Topological defects such as dislocations and disclinations are predicted to determine the twodimensional (2-D) melting transition. In 2-D superconducting vortex lattices, macroscopic measurements evidence melting close to the transition to the normal state. However, the direct observation at the scale of individual vortices of the melting sequence has never been performed. Here we provide step by step imaging through scanning tunneling spectroscopy of a 2-D system of vortices up to the melting transition in a focused-ion-beam nanodeposited W-based superconducting thin film. We show directly the transition into an isotropic liquid below the superconducting critical temperature. Before that, we find a hexatic phase, characterized by the appearance of free dislocations, and a smectic-like phase, possibly originated through partial disclination unbinding. These results represent a significant step in the understanding of melting of 2-D systems, with impact across several research fields, such as liquid crystal molecules, or lipids in membranes.
We consider the jump in resistance at the melting transition, which is experimentally observed to be constant, independent of magnetic field (vortex density). We present an explanation of this effect based on vortex cuttings, and universalities of the structure factor at the freezing transition (the Hansen-Verlet criterion).
We discuss the effect of an (ab)-surface on the melting transition of the pancake-vortex lattice in a layered superconductor within a density functional theory approach. Both discontinuous and continuous surface melting are predicted for this system, although the latter scenario occupies the major part of the low-field phase diagram. The formation of a quasi-liquid layer below the bulk melting temperature inhibits the appearance of a superheated solid phase, yielding an asymmetric hysteretic behavior which has been seen in experiments.
The pre-melting of high vortex density planes observed recently in layered superconductors in tilted magnetic field is explained theoretically. Based on the structural information of the crossing lattices of pancake and Josephson vortices the effective vortex cage potential at different lattice sites is determined numerically. Melting takes place when the thermal energy allows proliferation of vacancy-interstitial pairs. It is found that the increased density of pancake vortex stacks in the planes containing Josephson vortices, rather than their incommensurate structure, is the main cause for …
Abrikosov vortex melting in high-temperature superconductors of ErBa2Cu3O7-δ system is investigated using mechanical contactless method of energy dissipation.
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.
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 report a numerical study of the vortex system in the two dimensional II-type superconductors. We have proposed a phenomenological model that takes into account quantum fluctuations of Abrikosov's vortices. The results of the quantum Monte-Carlo simulations by the SSE algorithm show that the thermal fluctuations are dominated by quantum fluctuations at low temperatures. In particular, we demonstrate the possibility of the quantum melting transition for vortex system in the temperature region where thermal melting transition is improbable.
Theory of melting of the vortex lattice in type II superconductors in the framework of Ginzburg - Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by 1.8% irrespective of the melting temperature, while the specific heat jump is about 6% and decreases slowly with temperature. The magnetization curves agrees with experimental results on YBCO and Monte Carlo simulations.
The melting of the magnetic vortex lattice has been observed in high-Tc superconductors in many experiments by different groups and is regarded as confirmed. To date, only one group claims to have observed the vortex-lattice melting in the low-Tc superconductor Nb3Sn in specific-heat measurements. We measured the same Nb3Sn single crystal with a differential-thermal analysis method. We report on the absence of any sign of vortex-lattice melting in our data and discuss the possible reasons for this discrepancy. In addition we confirm the observation of a small peak-like anomaly near the transit…
Distinct discontinuities in the thermal expansion of the crystal lattice are observed at the melting-transition of the vortex lattice in a naturally untwinned reversible YBa2Cu3O7-d-single crystal using high-resolution dilatometry. This coupling between the vortex transition and the crystal lattice demonstrates that the crystal lattice is more than a mere host for the vortices, and it is attributed to a strong pressure dependence of the superconducting transition temperature and thus to the condensation energy at the vortex melting temperature.
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…
Sub-nanovolt resolution longitudinal and Hall voltages are measured in an ultra pure YBa2Cu3O7-d single crystal. The Hall anomaly and the first-order vortex-lattice melting transition are observed simultaneously. Changes in the dynamic behavior of the vortex solid and liquid are correlated with features of the Hall conductivity sxy. With the magnetic field oriented at an angle from the twin-boundaries, the Hall conductivity sharply decreases toward large negative values at the vortex-lattice melting transition.
