Theoretically, the vortex melting phenomenon occurs at both low and high magnetic fields at a fixed temperature. While the high field melting has been extensively investigated in high Tc cuprates, the low field melting phenomena in the presence of disorder hasn't been well explored. Using bulk magnetization measurement and high-sensitivity differential magneto-optical imaging technique, we detect a low-field vortex melting phenomenon in a single crystal of Ba0.6K0.4Fe2As2. The low field melting is accompanied by a significant change in local magnetization ~ 3 G, which decreases with increasing applied field. The observed vortex melting phenomena is traced on a field temperature phase diagram and which lies very close to theoretically predicted Lindemann criteria based low field melting line. Our analysis shows a Lindemann number cL = 0.14 associated with the low field melting. Imaging of low-field vortex melting features shows the process nucleates via formation of extended finger-like projections which spreads across the sample with increasing field or temperature, before entering into an interaction-dominated vortex solid phase regime. Magnetization scaling analysis shows that the dimensionality of melting vortex state is close to one. Angular dependence of bulk magnetization hysteresis loop in our sample shows the presence of extended defects. From our studies, we propose the sample contains a peculiar geometry of extended defects arranged in a plane in the sample, with these planes extending through the sample thickness. In the weak intervortex interaction limit, we argue that reduced vortex dimensionality due to pinning by these peculiar extended defect planes strongly enhances thermal fluctuations. It is these extended defects planes, which we propose are promoting low dimensional vortex melting in the pnictide system.
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. We show that the derived equation for the melting line is equivalent to some Lindemann criterion, which however d…
The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for th…
The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical be…
Melting of moving vortex lattices in clean superconducting films with periodic pinning is studied by a dynamical "cage" model, based on a mean-field treatment of Langevin's equations for the whole vortex lattice, assuming elastic flow. In the frame moving with the velocity of the vortex lattice center of mass, the model describes forced vibrations of a single vortex tied to a spring. The vortex displacements due to thermal fluctuations and to the periodic pinning force, and the relationship between the driving force and the vortex velocity (V-I curves) are obtained by a perturbation method, va…
We study numerically the effects of temperature on moving vortex lattices interacting with periodic pinning arrays. For low temperatures the vortex lattice flows in channels, forming a hexatic structure with long range transverse and longitudinal ordering. At higher temperatures, a transition to a smectic state occurs where vortices wander between channels and longitudinal order is lost while transverse order remains. At the highest temperatures the vortex lattice melts into an isotropic liquid.
We examine the melting of commensurate and incommensurate vortex lattices interacting with square pinning arrays through the use of numerical simulations. For weak pinning strength in the commensurate case we observe an order-order transition from a commensurate square vortex lattice to a triangular floating solid phase as a function of temperature. This floating solid phase melts into a liquid at still higher temperature. For strong pinning there is only a single transition from the square pinned lattice to the liquid state. For strong pinning in the incommensurate case, we observe a multi-st…
Magneto-optical observations of a second flux front, which occurs at the second peak in the magnetization of Bi_2 Sr_2 CaCu_2 O_x single crystals related to the known first order ``vortex-lattice melting'', are reconsidered. We show that, in thin samples, electrodynamics necessarily leads to an extended region in which the magnetic induction adopts a nearly constant value close to that at which the phase transition occurs at thermal equilibrium. In this region a dynamical phase mixture of vortex ``solid'' and ``liquid'' should exist. Interestingly, the observed second flux front does not mark …
We study the non-equilibrium dynamical regimes of a moving vortex lattice in the periodic pinning of a Josephson junction array (JJA) for {\it finite temperatures} in the case of a fractional or submatching field. We obtain a phase diagram for the current driven JJA as a function of the driving current I and temperature T. We find that when the vortex lattice is driven by a current, the depinning transition at $T_p(I)$ and the melting transition at $T_M(I)$ become separated even for a field for which they coincide in equilibrium. We also distinguish between the depinning of the vortex lattice …
The dynamic melting of vortex lattices in type II superconductors is considered. A field-theoretic formulation of the pinning problem allows the average over the quenched disorder to be performed exactly. A self-consistent theory is constructed using a functional method for the effective action, allowing a determination of the pinning force and the vortex fluctuations. The phase diagram for the dynamic melting transition is determined numerically. In contrast to perturbation theory, the self-consistent theory is in quantitative agreement with the prediction of a recent phenomenological theory …
