Density-functional theory of freezing of vortex-liquid in quasi two-dimensional superconductors

We present a theory of vortex liquid-to-solid transition in homogeneous quasi 2D superconductors. The free energy is written as a functional l of density of zeroes of the fluctuating order parameter. The transition is weakly first-order and well below the Hc2(T) line. Transition temperature, discontinuities of the average Abrikosov ratio and of the average superfluid density, the Debay-Waller factor and the latent heat are in good agreement with Monte Carlo simulations. The density is only weakly modulated in the "vortex-solid" phase, consistent with the density-wave behavior.Comment: 12 pages and 1 figure available upon request, LaTex Version 2.09, submitted to Phys. Rev. Let

Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.Comment: 15 pages, RevTex v3.0, followed by 5 postscript figure

First-Order Vortex Lattice Melting and Magnetization of YBa2_2Cu3_3O$_{7-\delta}

We present the first non-mean-field calculation of the magnetization $M(T)$ of YBa$_2$Cu$_3$O$_{7-\delta}$ both above and below the flux-lattice melting temperature $T_m(H)$. The results are in good agreement with experiment as a function of transverse applied field $H$. The effects of fluctuations in both order parameter $\psi({\bf r})$ and magnetic induction $B$ are included in the Ginzburg-Landau free energy functional: $\psi({\bf r})$ fluctuates within the lowest Landau level in each layer, while $B$ fluctuates uniformly according to the appropriate Boltzmann factor. The second derivative $(\partial^2 M/\partial T^2)_H$ is predicted to be negative throughout the vortex liquid state and positive in the solid state. The discontinuities in entropy and magnetization at melting are calculated to be $\sim 0.034\, k_B$ per flux line per layer and $\sim 0.0014$~emu~cm$^{-3}$ at a field of 50 kOe.Comment: 11 pages, 4 PostScript figures in one uuencoded fil

Superconducting zero temperature phase transition in two dimensions and in the magnetic field

We derive the Ginzburg-Landau-Wilson theory for the superconducting phase transition in two dimensions and in the magnetic field. Without disorder the theory describes a fluctuation induced first-order quantum phase transition into the Abrikosov lattice. We propose a phenomenological criterion for determining the transition field and discuss the qualitative effects of disorder. Comparison with recent experiments on MoGe films is discussed.Comment: 7 pages, 2 figure

Flux Lattice Melting and Lowest Landau Level Fluctuations

We discuss the influence of lowest Landau level (LLL) fluctuations near H_{c2}(T) on flux lattice melting in YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO). We show that the specific heat step of the flux lattice melting transition in YBCO single crystals can be attributed largely to the degrees of freedom associated with LLL fluctuations. These degrees of freedom have already been shown to account for most of the latent heat. We also show that these results are a consequence of the correspondence between flux lattice melting and the onset of LLL fluctuations.Comment: 4 pages, 2 embedded figure

Flux-line entanglement as the mechanism of melting transition in high-temperature superconductors in a magnetic field

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-T_c superconductors in ${\bf B}\parallel {\bf \hat{c}}$ is clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature T_m, while no sharp change can be found in the number and size distribution of vortex loops around T_m. Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of physical quantities are consistent with the above mechanism of the FLL melting. The Lindemann number is also evaluated without any phenomenological arguments.Comment: 10 pages, 5 Postscript figures, RevTeX; changed content and figures, Phys. Rev. B Rapid Commun. in pres

Topological Defects in the Abrikosov Lattice of Vortices in Type-II Superconductors

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.Comment: 30 pages, 17 Encapsulated PostScript figures, uses Revtex (with epsf

Instabilities and disorder-driven first-order transition of the vortex lattice

Transport studies in a Corbino disk geometry suggest that the Bragg glass phase undergoes a first-order transition into a disordered solid. This transition shows a sharp reentrant behavior at low fields. In contrast, in the conventional strip configuration, the phase transition is obscured by the injection of the disordered vortices through the sample edges, which results in the commonly observed vortex instabilities and smearing of the peak effect in NbSe2 crystals. These features are found to be absent in the Corbino geometry, in which the circulating vortices do not cross the sample edges.Comment: 12 pages 3 figures. Accepted for publication in Physical Review Letter

Phase Transitions in a Model Anisotropic High Tc Superconductor

We carry out simulations of the anisotropic uniformly frustrated 3D XY model, as a model for vortex line fluctuations in high Tc superconductors. We compute the phase diagram as a function of temperature and anisotropy, for a fixed applied magnetic field. We find that superconducting coherence parallel to the field persists into the vortex line liquid state, and that this transition lies well below the "mean-field" cross-over from the vortex line liquid to the normal state.Comment: 23 pages + 19 ps figure

Is there a Phase Transition to the Flux Lattice State?

The sharp drops in the resistance and magnetization which are usually attributed to a phase transition from the vortex liquid state to a crystal state are explained instead as a crossover between three and two dimensional behavior, which occurs when the phase coherence length in the liquid becomes comparable to the sample thickness. Estimates of the width of the crossover region and the phase coherence length scales are in agreement with experiment.Comment: 4 pages, RevTe