Molecular Nanoscience CSD2007-00010), the Comunidad de Madrid through program Nanobiomagnet (S2009/MAT-1726) and by the Marie Curie Actions under the project FP7-PEOPLE-2013-CIG-618321 and contract no. FP7-PEOPLE-2010-IEF-273105.

We calculate collective modes and study stability of the flux-flow regime of the Josephson vortex lattice driven by a transport current perpendicular to the conducting layers of a layered superconductor in the limits of high and low magnetic fields. The sliding triangular vortex lattice is found to be stable at small velocities up to a critical value. At larger velocities the uniform motion of neither triangular nor quadrangular vortex lattice is stable. In the flux-flow regime we calculate intensity of the radiation emitted from a semi-infinite sample. The radiation power exhibits a large maximum at the lattice velocities corresponding to the Josephson plasma frequency. However, this maximum can be observed only in large enough magnetic field. We demonstrate that the convective term in the equation of motion for the lattice displacement that was reported to be responsible for dynamical phase transitions is small in high magnetic field.

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 Tc, where the mixed s-dx2-y2 state is expected to have the lowest energy. Whereas, very close to Tc, the dx2-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 HC2(T), as observed in dc magnetization measurements on single-crystal YBa2Cu3O7 samples.

The vortex-lattice melting transition in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ single crystals was studied using in-plane resistivity measurements in magnetic fields tilted away from the $c$ axis to the $\mathrm{ab}$ plane. In order to avoid the surface barrier effect which hinders the melting transition in the conventional transport measurements, we used the Corbino geometry of electric contacts. The complete ${H}^{c}\ensuremath{-}{H}^{\mathrm{ab}}$ phase diagram of the melting transition in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ is obtained for the first time. The $c$-axis melting field component ${H}_{\mathrm{melt}}^{c}$ exhibits the novel, stepwise dependence on the in-plane magnetic fields ${H}^{\mathrm{ab}}$ which is discussed on the basis of the crossing vortex-lattice structure. The peculiar resistance behavior observed near the $\mathrm{ab}$ plane suggests the change of phase transition character from first to second order.

We measure current–voltage characteristics at high driving currents for different magnetic fields and temperatures in Nb thin films of rather strong pinning. In a definite range of the B – T phase diagram we find that a current induced transition occurs in the flux flow motion of the vortex lattice, namely a dynamic ordering (DO). Contrary to the case of weaker pinning materials, DO is observed only at low fields, due to the stronger intrinsic disorder that can deform plastically the moving vortex lattice even for small applied fields.

The most fascinating phenomenon of vortex matter is the first-order melting transition from flux line lattice to liquid. In low- T c superconductors, the transition is extremely difficult to observe, because it occurs in the immediate vicinity of the mean field upper critical field H c2 . In contrast, the melting transition is established in high- T c cuprates at several tens of Kelvin, owing to large thermal fluctuations. Here we find that in ultraclean heavy-fermion superconductor URu 2 Si 2 ( T c = 1.45 K) a distinct melting transition with outstanding characters occurs well below H c2 . We show that very low carrier number with heavy mass results in exceptionally large fluctuations even at subkelvin temperatures. We also find a thermal conductivity anomaly below the melting transition, indicating enhancement of the quasiparticle mean free path possibly due to the formation of a quasiparticle Bloch state.

Small phase oscillation modes of a triangular Josephson vortex lattice in a stack of intrinsic Josephson junctions are clarified. The eigen-frequency of the lowest excitation mode, ω 1 , is less than the zero-field plasma frequency, ω pl , and is a decreasing function of the magnetic field H . The eigen-frequencies ω n with n ⩾2 is located above ω pl and increases with increasing H . This result is consistent with the field dependence of the Josephson plasma resonance observed in Bi-2212 and YBCO.

The vortex patterns stabilized by the square array of artificial pinning sites with a tunable pinning strength are studied by using a phenomenological approach in the London limit. The transitions between pinned and deformed triangular lattices are analyzed as a function of the amplitude of vortex-pinning site interaction and the length-scale characteristic of this interaction. The critical current and different phases of vortex lattice are studied in presence of external transport current.