Using numerical simulations we study the configurations, dynamics, and melting properties of vortex lattices interacting with elliptical pinning sites at integer matching fields with as many as 27 vortices per pin. Our pinning model is based on a recently produced experimental system [G. Karapetrov et al., Phys. Rev. Lett. 95, 167002 (2005)], and the vortex configurations we obtain match well with experimental vortex images from the same system. We find that the strong pinning sites capture more than one vortex each, and that the saturation number of vortices residing in a pin increases with a…
In this communication we argue that the Vortex Lattice Melting scenario fails to explain several key experimental results published in the literature. From a careful analysis of these results we conclude that the Flux Line Lattice (FLL) does not melt along a material- and sample-dependent boundary $H_j(T)$ but the opposite, it de-couples from the superconducting matrix becoming more ordered. When the FLL depinning is sharp, the difference between the equilibrium magnetization $M_{eq}(T,H)$ of the pinned and unpinned FLL leads to the observed step-like change $ΔM_{eq}(T,H)$. We demonstrate that…
Disorder induced melting, where the increase in positional entropy created by random pinning sites drives the order-disorder transition in a periodic solid, provides an alternate route to the more conventional thermal melting. Here, using real space imaging of the vortex lattice through scanning tunneling spectroscopy, we show that in the presence of weak pinning, the vortex lattice in a type II superconductor disorders through two distinct topological transitions. Across each transition, we separately identify metastable states formed through superheating of the low temperature state or super…
A set of interacting vortices in $2D$ in the presence of a substrate with square symmetry and at filling ratio $1$ can display a low temperature solid phase where only one of the reciprocal lattice vectors of the substrate is present\cite{toby1,fasano}. This partially pinned vortex lattice melts to a modulated liquid via a continuous transition \cite{toby1}. Brownian dynamics simulation is carried out to study the behavior of driven partially pinned solid at different temperatures. The average vortex velocity for forces above the depinning threshold shows a non-monotonic behavior with temperat…
We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.
We examine the vortex states in a 2D superconductor interacting with a square array of pinning sites. As a function of pinning size or strength we find a series of novel phases including multi-vortex and composite superlattice states such as aligned dimer and trimer configurations at individual pinning sites. Interactions of the vortices give rise to an orientational ordering of the internal vortex structures in each pinning site. We also show that these vortex states can give rise to a multi-stage melting behavior.
The two-dimensional (2D) vortex lattice in the extreme type-II limit is studied by Monte Carlo simulation of the corresponding 2D Coulomb gas, with identical pins placed at sites coinciding with the zero-temperature triangular vortex lattice. At weak pinning we find evidence for 2D melting into an intermediate hexatic phase. The strong pinning regime shows a Kosterlitz-Thouless transition, driven by interstitial vortex/anti-vortex excitations. A stack of such identical layers with a weak Josephson coupling models a layered superconductor with a triangular arrangement of columnar pins at the ma…
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 shea…
Using dynamic cantilever magnetometry, we study the vortex lattice and its corresponding melting transition in a micrometer-size crystallite of superconducting NbSe2. Measurements of the cantilever resonance frequency as a function of magnetic field and temperature respond to the magnetization of the vortex-lattice. The cantilever dissipation depends on thermally activated vortex creep motion, whose pinning energy barrier is found to be in good agreement with transport measurements on bulk samples. This approach reveals the phase diagram of the crystallite, and is applicable to other micro- or…
An analytic formula describing the suppression of the equilibrium melting line by quenched point pinning disorder is compared to data from ac susceptibility and magnetization measurements in the mixed phase of the layered dichalcogenide low T_c superconductor 2H-NbSe_2. This material exhibits a sharp peak effect in the critical current close to the upper critical field H_c2(T). Arguing that the disorder-suppressed melting line in this system is to be identified with the locus of peak positions of the critical current as magnetic field and temperature are varied, we demonstrate that this formul…
We study the melting transition of the low-temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines. Both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers Our method, involving numerical minimization of a model free energy functional, yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each m…
We have measured the microwave dissipation at 10 GHz in a Bi2Sr2CaCu2O8 single crystal, between 75 and 50 K, as a function of the static magnetic field applied parallel to the c axis. We observe a clear-cut onset in the dissipation precisely at the melting field Hm(T), that we identify in the same sample by a step in the static magnetization. We show that this onset can be assigned to the c-axis resistivity becoming finite in our whole temperature range, whereas the in-plane resistivity displays a thermally activated behavior. This suggests that pinning is efficient even at 10 GHz. The normal …
