A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in BSCCO crystals into alternating segments of first-order and second-order transitions separated by two critical points. As the density of CDs is increased, the critical points shift apart and the range of the intermediate second-order transition expands. A third, low temperature critical point was also observed in one sample. The measurement of equilibrium magnetization and the mapping of the melting line down to 27K was made possible by employment of the shaking technique.
Using a novel differential magneto-optical imaging technique we investigate the phenomenon of vortex lattice melting in crystals of Bi_2Sr_2CaCu_2O_8 (BSCCO). The images of melting reveal complex patterns in the formation and evolution of the vortex solid-liquid interface with varying field (H) or temperature (T). We believe that the complex melting patterns are due to a random distribution of material disorder or inhomogeneities across the sample, which create fluctuations in the local melting temperature or field value. To study the fluctuations in the local melting temperature / field, we h…
Monte Carlo simulations of layered BSCCO samples are used to investigate the behavior of vortex matter at low fields, particularly in connection with the possible occurrence of a Bragg glass (BrG) phase at low density of columnar defects, a phenomenon characterized by the prevalence of short-range over long-range order. In this dislocation-free topological phase the translational order correlation function displays a power law decay. For magnetic induction $B=0.1$ kG the analysis of the data for the first Bragg peak of the planar structure factor, the hexatic order parameter, and the Delaunay …
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…
The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic properties and equilibrium density distributions are obtained from numerical minimizations of an appropriate free-energy functional. We find a line of first-order transitions that ends at a critical point as the pin concentration is increased. A simple Landau theory providing a semi-quantitative explanation of the numerical results is proposed.
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.
The angular dependence of the first-order phase transition (FOT) in the vortex lattice in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ crystals was investigated by a low frequency AC shielding technique (with the AC field $\parallel c$), in which the static-field component parallel to $c$- ($H_{\perp}$) was varied with the in-plane field $H_{\parallel}$ held constant. The linear decrease of the FOT field $H_{\perp}^{FOT}$ with increasing $H_{\parallel}$ ends at a temperature--dependent critical value of $H_{\parallel}$. A new transition, marked by the abrupt drop of the $ab$-plane shielding current, appe…
Coupling losses were studied in composite tapes containing superconducting material in the form of two separate stacks of densely packed filaments embedded in a metallic matrix of Ag or Ag alloy. This kind of sample geometry is quite favorable for studying the coupling currents and in particular the role of superconducting bridges between filaments. By using a.c. susceptibility technique, the electromagnetic losses as function of a.c. magnetic field amplitude and frequency were measured at the temperature T = 77 K for two tapes with different matrix composition. The length of samples was varie…
The c-axis resistivity in irradiated and in pristine BSCCO(2212) crystals is measured as a function of the in-plane magnetic field component at fixed out-of-plane component B_\perp in the vortex liquid phase at T=67 K. From this data we extract the dependence of the phase difference correlation length inside layers on B_\perp and estimate the average length of pieces of vortex lines confined inside columnar defects as a function of the filling factor f=B_\perp / B_ϕ. The maximum length, about 15 interlayer distances, is reached near f=0.35.
The effect of columnar pins on the flux-lines melting transition in high-temperature superconductors is studied using Path Integral Monte Carlo simulations. We highlight the similarities and differences in the effects of columnar disorder on the melting transition in YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) and the highly anisotropic Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO) at magnetic fields such that the mean separation between flux-lines is smaller than the penetration length. For pure systems, a first order transition from a flux-line solid to a liquid phase is seen as the temperature is increased. When…
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…
Multilevel Monte Carlo simulations of a BSCCO system are carried out including both Josephson as well as electromagnetic couplings for a range of anisotropies. A first order melting transition of the flux lattice is seen on increasing the temperature and/or the magnetic field. The phase diagram for BSCCO is obtained for different values of the anisotropy parameter $γ$. The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev. Lett. {\bf 75}, 1166 (1995)] is obtained for $γ\approx 250$ provided one assumes a temperature dependence $λ^2(0)/λ^2(T)=1-t$ of the penetration depth…
We show that thermally activated interstitial and vacancy defects can lead to first order melting of a vortex lattice. We obtain good agreement with experimentally measured melting curve, latent heat, and magnetization jumps for YBCO and BSCCO. The shear modulus of the vortex liquid is frequency dependent and crosses over from zero at low frequencies to a finite value at high frequencies. We also find a small surface tension between the vortex line liquid and the vortex lattice.