We present small-angle neutron scattering (SANS) measurements of the vortex lattice (VL) in single crystal MgB 2 ––a two-band superconductor. Bragg diffraction of neutrons visualizes the structure and orientation of the VL while the scattered intensity probes the super-carrier density. Superconductivity in the π-band is rapidly suppressed with increasing field with a corresponding decrease in scattered intensity and a re-orientation of the VL between 0.5 and 0.9 T. Both these observations are consistent with superconductivity in the π-band being weaker than in the σ-band ( Δ π Δ σ ), and a changing influence of different parts of the Fermi surface determining the VL orientation. SANS measurements of the VL for fields applied at an angle to the c -axis allow the penetration depth anisotropy, γ λ , to be estimated.

Some features of the vortex lattice in ideal type-II superconductors are calculated from Ginzburg–Landau theory for the entire ranges of applied magnetic fields H c2 ⩽ H ⩽ H c2 or induction 0⩽ B ⩽ μ 0 H c2 and Ginzburg–Landau parameters κ ⩾2 −1/2 . Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B ( x , y ) and magnetization M ( H , κ ) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting and fitting expressions are presented.

The vortex-lattice melting line in three-dimensional type II superconductors with pinning is derived by equating the free energies of the vortex system in the solid and liquid phases. We account for the elastic and pinning energies and the entropy change that originates from the disappearance of the phonon shear modes in the liquid. The pinning is assumed to be caused by point defects and to be not too strong so that the melting line lies inside the so-called bundle-pinning region. The derived equation for the melting line may be expressed in the form of some Lindemann criterion which now includes a characteristic vortex displacement caused by the pinning. Estimating the effect of pinning on the entropy jump at melting, we find the upper critical point of the melting line from the condition that this jump vanishes. Some recent experimental results on the T – H phase diagrams of type II superconductors are discussed.

Using random pinning force simulations, we study numerically the alternating current (ac) response of the driven disordered vortex lattice. In the presence of a superimposed ac force, mode-locking steps are observed in the velocity–direct current (dc) force characteristics at high dc forces, where a smectic order occurs. The step width shows damped oscillations with the strength of interaction between vortices, in good agreement with recent experiments.

The field distribution above the surface of a superconducting sample in the ideal Vortex state is calculated. Pulsed ESR as well as continuous wave ESR experiments were performed on a very thin layer (approximate to 100 nm) of an ESR surface probe (Pc(2) Y or BDPA) deposited on epitactic thin films of YBa2CU3O7 It is shown that pulsed ESR technique is appropriate for the determination of the magnetic flux distribution in the superconducting sample. [References: 3]

The vortex lattice in YNi 2 B 2 C has been observed through the measurements of the local quasi-particle density of states with low temperature scanning tunneling microscopy and spectroscopy. The vortex lattice has shown the hexagonal to the square lattice transition around 0.1T under the magnetic field applied along the c-axis. On the other hands, under the magnetic field along the a-axis, the transition has occurred at much higher magnetic field of 1.0T. We have also observed that the vortex lattice gets disordered above 2.0T.

Scanning tunneling microscopy (STM) and spectroscopy (STS) measurements have been performed on an intermetallic compound CeRu 2 down to 2.2 K. Vacuum tunneling spectra have been measured on the surface prepared by cracking the sample in helium gas at 4.2 K. The shape and temperature dependence of the quasiparticle density of states, N s ( E , r ), have been well interpreted in terms of s-wave BCS superconductors. In magnetic fields, the hexagonal vortex lattice has been imaged by measurements of N s ( E =0, r ) up to 2 T. This is the first observation of the vortex lattice by STS in heavy-fermion superconductors.