We present the results of a detailed investigation of the low-temperature properties of the vortex system in strongly anisotropic layered superconductors with a random array of columnar pinning centers. Our method involves numerical minimization of a free energy functional in terms of the time-averaged local vortex density. It yields the detailed vortex density distribution for all local free-energy minima, and therefore allows the computation of any desired correlation function of the time-averaged local vortex density. Results for the phase diagram in the temperature vs. pin concentration pl…
The linear dynamic response of the two-dimensional (2D) vortex medium in ultrathin YBa_2Cu_3O_7 films was studied by measuring their ac sheet impedance Z over a broad range of frequencies ω. With decreasing temperature the dissipative component of Z exhibits, at a temperature T*(ω) well above the melting temperature of a 2D vortex crystal, a crossover from a thermally activated regime involving single vortices to a regime where the response has features consistent with a description in terms of a collectively pinned vortex manifold. This suggests the idea of a vortex liquid which, below T*(ω),…
We study numerically correlation and response functions in non-equilibrium driven vortex lattices with random pinning. From a generalized fluctuation-dissipation relation we calculate an effective transverse temperature in the fluid moving phase. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs. We also discuss how the effective temperature can be measured experimentally from a generalized Kubo formula.
We measured the effects of periodic surface holes, created using a focused ion beam, on the phase diagram of the vortex matter in high-T_c Bi_2Sr_2CaCu_2O_{8+δ} crystals. Differential magneto-optical measurements show that the irreversibility line is shifted to higher fields and temperatures, with respect to the pristine melting line. The irreversibility line displays weak field dependence between integer matching fields indicating multiple-flux-quanta pinning at holes. We find reduced equilibrium compressibility of the vortex matter at integer matching fields, which is strong evidence for the…
We investigate the order - disorder transition line from a Bragg glass to an amorphous vortex glass in the H-T phase diagram of three-dimensional type-II superconductors with account of both pinning-caused and thermal fluctuations of the vortex lattice. Our approach is based on the Lindemann criterion and on results of the collective pinning theory and generalizes previous work of other authors. It is shown that the shapes of the order - disorder transition line and the vortex lattice melting curve are determined only by the Ginzburg number, which characterizes thermal fluctuations, and by a p…
We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, {\it tilted} with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at l…
Theory alternative to the vortex lattice melting theories is advertised. The vortex lattice melting theories are science fiction cond-mat/9811051 because the Abrikosov state is not the vortex lattice with crystalline long-range order. Since the fluctuation correction to the Abrikosov solution is infinite in the thermodynamic limit (K.Maki and H.Takayama, 1972) any fluctuation theory of the mixed state should consider a superconductor with finite sizes. Such nonperturbative theory for the easiest case of two-dimensional superconductor in the lowest Landau level approximation is presented in thi…
Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by the formation of nonequilibrium states which conceal the thermodynamic phase transition, or by intermediate phases, as was recently shown in a polymeric system. Here we report a first-order inverse melting of the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low temperatures, the material disorder causes significant pinning of the vortices, …
We report on the realization of artificial ice using superconducting vortices in geometrically frustrated pinning arrays. This vortex ice shows two unique properties among artificial ice systems. The first comes from the possibility to switch the array geometric frustration on/off through temperature variations, which allows "freezing" and "melting" the vortex ice. The second is that the depinning and dynamics of the frozen vortex ice are insensitive to annealing, which implies that the ordered ground state is spontaneously approached. The major role of thermal fluctuations and the strong vort…
In a recent paper, Matl et al present a high-frequency study of the complex resistivity of a pinned vortex lattice in YBaCuO . They focus on the inductive-to-resistive transition which is investigated as a function of temperature at a constant field $B_0=2$ T, so that the transition is associated with the vanishing of vortex pinning strength. To our view, their conclusions rely on a rather brittle experimental body and the collapse of C66 results from an involved analysis of the finite frequency corrections to $ρ(ω)$. These corrections are not necessary since the complex frequency spectrum has…
We study the effect of thermal fluctuations in a vortex lattice driven in the periodic pinning of a Josephson junction array. The phase diagram current ($I$) vs. temperature ($T$) is studied. Above the critical current $I_c(T)$ we find a moving vortex lattice (MVL) with anisotropic Bragg peaks. For large currents $I\gg I_c(T)$, there is a melting transition of the MVL at $T_M(I)$. When applying a small transverse current to the MVL, there is no dissipation at low $T$. We find an onset of transverse vortex motion at a transverse depinning temperature $T_{tr}(I)<T_M(I)$.