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…
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 …
From muon spin rotation measurements on under- to overdoped Bi-2212 crystals we obtain evidence for a two-stage transition of the vortex matter as a function of temperature. The first transition is well known and related to the irreversibility line (IL). The second one is located below the IL and has not been previously observed. It occurs for all three sets of crystals and is unrelated to the vortex mobility. Our data are consistent with a two-stage melting scenario where the intra-planar melting of the vortex lattice and the inter-planar decoupling of the vortex lines occur independently.
Differential magneto-optical imaging of the vortex-lattice melting process in Bi_2Sr_2CaCu_2O_8 crystals reveals unexpected effects of quenched disorder on the broadening of the first-order phase transition. The melting patterns show that the disorder-induced melting landscape T_m(H,r) is not fixed, but rather changes dramatically with varying field and temperature along the melting line. The changes in both the scale and shape of the landscape are found to result from the competing contributions of different types of quenched disorder which have opposite effects on the local melting transitio…
In the framework of elastic theory, we study the vortex-lattice melting transitions in magnesium diboride for magnetic fields both parallel and perpendicular to the anisotropy axis. Using the parameters from experiments, the vortex-lattice melting lines in the H-T diagram are located systematically by various groups of Lindemann numbers and the anisotropic parameters. It is observed that the theoretical result for the vortex melting with parallel and perpendicular fields agrees well with the experimental data.
A modified form of the vortex-lattice melting line is arrived at by incorporating the effects of critical behavior at the melting transition. Beginning with the universal form established by Blatter and Ivlev [Physical Review Letters 70, 2621 (1993)] which includes both thermal and quantum fluctuations, we then use the vortex relaxation time of a vortex-glass with a finite transition temperature that follows from the scaling theory of Fisher, Fisher, and Huse [Physical Review B, 43, 130 (1991)]. This new form of the melting line is demonstrated to fit over the entire melting line of Y(1-x)Pr(x…
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 question of thermal melting of the triangular Abrikosov vortex solid in two-dimensional superconductors or neutral superfluids. We introduce a model, which combines lowest Landau level (LLL) projection with the magnetic Wannier basis to represent degenerate eigenstates in the LLL. Solving the model numerically via large-scale Monte Carlo simulations, we find clear evidence for a continuous melting transition, in perfect agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory and with recent experiments.
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.
We study {\em dynamic} melting of confined vortex matter moving in disordered, mesoscopic channels by mode-locking experiments. The dynamic melting transition, characterized by a collapse of the mode-locking effect, strongly depends on the frequency, i.e. on the average velocity of the vortices. The associated dynamic ordering velocity diverges upon approaching the equilibrium melting line $T_{m,e}(B)$ as $v_c \sim (T_{m,e}-T)^{-1}$. The data provide the first direct evidence for velocity dependent melting and show that the phenomenon also takes place in a system under disordered confinement. …
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…
Self-field imaging of current distribution in Ba0.6K0.4Fe2As2 superconductor is used to study the effect of drive on the low-field vortex solid to liquid melting phase transformation. At low fields, the current induced drive on the vortices aids in thermally destabilizing the vortex state thereby shifting the low field melting phase boundary. We show that the current induced drive shifts solid-liquid boundaries and prepones the vortex melting phenomenon compared to the equilibrium situation. The analysis shows that for currents above 50 mA, Joule heating effects shift the melting line while be…
We present a mode locking (ML) phenomenon of vortex matter observed around the peak effect regime of 2H-NbSe$_2$ pure single crystals. The ML features allow us not only to trace how the shear rigidity of driven vortices persists on approaching the second critical field, but also to demonstrate a dynamic melting transition of driven vortices at a given velocity. We observe the velocity dependent melting signatures in the peak effect regime, which reveal a crossover between the disorder-induced transition at small velocity and the thermally induced transition at large velocity. This uncovers the…
A phenomenological model is proposed for melting of a vortex lattice, based on screening of the elastic shear modulus by mobile or partially pinned dislocations. A first-order softening line is found and ends at a critical point beyond which the lattice crosses over to an hexatic vortex solid. The consequences of softening on vortex dynamics are explored, as fingerprints of plastic dynamics: a reentrance of single vortex behaviour, for both depinning and collective creep, occurs as the field increases, with non-monotonous creep exponents. This general scenario is supported by recent experiment…
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…
A sharp resistance drop associated with vortex lattice melting was observed in high quality YBa_2Cu_4O_8 single crystals. The melting line is well described well by the anisotropic GL theory. Two thermally activated flux flow regions, which were separated by a crossover line B_cr=1406.5(1-T/T_c)/T (T_c=79.0 K, B_cr in T), were observed in the vortex liquid phase. Activation energy for each region was obtained and the corresponding dissipation mechanism was discussed. Our results suggest that the vortex lattice in YBa_2Cu_4O_8 single crystal melts into disentangled liquid, which then undergoes …
We study the melting of a moving vortex lattice through numerical simulations with the current driven 3D XY model with disorder. We find that there is a first-order phase transition even for large disorder when the corresponding equilibrium transition is continuous. The low temperature phase is an anisotropic moving glass.