Phase diagrams and phase transitions in a two-dimensional vortex lattice with defects have been investigated by Monte Carlo (MC) simulation techniques. 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 into islands, which are pinned to the defects and rotate around them (“rotating lattice” phase). Then, at a higher temperature, the boundaries of the “vortex lattice islands” become smeared and the system transforms into a vortex liquid. The dependencies of phase transition temperatures on pinning potential have been obtained. The visual pictures of the flux lattice structures have been calculated. The current–voltage characteristics (IVC) of the vortex structures with defects in forms of points, lines and squares were simulated at different temperatures and defects concentration. We have found that the point defects are more efficient than the other type of defects with equivalent specific concentration. It was shown that the dependencies of critical current on temperature and defects' concentrations are directly associated with the phase state of the vortex system.

In this contribution, we report (i) on the observation of commensurability effects between regular arrays of artificial defects and the vortex lattice in high-temperature superconductor (HTS) films and (ii) on the reduction of low-frequency 1/ f noise in high- T c superconducting quantum interference devices (SQUIDs) caused by these regular arrays of artificial defects. Arrays of submicrometer holes (antidots) with periodicity down to 0.5 μm were patterned into YBCO thin films without deterioration of superconducting properties. Commensurability effects between the antidot and vortex lattice were observed via resistive and inductive measurements, which clearly prove the presence of an attractive interaction between vortices and antidots and the existence of multiquanta vortices. Consequently, the attractive interaction between antidots and vortices was used to reduce the vortex motion in superconducting devices, thus leading to a strong reduction of 1/ f noise. For a proof of the principle, YBCO films with antidot lattices (5 μm spacing) were mounted in flip-chip configuration onto bicrystal rf-SQUIDs. Commensurability between vortex lattice in film, fluxons in the bicrystal boundary and the antidot array was observed in the form of a strong reduction and increase of the 1/ f noise at discrete magnetic inductions, which are predicted by simple geometric considerations. The transfer of this very promising technology for 1/ f noise reduction to standard HTS SQUIDs used in applications (e.g., NDE, MGC) is presently under way.

The vortex lattices in ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ under the magnetic fields $H$ up to 3 T applied along both the $a$ and the $c$ axes have been studied by scanning tunneling spectroscopy at 4.2 K. The vortex lattice transition has been found to occur in different manners for $H\ensuremath{\parallel}a$ and $H\ensuremath{\parallel}c$; in $H\ensuremath{\parallel}a$ a slightly distorted hexagonal vortex lattice has been found to transform to a nearly square one above 1.0 T with increasing $H$, while in $H\ensuremath{\parallel}c$ the transition occurs at a much lower field around 0.1 T. The unconventional steep increase of the quasiparticle density of states outside the vortex core has also been found well below ${H}_{c2}$.

We measured the magnetic torque \ensuremath{\tau} experienced by an untwinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal in external magnetic fields up to ${\ensuremath{\mu}}_{0}H=7\mathrm{T}$ below the critical temperature ${T}_{c}=93.3\mathrm{K},$ as a function of \ensuremath{\Theta}, the angle between H and the c axis of the crystal. At the vortex-lattice melting transition we observe discontinuities in both \ensuremath{\tau} and $(\ensuremath{\partial}\ensuremath{\tau}/\ensuremath{\partial}{H)}_{T},$ that are related to changes in the transverse components of the magnetization vector M and $(\ensuremath{\partial}\mathbf{M}/\ensuremath{\partial}{H)}_{T},$ respectively. We use thermodynamic relationships to determine the direction of the vector $\ensuremath{\Delta}\mathbf{M}$ in space, and show that $\ensuremath{\Delta}\mathbf{M}$ is always directed parallel to M. The discontinuities in magnetization $\ensuremath{\Delta}\mathbf{M}$ and in entropy $\ensuremath{\Delta}S$ vanish slightly below the temperature where the melting field ${H}_{m}(T)$ extrapolates to zero, which could indicate the existence of a lower critical point of the vortex-lattice melting line. From our $(\ensuremath{\partial}\ensuremath{\tau}/\ensuremath{\partial}{H)}_{T}$ data we are able to extract the differences in the reduced specific heat $\ensuremath{\Delta}C/T$ between the vortex-fluid and the vortex-solid phases, and we compare these results with corresponding thermal data. We finally examine the validity of standard angular scaling rules for anisotropic superconductors for the melting fields ${H}_{m}(T,\ensuremath{\Theta})$ at temperatures as high as ${T/T}_{c}=0.99.$