We study finite-size effects at the onset of the irreversible magnetic behaviour of micron-sized Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals by using silicon micro-oscillators. We find an irreversibility line appearing well below the thermodynamic Bragg-glass melting line at a magnetic field which increases both with increasing the sample radius and with decreasing the temperature. We show that this size-dependent irreversibility line can be identified with the crossover between the Larkin and the random manifold regimes of the vortex lattice transverse roughness. Our method allows to determ…
The diversity of vortex melting and solid-solid transition lines measured in different high-T$_{c}$ superconductors is explained, postulating a unified order-disorder phase transition driven by both thermally- and disorder-induced fluctuations. The temperature dependence of the transition line and the nature of the disordered phase (solid, liquid, or pinned liquid) are determined by the relative contributions of these fluctuations and by the pinning mechanism. By varying the pinning mechanism and the pinning strength one obtains a spectrum of monotonic and non-monotonic transition lines simila…
In-plane complex surface impedance of a Bi2Sr2CaCu2Oy single crystal was measured in the mixed state at 40.8 GHz.The surface reactance, which is proportional to the real part of the effective penetration depth, increased rapidly just above the first-order vortex-lattice melting transition field and the second magnetization peak field.This increase is ascribed to the decrease in the superfluid density rather than the loss of pinning.This result indicates that the vortex melting transition changes the electronic structure as well as the vortex structure.
We study muon-spin rotation (muSR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta (BSCCO), by modeling the fluid and solid phases of pancake vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of muSR lineshapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid state correlations and a replicated density functional theory. Our r…
The theory presented is based on a simple Hamiltonian for a vortex lattice in a weak impurity background which includes linear elasticity and plasticity, the latter in the form of integer valued fields accounting for defects. Within a quadratic approximation in the impurity potential, we find a first-order Bragg-glass, vortex-glass transition line showing a reentrant behavior for superconductors with a melting line near $ H_{c2} $. Going beyond the quadratic approximation by using the variational approach of Mézard and Parisi established for random manifolds, we obtain a phase diagram containi…
We analyze transverse phase locking for vortex motion in a superconductor with a longitudinal DC drive and a transverse AC drive. For both square and triangular arrays we observe a variety of fractional phase locking steps in the velocity versus DC drive which correspond to stable vortex orbits. The locking steps are more pronounced for the triangular arrays which is due to the fact that the vortex motion has a periodic transverse velocity component even for zero transverse AC drive. All the steps increase monotonically in width with AC amplitude. We confirm that the width of some fractional s…
Muon spin rotation measurements of the magnetic field distribution in the vortex state of the oxygen deficient high-Tc superconductor YBa{2}Cu{3}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. Evidence is also found for a pinning-induced crossover from a solid 3D to quasi-2D vortex lattice, similar to that observed in the highly anisotropic superconductor Bi{2+x}Sr{2-x}CaCu{2}O{8+y}.