We develop a theory for dislocation-mediated structural transitions in the vortex lattice which allows for a unified description of phase transitions between the three phases, the elastic vortex glass, the amorphous vortex glass, and the vortex liquid, in terms of a free energy functional for the dislocation density. The origin of a critical endpoint of the melting line at high magnetic fields, which has been recently observed experimentally, is explained.
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…
In cuprate high-temperature superconductors the small coherence lengths and high transition termperatures result in strong thermal fluctuations, which render the superconducting transition in applied magnetic fields into a wide continuous crossover. A state with zero resistance is found only below the vortex melting transition, which occurs well below the onset of superconducting correlations. Here we investigate the vortex phase diagram of the novel Fe-based superconductor in form of a high-quality single crystal of Ba0.5K0.5Fe2As2, using three different experimental probes (specific heat, th…
In his the Comment, P. Ao affirms that his vortex many-body theory explains the observations reported in G. D'Anna et al., Phys. Rev. Lett. 81, 2530 (1998). Indeed, we provide here some arguments to show the lack of a satisfactory explanation within the known theoretical frameworks.
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…
The vortex-lattice melting transitions in two typical iron-based high-Tc superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ (122-type) and$Nd(O_{1-x}F_{x})FeAs$ (1111-type) for magnetic fields both parallel and perpendicular to the anisotropy axis are studied within the elastic theory. Using the parameters from experiments, the vortex-lattice melting lines in the H-T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical result for the vortex melting on $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ for parallel fields agrees well the recent experimental data…
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…
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…
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.
Vortex matter phase transitions in the high-temperature superconductor Bi2Sr2CaCu2O8 were studied using local magnetization measurements combined with a vortex 'shaking' technique. The measurements revealed thermodynamic evidence of a first-order transition along the second magnetization peak line, at temperatures below the apparent critical point Tcp. We found that the first-order transition line does not terminate at Tcp, but continues down to at least 30 K. This observation suggests that the ordered vortex lattice phase is destroyed through a unified first-order transition that changes its …
Phase fluctuations in the superconducting order parameter, which are responsible for the melting of the Abrikosov vortex lattice below the mean field $H_{c2}$, are shown to dramatically enhance the scattering of quasi-particles by the fluctuating pair potential, thus leading to enhanced damping of the dHvA oscillations in the liquid mixed state. This effect is shown to quantitatively account for the detailed field dependence of the dHvA amplitude observed recently in the mixed state of a Quasi 2D organic SC.
The first-order nature of the vortex-lattice melting transition in copper-based layered high-Tc superconductors is well established. The associated discontinuities in magnetization have been extensively studied, for example, in YBa2Cu3O7 and Bi2Sr2CaCu2O8, while the respective latent heats have been systematically investigated only in YBa2Cu3O7 and related compounds. The apparent absence of such signatures in conventional superconductors such as Nb raises the question whether or not the concept of vortex-lattice melting is applicable at all in such materials. Based on available literature to d…
To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the meltin…
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.