Flow behavior of the driven two-dimensional vortex lattice is numerically studied with different densities of randomly distributed pointlike pinning centers. Different features in the curves of velocity–force dependence are found between the elastic and plastic regimes. Scaling fit between force and velocity above the critical driving force can be obtained in the elastic regime but fails in the plastic regime. Transition from the elastic to plastic regimes is accompanied by maximum peaks in the differential curves of velocity–force dependence in the disordered vortex lattice.

Muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ measurements of the magnetic-field distribution $n(B)$ in the vortex state of the oxygen deficient high-${T}_{c}$ superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.60}$ reveal a vortex-lattice melting transition at much lower temperature than that in the fully oxygenated material. The transition is best described by a model in which adjacent layers of ``pancake'' vortices decouple in the liquid phase. In some samples we also observe changes in $n(B)$ which are consistent with a vortex lattice which becomes disordered along the field direction above a crossover field ${B}_{\mathrm{cr}}.$ A transition of this nature has previously been reported in the highly anisotropic superconductor ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+y}.$

In this paper, we report observation of the vortex lattice above the surface of high-temperature superconductors Pr 2 - x Ce x CuO 4 - δ using beta-detected NMR ( β -NMR) of Li + 8 implanted in a 40 nm thick Ag overlayer. The resonance in Ag broadens dramatically below the transition temperature T c as expected from the vortex lattice in the underlying superconductor. However, the lineshape is nearly symmetric with the absence of a high-field tail and exhibits a slight positive shift of the average field below T c .

The small angle neutron scattering diffraction patterns from the flux line lattice state in the layered hexagonal superconductor CaAlSi are observed. Under an applied magnetic field (H) parallel to the crystalline c-axis, a hexagonal vortex structure is observed over the entire temperature/field regions. On the other hand, the vortex configuration under H∥a shows an ellipsoidal arrangement of the first-order Bragg peaks due to the anisotropic penetration depth. It was inferred from these results that the vortex state characterized by penetration depth and coherence length in CaAlSi may be described by that of anisotropic uniaxial superconductor using London theory.

The vortex state defined by two characteristic length scales, magnetic penetration depth ( λ ) and coherence length ( ξ ) , in a layered hexagonal superconductor CaAlSi was probed using muon spin rotation. From preliminary analysis using modified London model, we found that the in-plane λ increases with increasing magnetic field while inter-plane λ is almost independent of magnetic field. The presence of field-induced quasiparticle excitation manifested in the field dependence of λ suggests that CaAlSi has an anisotropic gap structure (nodes/dips or multi-gapped).

A two-dimensional periodic optical force field, which combines conservative dipolar forces with vortices from radiation pressure, is proposed in order to influence the diffusion properties of optically susceptible nano-particles. The different deterministic flow patterns are identified. In the low noise limit, the diffusion coefficient is computed from a Mean First Passage Time (MFPT) and the Most Probable Escape Paths (MPEP) are identified for those flow patterns which possess an stable stationary point. Numerical simulations of the associated Langevin equations show remarkable agreement with the analytically deduced expressions. Modifications of the force field are proposed so that a wider range of phenomena could be tested., 15 pages, 7 figures