Using a two-coil mutual inductance method, we have measured the complex resistivity, rho_v(T,Be), of pinned vortices in c-axis pulsed laser deposited YBa2Cu3O7-d films with magnetic field Be applied perpendicular to the film. At low frequencies, (<100 kHz), rho_v is inductive and is inversely proportional to the Labusch parameter, the average vortex pinning force constant, kappa_exp. The observed weakening of kappa_exp with Be is consistent with a simple model based on linear pinning defects. Adding classical thermal fluctuations to the model in a simple way describes the observed linear T dep…
We report a pronounced peak effect in the magnetization and the magnetocaloric coefficient in a single crystal of the superconductor Nb3Sn. As the origin of the magnetization peak effect in classical type-II superconductors is still strongly debated, we performed an investigation of its underlying thermodynamics. Calorimetric experiments performed during field sweeps at constant temperatures reveal that the sharp increase in the current density occurs concurrently with additional degrees of freedom in the specific heat due to thermal fluctuations and a liquid vortex phase. No latent heat due t…
We use numerical minimization of a model free energy functional to study the effects of columnar pinning centers on the structure and thermodynamics of a system of pancake vortices in the mixed phase of highly anisotropic layered superconductors. The magnetic field and the columnar pins are assumed to be perpendicular to the layers. Our methods allow us to study in detail the density distribution of vortices in real space. We present results for the dependence of the average number of vortices trapped at a pinning center on temperature and pinning strength, and for the effective interaction be…
The effect of a magnetic field component parallel to the superconducting layers on longitudinal Josephson plasma oscillations in the layered high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ is shown to depend on the thermodynamic state of the underlying vortex lattice. Whereas the parallel magnetic field component depresses the Josephson Plasma Resonance (JPR) frequency in the vortex solid phase, it may enhance it in the vortex liquid. There is a close correlation between the behavior of microwave absorption near the JPR frequency and the effectiveness of pancake vortex pinning, w…
The complex resistivity $\hatρ(ω)$ of the vortex lattice in an untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies $ω/2π$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$, using a 4-probe RF transmission technique that enables continuous measurements versus $ω$ and temperature $T$. As $T$ is increased, the inductance ${\cal L}_s(ω) ={\rm Im} \hatρ(ω)/ ω$ increases steeply to a cusp at the melting temperature $T_m$, and then undergoes a steep collapse consistent with vanishing of the shear modulus $c_{66}$. We discuss in detail the separation of the vortex-…
The irreversible magnetization of the layered high-T_{c} superconductor Bi_{2+x}Sr_{2-(x+y)}Cu_{1+y}O_{6 +- delta} (Bi-2201) has been measured by means of a capacitive torquemeter up to B=28 T and down to T=60 mK. No magnetization jumps, peak effects or crossovers between different pinning mechanisms appear to be present. The deduced irreversibility field B_{irr} can not be described by the law B_{irr}(T)=B_{irr}(0)(1-T/T_{c})^n based on flux creep, but an excellent agreement is found with the analytical form of the melting line of the flux lattice as calculated from the Lindemann criterion. T…
We carry out extensive Monte Carlo simulations of the three-dimensional (3D) uniformly frustrated XY model with uncorrelated randomly perturbed couplings, as a model for the equilibrium behavior of an extreme type-II superconductor with quenched uncorrelated random point vortex pinning, in the presence of a uniform applied magnetic field. We map out the resulting phase diagram as a function of temperature T and pinning strength p for a fixed value of the vortex line density. At low p we find a sharp first order vortex lattice melting phase boundary separating a vortex lattice from a vortex liq…
Vortex penetration and flux relaxation phenomenon carry the information about the pinning ability, and consequently current-carrying ability, of a type-II superconductor. However, the theoretical descriptions to these phenomena are currently limited to the cases with special initial conditions. A generalization to the recently developed infinite series models is presented here. It is shown that one can convert a vortex penetration process with a non-zero initial internal field into a process with a zero initial internal field by introducing some time parameters. Similarly, one can also convert…
In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice forms, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature $T_c$ increases with the applied …
The competition between intrinsic disorder in superconducting YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) thin films and an ultradense triangular lattice of cylindrical pinning centers spaced at 30 nm intervals results in an ordered Bose glass phase of vortices. The samples were created by scanning the focused beam of a helium-ion microscope over the surface of the YBCO thin film to form columns of point defects where superconductivity was locally suppressed. The voltage-current isotherms reveal critical behavior and scale in the vicinity of the second-order glass transition. The latter exhibits a disti…
