Vortex Lattice Melting in 2D Superconducting Networks and Films (original) (raw)
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Vortex sublattice melting in a two-component superconductor
We consider the vortex matter in a three-dimensional two-component superconductor with individually conserved condensates with different bare phase stiffnesses in a finite magnetic field, such as the projected superconducting state of liquid metallic hydrogen. The ground state is a lattice of composite, i.e. co-centered, vortices in both order parameters. We investigate quantitatively two novel phase transitions when temperature is increased at fixed magnetic field. i) A "vortex sub-lattice melting" phase transition where vortices in the field with lowest phase stiffness ("light vortices") loose co-centricity with the vortices with large phase stiffness ("heavy vortices"), thus entering a liquid state. Remarkably, the structure factor of the light vortex sub-lattice vanishes continuously. This novel transition, which has no counterpart in one-component superconductors, is shown to be in the 3Dxy universality class. Across this transition, the lattice of heavy vortices remains intact. ii) A first order melting transition of the lattice of heavy vortices, with the novel feature that these are interacting with a background liquid of light vortices. These findings are borne out in large-scale Monte Carlo simulations.
Journal of Experimental and Theoretical Physics Letters, 1997
The phase transition ''triangular lattice-vortex liquid'' in layered high-T c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (Ӎ3 K͒ into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (Ӎ8 K for T c ϭ84 K͒, the boundaries of the ''islands'' become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point ''triangular lattice-rotating lattice'' decreases slightly ͑to Ӎ2 K͒ and the temperature of the phase transition ''rotating lattice-vortex liquid'' increases substantially (Ӎ70 K͒.
Continuous Two-Dimensional Melting of Vortex-Solid in High Temperature Superconductors
MRS Proceedings, 1989
A model of continuous two-dimensional melting in the mixed state of high temperature superconductors is proposed. Two-dimensional melting sets in at a cross-over temperature Tx(H) below the three-dimensinal phase transition Tx(H) due to finite size effects, and Tx(H) is a function of the sample thickness (lc), applied magnetic field (H), and k(= λ/ξ) For a given zero-field transition temperature Tc0 and material properties, (such as defect density), the onset temperature of 2D-melting (Tx(H)) decreases with decreasing sample thickness and increasing magnetic field. In transport studies, thermally induced melting is further complicated by the depinning effect of high current densities.
Finite-size effects and anisotropic melting of the vortex solid in high-temperature superconductors
Physical review. B, Condensed matter, 1990
A mean-field model of anisotropic melting of the vortex solid in high-temperature superconductors is proposed. For a slab sample with dimensions I,b» l"where 2l,b and 2l, are the average diameter of the ab plane and the c axis thickness, respectively, large thermal fluctuations and finite-size eft'ects may result in anisotropic two-dimensional melting at crossover temperatures Ts(H) below the three-dimensional-melting transition Tss(H). Thus a quasi-two-dimensionally ordered vortex-liquid phase may exist in Tx(H) & T & Tst(H). Generally, Tz(H) decreases with the decreasing sample thickness, increasing magnetic field, and larger Ginzburg-Landau parameter x(=-X/g). In the limit of-, H, 2&&H &H, 2, the geometric anisotropy plays a more important role in determining Ts(H) than the electronic-mass anisotropy.
Flux-lattice melting in two-dimensional disordered superconductors
Physical Review B, 2003
The flux line lattice melting transition in two-dimensional pure and disordered superconductors is studied by a Monte Carlo simulation using the lowest Landau level approximation and quasiperiodic boundary condition on a plane. The position of the melting line was determined from the diffraction pattern of the superconducting order parameter. In the clean case we confirmed the results from earlier studies which show the existence of a quasi-long range ordered vortex lattice at low temperatures. Adding frozen disorder to the system the melting transition line is shifted to slightly lower fields. The correlations of the order parameter for translational long range order of the vortex positions seem to decay slightly faster than a power law (in agreement with the theory of Carpentier and Le Doussal) although a simple power law decay cannot be excluded. The corresponding positional glass correlation function decays as a power law establishing the existence of a quasi-long range ordered positional glass formed by the vortices. The correlation function characterizing a phase coherent vortex glass decays however exponentially ruling out the possible existence of a phase coherent vortex glass phase.
Direct observation of melting in a two-dimensional superconducting vortex lattice
Nature Physics, 2009
Topological defects such as dislocations and disclinations are predicted to determine the twodimensional (2-D) melting transition 1-3 . 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,
Dynamic melting and decoupling of the vortex lattice in layered superconductors
Physical Review B, 1998
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 transitions.
Physical Review B, 2004
A metastable homogeneous state exists down to zero temperature in systems of repelling objects. Zero ''fluctuation temperature'' liquid state therefore serves as a (pseudo) ''fixed point'' controlling the properties of vortex liquid below and even around melting point. There exists Madelung constant for the liquid in the limit of zero temperature which is higher than that of the solid by an amount approximately equal to the latent heat of melting. This picture is supported by an exactly solvable large NNN Ginzburg - Landau model in magnetic field. Based on this understanding we apply Borel - Pade resummation technique to develop a theory of the vortex liquid in type II superconductors. Applicability of the effective lowest Landau level model is discussed and corrections due to higher levels is calculated. Combined with previous quantitative description of the vortex solid the melting line is located. Magnetization, entropy 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. We compare the result with experiments on high TcT_{c}Tc cuprates YBa2Cu3O7YBa_{2}Cu_{3}O_{7}YBa2Cu3O7, DyBCODyBCODyBCO, low % T_{c} material (K,Ba)BiO3(K,Ba)BiO_{3}(K,Ba)BiO3 and with Monte Carlo simulations.
Physical Review B, 2004
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 minimum: this allows us to study in detail the structure of the different phases. We find that at these pin concentrations and low temperatures, the thermodynamically stable state is a topologically ordered Bragg glass. This nearly crystalline state melts into an interstitial liquid (a liquid in which a small fraction of vortex lines remain localized at the pinning centers) in two steps, so that the Bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline Bose glass. Both the Bragg glass to Bose glass and the Bose glass to interstitial liquid transitions are first-order. We also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments.
Theory of melting of vortex lattice in high Tc superconductors
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 Y BCO and Monte Carlo simulations.