Certain types of topological superconductors and superfluids are known to host protected Majorana zero modes in cores of Abrikosov vortices. When such vortices are arranged in a dense periodic lattice one expects zero modes from neighboring vortices to hybridize and form dispersing bands. Understanding the structure of these bands is essential for the schemes that aim to employ the zero modes in quantum computation applications and in studies of their strongly interacting phases. We investigate here the band formation phenomenon in two concrete models, describing a two dimensional p + ip superconductor and a superconducting surface of a three-dimensional strong topological insulator (Fu-Kane model), using a combination of analytical and numerical techniques. We find that the physics of the Majorana bands is well described by tight binding models of Majorana fermions coupled to a static Z2 gauge field with a non-trivial gauge flux through each plaquette, in accord with expectations based on very general arguments. In the case of the Fu-Kane model we also find that, irrespective of the lattice geometry, the Majorana band becomes completely flat at the so called neutrality point (chemical potential coincident with the Dirac point) where the model exhibits an extra chiral symmetry. In this limit the low energy physics will be dominated by four-fermion interaction terms which are permitted by symmetries and may arise from the Coulomb interaction between the constituent electron degrees of freedom., 14 pages, 10 figures; v2 minor changes, version to appear in PRB

Hollow YBaCuO superconducting cylinder has been placed in a d.c. magnetic field H ⩽1200 Oe creating a mixed state in the sample and a.c. magnetic field h ⩽1 Oe applied to its outer surface. An inductance coil was used inside to measure the response. Judgments are made on the elastic and viscous properties of vortices originated in the sample. Particularly, the character of the response signal (amplitude and phase) is explained by irreversible magnetization of the sample, due to vortices’ pinning and interaction with surface. Well-calibrated grains used in the ceramic (∼50 μm in average) allowed observation of the “commensurability” effect between the pinning centers’ and vortex–lattice periods, enhancing the volume force of pinning.

The structure of the flux-line lattice in the superconducting film with the periodic system of artificial pinning sites is studied theoretically using the London model. The existence of different vortex phases (pinned square phase, depinned deformed triangular phase, and "intermediate" phase) is revealed. The phase diagrams of the vortex lattice are obtained.

We present kinetic inductance measurements in current driven Josephson junction arrays. Measurements performed with circular coils indicate that this technique is very sensitive to the vortex mobility. Results obtained with anisotropic detection coils provide experimental evidence for the anisotropic response of a driven vortex lattice. Anisotropic behavior is obtained when rising the temperature or the mean vortex velocity as indicated by the loss of the superconducting shielding capability, first in the direction of vortex motion and then in the perpendicular direction.

Making use of the Ginzburg Landau equation for isotropic p-wave superconductors, we construct the single vortex solution in part analytically. The fourfold symmetry breaking term arising from the tetragonal symmetry distortion of the Fermi surface is crucial, since this term indicates a fourfold distortion of the vortex core somewhat similar to the one found in d-wave superconductors. This fourfold distortion of the vortex core in turn favors the square vortex lattice as observed recently by small angle neutron scattering (SANS) experiment from Sr 2 RuO 4 . We find that the hexagonal vortex lattice at H = R c1 transforms into the square one for H = H cr = 0.26H c2 . On the other hand the SANS data does not reveal such transition. The square vortex covers everywhere studied by the SANS implying R cr is very close to H c1 . Therefore some improvement in the present model is certainly desirable.

The melting of the Abrikosov vortex lattice in a 2D type-II superconductor at high magnetic fields is studied analytically within the framework of the phenomenological Ginzburg-Landau theory. It is shown that local phase fluctuations in the superconducting order parameter, associated with low energies sliding motions of Bragg chains along the principal crystallographic axes of the vortex lattice, lead to a weak first order 'melting' transition at a certain temperature $T_{m}$, well below the mean field $T_{c\text{}}$, where the shear modulus drops abruptly to a nonzero value. The residual shear modulus above $T_{m}$ decreases asymptotically to zero with increasing temperature. Despite the large phase fluctuations, the average positions of Bragg chains at fimite temperature correspond to a regular vortex lattice, slightly distorted with respect to the triangular Abrikosov lattice. It is also shown that a genuine long range phase coherence exists only at zero temperature; however, below the melting point the vortex state is very close to the triangular Abrikosov lattice. A study of the size dependence of the structure factor at finite temperature indicates the existence of quasi-long range order with $S(\overrightarrow{G}) \sim N^{\sigma}$, and $1/2

By use of the multi-Josephson junction model, we investigate the electromagnetic properties of high-Tc superconductors, by deriving coupled equations among phase differences and electromagnetic fields inside and outside of junctions. We consider both of the capacitive and inductive effects. Relation between Josephson plasma modes and Josephson vortex lattices is discussed by calculating the reflectivity. Below the usual Josephson plasma edge, there appear structures of absorption due to collective motions of Josephson vortices. Emission of the electromagnetic field from the boundary wall is also investigated in various conditions, and relation between vortex motions and emitted modes will be discussed.