The tetragonal FeSe phase is an intensively investigated iron based superconductor. In this study we examined the influence of Ag addition on the superconducting properties of selenium deficient polycrystalline FeSe0.94. The samples were obtained by solid state reaction and melting methods. XRD analysis shows the presence of tetragonal phase and EDX analysis establishes inhomogeneous Ag distribution in the grains. The superconducting properties were investigated by fundamental and third harmonic AC magnetic susceptibility. The intergranular critical current determined from AC magnetic suscepti…
Phase diagram of vortex states of high-$T_{\rm c}$ superconductors with {\it sparse and weak} columnar defects is obtained by large-scale Monte Carlo simulations of the three-dimensional anisotropic, frustrated XY model. The Bragg-Bose glass phase characterized by hexagonal Bragg spots and the diverging tilt modulus is observed numerically for the first time at low density of columnar defects. As the density of defects increases, the melting temperature increases owing to "selected pinning" of flux lines. When the density of defects further increases, the transition to the Bose glass phase occ…
In a type II superconductor in a moderate magnetic field, the superconductor to normal state transition may be described as a phase transition in which the vortex lattice melts into a liquid. In a biaxial superconductor, or even a uniaxial superconductor with magnetic field oriented perpendicular to the symmetry axis, the vortices acquire elongated cross sections and interactions. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. We examine the possibility of a two step melting in homogeneous type II superconductors with anisotropic superfluid stiffn…
We have studied electrical transport properties of a high quality Bi2Sr2Ca2Cu3O10+x crystal below a superconducting critical temperature, Tc. In magnetic fields B parallel to the c-axis just above a voltage response onset resistance vs temperature data are well fitted to the vortex-glass model. Obtained from the vortex-glass analysis a melting transition boundary for Bi-2223 crystal shifted towards lower temperatures compared to previously reported data for a (Bi,Pb)-2223 single crystal. The critical current density, Jc, of Bi-2223 crystals is close to presented elsewhere Jc values for Bi-2223…
We report the results of high-field, low-temperature MuSR measurements of the quasi two-dimensional organic superconductors \k{appa}-(ET)2Cu(NCS)2 and \k{appa}-(ET)2Cu[N(CN)2]Br. The MuSR lineshapes for these compounds indicate the existence of partially-ordered vortex lattice phases in the high magnetic field regime, up to 2.5 T for the former compound and 4 T for the latter compound. The observed sharp loss of order is found to be consistent with a vortex-lattice melting transition that is predicted by numerical simulations of weakly coupled layers of pancake vortices. It is argued that the …
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 c…
We consider the magnetic field dependence of the plasma resonance frequency in pristine and in irradiated Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals near $T_c$. At low magnetic fields we relate linear in field corrections to the plasma frequency to the average distance between the pancake vortices in the neighboring layers (wandering length). We calculate the wandering length in the case of thermal wiggling of vortex lines, taking into account both Josephson and magnetic interlayer coupling of pancakes. Analyzing experimental data, we found that (i) the wandering length becomes comparable with the Lon…
We measure current-voltage characteristics as function of magnetic field and temperature in Nb strips of different thickness and width. The instability voltage of the flux flow state related to the vortex critical velocity v* is studied and compared with the Larkin-Ovchinnikov theory. Beside the usual power-law dependence v* ~ B^-1/2, in the low field range a new cross-over field, Bcr1, is observed below which v* decreases by further lowering the external magnetic field B. We ascribe this unexpected cross-over to vortex channeling due to a fan-like penetration of the applied magnetic field as …
The phase transition from the Abrikosov state to the normal state with superconducting fluctuations observed below the second critical field and well-known as vortex lattice melting was one of the most popular problems in the nineties. This problem had became popular after the discovery of high-Tc superconductors because the fluctuation phenomena are much stronger in the HTSC than in the conventional superconductors. Most people are sure that this sharp transition was observed for the present only in HTSC and are ignorant that it was observed as far back as 1981, before the HTSC discovery. In …
Ultrasound velocity measurements of the unconventional superconductor CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an unusual structural transformation of the flux line lattice (FLL) in the vicinity of the upper critical field. The transition field coincides with that at which heat capacity measurements reveal a second order phase transition. The lowering of the sound velocity at the transition is consistent with the collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL pinning. These results provide a strong evidence that the high field state …
