Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks

Abstract

When an ideal (no bulk pinning) flat type-II superconducting disk is subjected to a perpendicular magnetic field Ha, the first vortex nucleates at the rim when Ha = H0, the threshold field, and moves quickly to the center of the disk. As Ha increases above H0, additional vortices join the others, and together they produce a domelike field distribution of radius b. In this paper I present analytic solutions for the resulting magnetic-field and sheet-current-density distributions. I show how these distributions vary as b increases with Ha, and I calculate the corresponding field-increasing magnetization.

Suppression of geometrical barrier in $Bi_2Sr_2CaCu_2O_{8+δ}$ crystals by Josephson vortex stacks

“…The barrier is formed by the interplay between the vortex line tension and the Lorentz force that is induced by the circulating Meissner currents. [4][5][6][7][8][9][10] In a sample with elliptical cross section, for example, the energy of a test vortex has two contributions: the positive vortex line energy increases gradually from zero at the edge of the sample to a value of ǫ 0 d in the center (ǫ 0 is the vortex line energy per unit length and d is the sample thickness). The Meissner currents that flow over the entire surface exert inward forces on the vortex that gradually lower its energy as it moves toward the center.…”

“…In a platelet sample of rectangular cross section, in contrast, by cutting through the sharp rims, the vortex attains its full line energy ǫ 0 d within a distance of the order of d/2 from the edge, 4 while the Meissner currents remain distributed as in elliptical sample. 39 As a result, a geometry related barrier of height of the order of ǫ 0 d is formed that extends over a width of the order of the half width of the sample, w. [4][5][6][7][8][9][10]25 Consequently, when the field H z is increased above the penetration field H p ≃ (2H c1 /π) d/w vortices entering through the edges are swept by the Meissner currents toward the center where they accumulate giving rise to a dome shaped induction profile of width 2b, see Fig. 1(c).…”

“…1 There are several sources of potential barriers: pinning due to quenched material disorder in the bulk of the sample, surface pinning produced by the roughness of the sample surface, 2 Bean-Livingston surface barrier arising from the force between a vortex parallel to a surface and its image, 3 and geometrical barrier (GB) that arises from the force due to Meissner currents in thin slab-shaped superconducting samples in perpendicular field. [4][5][6][7][8][9][10] Strong vortex pinning and the associated magnetic hysteresis are vital elements in superconductor applications that are based on high critical currents. The magnetic hysteresis, however, masks the equilibrium magnetization properties, the study of which is essential for comprehension of the thermodynamic structure of the vortex matter.…”

Enhancement of penetration field in vortex matter in mesoscopic superconductors due to Andreev bound states

“…[5][6][7][8][9] Surface effects in vortex nanocrystals affect its thermodynamic, structural and magnetic properties. [10][11][12][13] For instance, due to surface barriers, the field at which the first vortex penetrates, H P , [14,15] can be larger than the lower critical field H c1 (depending only on the penetration depth λ and the coherence length ξ of the material). This effect becomes more relevant when the surface-to-volume ratio of the number of vortices in nanocrystals enhances.…”