The vortex matter and related phenomena in superconducting films with periodic arrays of microholes (antidots) are studied within the nonlinear Ginzburg–Landau (GL) theory. By varying the GL parameter κ , the vortex–vortex interaction is fine tuned, from repulsive to attractive behavior. This interaction is of crucial importance for equilibrium vortex structures, the saturation number of the antidots, and the related quantities, such as critical current. Due to vortex attraction in effectively type-I samples, the giant-vortex state becomes energetically favorable (contrary to the type-II behavior). For the same reason, the number of vortices which can be captured by antidots, increases with decreasing κ . As a result, for given magnetic field, the critical current is larger for effectively type-I superconductors than in conventional type-II cases.

The vortex-lattice melting transition of a limited number of vortices confined in mesoscopic square superconductors was studied by $c$-axis resistance measurements using stacks of intrinsic Josephson junctions in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+y}$. In contrast to the melting transition in bulk crystals, we have first found a clear oscillatory behavior in the field dependence of the melting temperature in small samples of $5--10\text{ }\text{ }\ensuremath{\mu}m$ square. The periods of the oscillations roughly obey the regularity of the matching conditions of square vortex lattices surrounded by a square boundary and the melting temperatures are enhanced around the vortex number of ${i}^{2}$ (where $i$ is an integer). The results suggest that a confinement effect by the square boundary stabilizes square lattice structures which are realized around ${i}^{2}$ vortex number even in competition with the favorable Abrikosov triangular lattice in the bulk.

Using the high-sensitive mechanical method of measuring the dissipation processes in superconductors, the 3D-2D phase transition in magnetic field was investigated in the vortex lattice of strongly anisotropic high-temperature superconductors of Bi(2223) system. It was shown that with the increase of external magnetic field the dissipation connected with a motion of vortexes relative to the crystal lattice of a sample, first increases, reaching the maximum and then with a further increase of the magnetic field sharply reduces as a result of pinning enhancement in connection with the transition of three-dimensional vortex system in quasi-two-dimensional "pancake" one.

We have investigated the effect of an applied current on the vortex dynamics in superconducting amorphous Nb3Ge and crystalline Pb78Bi22 thin films. We have observed a major difference between the scenarios for the vortex dynamic phase transition at high currents for the samples studied. In the amorphous Nb3Ge films the transition of the flux line lattice from a pinning state to a moving coherent state occurs without an intermediate plastically deformed phase. In the Pb78Bi22 films the initial motion exhibits the characteristics of plastic (or incoherent) flow, which is ended by a sharp transition into the ordered state. We compare our data with the recent theories of ordering and phase transition in the moving vortex lattice.

We have studied experimentally critical behaviors of vortex-lattice-melting transitions in a square Josephson junction array with quenched bond disorder, with a focus on frustrations f=1/2, 2/5, 1/3, and 1/5. Critical scaling analyses of the current–voltage characteristics show that quenched disorder may drive the transitions continuous but not to the Ising universality class. This finding is contrary to what observed in Monte Carlo simulations.