In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi_2Sr_2CaCu_2O$_{8+δ}$ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furth…
Nernst and electrical resistivity measurements in superconducting YBCO and BSCCO with and without columnar defects show a distinctive thermodynamics of the respective liquid vortex matter. At a field dependent high temperature region in the phase diagram the Nernst signal is independent of structural defects in both materials. At lower temperatures, in YBCO, defects contribute only to the vortex mobility and the transport entropy is that of a system of vortex lines. The transition to lower temperatures in BSCCO has a different origin, the maximum in the Nernst signal when decreasing temperatur…
We use 3D numerical simulations to explore the phase diagram of driven flux line lattices in presence of weak random columnar disorder at finite temperature and high driving force. We show that the moving Bose glass phase exists in a large range of temperature, up to its melting into a moving vortex liquid. It is also remarkably stable upon increasing velocity : the dynamical transition to the correlated moving glass expected at a critical velocity is not found at any velocity accessible to our simulations. Furthermore, we show the existence of an effective static tin roof pinning potential in…
We consider layered superconductors with a flux lattice perpendicular to the layers and random columnar defects parallel to the magnetic field B. We show that the decoupling transition temperature Td, at which the Josephson coupling vanishes, is enhanced by columnar defects by an amount ~B^2 relative to Td. Decoupling by increasing field can be followed by a reentrant recoupling transition for strong disorder. We also consider a commensurate component of the columnar density and show that its pinning potential is renormalized to zero above a critical long wavelength disorder. This decommnesura…
The structure function of the vortex lattice of layered superconductor is calculated to one-loop order. Based on a phenomenological melting criterion concerning the Debye-Waller factor, we calculate the melting line of the vortex lattice, and compare our results to Monte Carlo simulation and experiment. We find that our results are quantitatively in good agreement with the Monte Carlo results. Moreover, our analytic calculation of the melting line of BSCCO fits the experiment reasonably well in a temperature range not far from Tc.
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…
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…
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…
The local effect of the Josephson vortices on the vortex lattice melting process in \BSCCO crystals in the presence of an in-plane field $H_{ab}$ is studied by differential magneto-optical imaging. The melting process is found to commence along the Josephson vortex stacks, forming a mesomorphic phase of periodic liquid and solid lamellas, the direction and spacing of which are controlled by $H_{ab}$. The reduction of the local melting field $H_m$ along the Josephson vortex stacks is more than an order of magnitude larger than the reduction of the average bulk $H_m$ by $H_{ab}$.
We study the entropy jump associated with the first-order vortex melting transition (FOT) in Bi2Sr2CaCu2O8+δ crystals by means of Hall probe magnetometry. The samples present a diluted distribution of columnar defects (CD) introduced by irradiation with Xe ions. The FOT is detected in ac transmittivity measurements as a paramagnetic peak, the height of which is proportional to the enthalpy difference entailed by the transition. By applying the Clausius-Clapeyron relation, we quantify the evolution of the entropy jump Δs as a function of the FOT temperature, TFOT, in both pristine crystals and …
Bitter decoration and magneto-optical studies reveal that in heavy-ion irradiated superconductors, a 'porous' vortex matter is formed when vortices outnumber columnar defects (CDs). In this state ordered vortex crystallites are embedded in the 'pores' of a rigid matrix of vortices pinned on CDs. The crystallites melt through a first-order transition while the matrix remains solid. The melting temperature increases with density of CDs and eventually turns into a continuous transition. At high temperatures a sharp kink in the melting line is found, signaling an abrupt change from crystallite mel…
The behavior of vortex matter in $\mathrm{Bi_{2}Sr_{2}CaCu_{2}O_{8}}$ in the presence of a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. We find that while the dynamic properties are significantly affected by tilting the field away from CDs, the thermodynamic lines are angle independent. Our simulations reveal that vortex pancakes remain localized along CDs even at large tilting angles thus preserving the thermodynamic features, while suppression of irreversible properties is caused by vortex kink sliding.
