Computation of the Nonlinear Magnetic Response of a Three Dimensional Anisotropic Superconductor

Many problems in computational magnetics involve computation of fields which decay within a skin depth $\delta$, much smaller than the sample size $d$. We discuss here a novel perturbation method which exploits the smallness of $\epsilon \equiv \delta / d$ and the asymptotic behavior of the solution in the exterior and interior of a sample. To illustrate this procedure we consider the computation of the magnetic dipole and quadrupole moments of an anisotropic, unconventional, three dimensional superconductor. The method significantly reduces the required numerical work and can be implemented in different numerical algorithms.Comment: Three pages. To appear in Journal of Applied Physics (MMM-Intermag issue

Phase diagram of randomly pinned vortex matter in layered superconductors: dependence on the details of the point pinning

We study the thermodynamic and structural properties of the superconducting vortex system in high temperature layered superconductors, with magnetic field normal to the layers, in the presence of a small concentration of strong random point pinning defects via numerical minimization of a model free energy functional in terms of the time-averaged local density of pancake vortices. Working at constant magnetic induction and point pinning center concentration, we find that the equilibrium phase at low temperature ($T$) and small pinning strength ($s$) is a topologically ordered Bragg glass. As $T$ or $s$ is increased, the Bragg glass undergoes a first order transition to a disordered phase which we characterize as a ``vortex slush'' with polycrystalline structure within the layers and interlayer correlations extending to about twenty layers. This is in contrast with the pinned vortex liquid phase into which the Bragg glass was found to melt, using the same methods, in the case of a large concentration of weak pinning centers: that phase was amorphous with very little interlayer correlation. The value of the second moment of the random pinning potential at which the Bragg glass melts for a fixed temperature is very different in the two systems. These results imply that the effects of random point pinning can not be described only in terms of the second moment of the pinning potential, and that some of the unresolved contradictions in the literature concerning the nature of the low $T$ and high $s$ phase in this system are likely to arise from differences in the nature of the pinning in different samples, or from assumptions made about the pinning potential.Comment: 13 pages including 11 figures. Typos in HTML abstract corrected in v

Non-classical Rotational Inertia in a Two-dimensional Bosonic Solid Containing Grain Boundaries

We study the occurrence of non-classical rotational inertia (NCRI) arising from superfluidity along grain boundaries in a two-dimensional bosonic system. We make use of a standard mapping between the zero-temperature properties of this system and the statistical mechanics of interacting vortex lines in the mixed phase of a type-II superconductor. In the mapping, the liquid phase of the vortex system corresponds to the superfluid bosonic phase. We consider numerically obtained polycrystalline configurations of the vortex lines in which the microcrystals are separated by liquid-like grain boundary regions which widen as the vortex system temperature increases. The NCRI of the corresponding zero-temperature bosonic systems can then be numerically evaluated by solving the equations of superfluid hydrodynamics in the channels near the grain boundaries. We find that the NCRI increases very abruptly as the liquid regions in the vortex system (equivalently, superfluid regions in the bosonic system) form a connected, system-spannig structure with one or more closed loops. The implications of these results for experimentally observed supersolid phenomena are discussed.Comment: Ten pages, including figure

Vortex lattice melting in layered superconductors with periodic columnar pins

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.Comment: Four pages, 3 Figure

Flux Lattice Melting and the onset of H_c2 fluctuations

The flux lattice melting temperature in optimally doped YBCO has been shown to be very close to that of the onset of fluctuations around H_{c2}(T). Here, we present a theoretical argument in support of the idea that this occurs because the increased strength of the fluctuations as a function of magnetic field pushes away the first order flux lattice melting transition. The argument is based on hydrodynamic considerations (the Hansen-Verlet freezing criterion). It is not specific to high-temperature superconductors and can be generalized to other systems.Comment: 2 pages, 1 embedded figure, LT22 proceedings, Physica