Making use of the extended Ginzburg-Landau theory, which includes the fourth-order derivative term, we study the vortex state in a magnetic field parallel to the c axis. The vortex core structure is distorted due to the higher-order term, which reveals the fourfold symmetry. Further, this distortion gives rise to the core interaction energy which favors a square lattice tilted by $45\ifmmode^\circ\else\textdegree\fi{}$ from the a axis. The triangular vortex lattice in small field region transforms into the rhombic vortex lattice (i.e., the square vortex lattice tilted $45\ifmmode^\circ\else\textdegree\fi{}$ from the a axis) at ${B=H}_{\mathrm{cr}}\ensuremath{\sim}{\ensuremath{\kappa}}^{\ensuremath{-}1}{H}_{c2}(t),$ where $\ensuremath{\kappa}$ is the Ginzburg-Landau parameter and ${H}_{c2}(t)$ is the upper critical field. Therefore, in most of the $B\ensuremath{-}T$ phase diagram the vortex lattice is rhombic. The transition is of the second order and the associated jump in the specific heat should be accessible experimentally.

We have numerically solved the overdamped equation of vortex motion in a two-dimensional driven vortex lattice with disordered pinning, in which the driving Lorentz force, the pinning force due to point defects, the intervortex interacting force, and the thermal fluctuation force are taken into account. It is found that the vortex density and pinning strength are two important factors of affecting the melting transition of a vortex lattice. At low magnetic fields, there exist hysteresis loops of the average vortex velocity and the average pinning force vs. the driving force, from which the feature of a first-order melting transition of the vortex motion can be clearly seen. As the magnetic field is increased beyond a critical value, the hysteresis loops disappear and the melting transition is replaced by a second-order glass transition. We have also studied the influence of intervortex interactions on the vortex melting transition by comparing several forms of repulsive forces between the vortices.

The B-T diagram of Josephson vortex lattice melting in Bi-2212 is analyzed (B is magnetic induction parallel to the layers, T is temperature). It is shown that the Josephson vortex lattice melting at B > B* = 0.6–0.7 T is associated with Berezinsky-Kosterlitz-Thouless transition in individual Bi-2212 superconducting layers and is a second-order phase transition.

We have performed local magnetization measurements on Bi 2 SrCa 2 Cu 2 O 8+ y (Bi2212) single crystals grown by TSFZ method using Bitter decoration technique and MO imaging technique, which provides information of static vortex structures at the surface of superconductors. MO image revealed the presence of micron-scale inhomogeneities of critical currents, which is ascribed to the chemical fluctuation as analyzed by WDS. We could successfully observe nanometer-scale line defects with Bitter decoration technique performed at 65 K. The observed structure was largely disordered, presumably due to thermally activated motion during the decoration.

We have observed a magnetic vortex lattice (VL) in BaFe2(As0.67P0.33)(2) (BFAP) single crystals by small-angle neutron scattering. With the field along the c axis, a nearly isotropic hexagonal VL was formed in the field range from 1 to 16 T, and no symmetry changes in the VL were observed. The temperature dependence of the VL signal was measured and confirms the presence of (non-d-wave) nodes in the superconducting gap structure for measurements at 5 T and below. The nodal effects were suppressed at high fields. At low fields, a VL reorientation transition was observed between 1 and 3 T, with the VL orientation changing by 45 degrees. Below 1 T, the VL structure was strongly affected by pinning and the diffraction pattern had a fourfold symmetry. We suggest that this (and possibly also the VL reorientation) is due to pinning to defects aligned with the crystal structure, rather than being intrinsic. The temperature dependence of the scaled intensity suggests that BFAP possesses at least one full gap and one nodal gap with circular symmetry. Judging from the symmetry, the node structure should take the form of an "accidental" circular line node, which is consistent with recent angle-resolved photoemission spectroscopy results.

We report on small angle neutron scattering measurements of the vortex lattice in twin-free YBa2Cu3O7, extending the previously investigated maximum field of 11~T up to 16.7~T with the field applied parallel to the c axis. This is the first microscopic study of vortex matter in this region of the superconducting phase. We find the high field VL displays a rhombic structure, with a field-dependent coordination that passes through a square configuration, and which does not lock-in to a field-independent structure. The VL pinning reduces with increasing temperature, but is seen to affect the VL correlation length even above the irreversibility temperature of the lattice structure. At high field and temperature we observe a melting transition, which appears to be first order, with no detectable signal from a vortex liquid above the transition.

The structure of a vortex lattice in thin (d