Vortex lattices in the high temperature superconductors undergo a first order phase transition which has thus far been regarded as melting from a solid to a liquid. We point out an alternative possibility of a two step process in which there is a first order transition from an ordinary vortex lattice to a soft vortex solid followed by another first order melting transition from the soft vortex solid to a vortex liquid. We focus on the first step. This premelting transition is induced by vacancy and interstitial vortex lines. We obtain good agreement with the experimental transition temperature…
Multilevel Monte Carlo simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced low concentration of columnar defects satisfying $B_ϕ\le B$. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in ag…
We investigate the vortex phase diagram in untwinned YBaCuO single crystals with columnar defects. These randomly distributed defects, produced by heavy ion irradiation, are expected to induce a ``Bose Glass'' phase of localized vortices characterized by a vanishing resistance and a Meissner effect for magnetic fields transverse to the defect axis. We directly observe the transverse Meissner effect using an array of Hall probe magnetometers. As predicted, the Meissner state breaks down at temperatures Ts that decrease linearly with increasing transverse magnetic field. However, Ts falls well b…
A vortex-glass transition due to point disorder in layered superconductors is studied for the case with an applied field {\it parallel} to the layers. Our calculation of tilt responses indicates that, irrespective of the magnitude of the field, the resulting glass phase, Josephson-vortex-glass (JG), should have a transverse Meissner effect, as in a planar splayed glass phase, only for a tilt perpendicular to the layers. Further, focusing on the high field (and/or high anisotropy) region $B \sqrtΓ > ϕ_0/d^2$, where $Γ$ is the mass anisotropy in the Lawrence-Doniach model, the JG transition line…
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…
Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto a system of interacting bosons in (2+1)D. With increasing temperature we find a first order melting of flux lines from an ordered solid to an entangled liquid signalled by a finite entropy jump and sharp discontinuities in the defect density and the structure factor $S({\bf G})$ at the first reciprocal lattice vector. In the presence of a small number of strong columnar pins, we find that the crystal is transformed into a Bose glass phase with patches of crystalline order nucleated arou…
In the HTC superconductor BSCCO, local measurements of magnetic field in the mixed state show sharp changes as a function of applied field or temperature, which have been interpreted as evidence for a first-order flux-lattice melting (or sublimation) transition . The entropy associated with such a transition was calculated from the magnetisation jumps using a Clausius-Clapeyron-type relationship and was found to increase with temperature up to a value of nearly 1.5kB per flux-line per CuO layer near Tc. This is considerably larger than would be expected, even if the fluid phase consisted of co…
Recent theoretical understanding of the vortex phase diagram in real layered type II superconductors is briefly described in both cases with fields perpendicular (B \parallel c) and parallel (B \perp c) to the superconducting layers. The description is based on a high field approximation of the Lawrence-Doniach model and on a vortex-glass ordering in each case. It is argued that, generically, the familiar thermal first order transition at B_m(T) occurs between the vortex liquid region and the so-called vortex slush region, and that, in systems with stronger fluctuation, most of the thermal fir…
We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate the existence of the intermediate superfluid state where the condensate and localized bosons present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto the three dimensiona…
The effect of fractal normal-phase clusters on vortex dynamics in a percolative superconductor is considered. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase, acting as pinning centers. A prototype of such a structure is YBCO film, containing clusters of columnar defects, as well as the BSCCO/Ag sheathed tape, which is of practical interest for wire fabrication. Transition of the superconductor into a resistive state corresponds to the percolation transition from a pinned vortex state to a resistive state when the vort…
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…