Using numerical results obtained within two models describing vortex matter (interacting elastic lines (Bose model) and uniformly frustrated XY-model) we establish universal properties of the melting transition within the linelike regime. These properties, which are captured correctly by both models, include the scaling of the melting temperature with anisotropy and magnetic field, the effective line tension of vortices in the liquid regime, the latent heat, the entropy jump per entanglement length, and relative jump of Josephson energy at the transition as compared to the latent heat. The uni…
Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromagnetic and Josephson interactions among pancake vortices were included. A special shaking and annealing process was introduced to let the system approach the equilibrium configuration. We are able to see the inverse melting transition from the Bragg-glass to the amorphous vortex glass state, in agreement with recent experiments.
We present a study of the vortex lattice in untwinned YBa$_2$Cu$_3$O$_{7-x}$ crystals, using a combination of muon spin rotation and neutron small angle scattering measurements. Both methods show a very sharp melting temperature consistent with a first order transition. The dependence of the melting temperature on the angle of the field with respect to the crystallographic c-axis is studied. The results are compared to thermal measurements.
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 …
The state of the vortex lattice extremely close to the superconducting to normal transition in an applied magnetic field is investigated in high purity niobium. We observe that thermal fluctuations of the order parameter broaden the superconducting to normal transition into a crossover but no sign of a first order vortex lattice melting transition is detected in measurements of the heat capacity or the small angle neutron scattering (SANS) intensity. Direct observation of the vortices via SANS always finds a well ordered vortex lattice. The fluctuation broadening is considered in terms of the …
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…
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 dynamic phase diagram of vortex lattices driven in disorder is calculated in two and three dimensions. A modified Lindemann criterion for the fluctuations of the distance of neighboring vortices is used, which unifies previous analytic approaches to the equilibrium and non-equilibrium phase transitions. The temperature shifts of the dynamic melting and decoupling transitions are found to scale inversely proportional to large driving currents. A comparison with two-dimensional simulations shows that this phenomenological approach can provide quantitative estimate for the location of these t…
Assuming that the order parameter corresponds to an equal spin triplet pairing symmetry state, we calculate the effect of phase fluctuations in quasi-one-dimensional superconductors at high magnetic fields applied along the y (b') axis. We show that phase fluctuations can destroy the theoretically predicted triplet reentrant superconducting state, and that they are responsible for melting the magnetic field induced Josephson vortex lattice above a magnetic field dependent melting temperature Tm.
The precise measurements of vortex melting point towards a need to develop a quantitative theoretical description of thermal fluctuations in vortex matter. To tackle the difficult problem of melting, the description of both the solid and the liquid phase should reach the precision level well below 0.1%. Such a theory in the framework of the Ginzburg - Landau approach is presented. The melting line location is determined and magnetization, specific heat jumps along it are calculated. We find that the magnetization in the liquid is larger than that in the solid by 1.8% regardless of the melting …
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, …
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 effects of an $ab$-surface on the vortex-solid to vortex-liquid transition in layered superconductors in the limit of vanishing inter-layer Josephson coupling. We derive the interaction between pancake vortices in a semi-infinite sample and adapt the density functional theory of freezing to this system. We obtain an effective one-component order-parameter theory which can be used to describe the effects of the surface on vortex-lattice melting. Due to the absence of protecting layers in the neighbourhood of the surface, the vortex lattice formed near the surface is more susceptibl…
The vortex lattice melting transition in single crystals Bi2Sr2CaCu2O8+d was studied by the in-plane resistivity measurements in magnetic fields tilted away from the c-axis to the 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. For the first time, the complete Hc-Hab phase diagram of the melting-transition in Bi2Sr2CaCu2O8+d is obtained. The c-axis melting field component Hc-melt exhibits the novel, step-wise dependence on the in-plane magnetic fields Hab w…
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 vortex correlation along the c-axis in high quality single crystals of YBa$_{2}$Cu$_{4}$O$_{8}$ has been investigated as a function of temperature T in different magnetic fields, using the quasi-flux transformer configuration. A simultaneous sharp drop associated with the vortex lattice melting is observed in both the primary and secondary voltages(V$_{top}$ and V$_{bot}$). Just above the melting temperature, the vortices form three-dimensional line liquid with the correlation length along the c direction $L_{c}\leq $ t, the sample thickness. The temperature where a resistive peak in R$_{b…
