Effect of the boundary condition on the vortex patterns in mesoscopic three-dimensional superconductors: Disk and sphere

Abstract

The vortex state of mesoscopic three-dimensional superconductors is determined using a minimization procedure of the Ginzburg-Landau free energy. We obtain the vortex pattern for a mesoscopic superconducting sphere and find that vortex lines are naturally bent and are closest to each other at the equatorial plane. For a superconducting disk with finite height, and under an applied magnetic field perpendicular to its major surface, we find that our method gives results consistent with previous calculations. The matching fields, the magnetization and H c3 , are obtained for models that differ according to their boundary properties. A change of the Ginzburg-Landau parameters near the surface can substantially enhance H c3 , as shown here.

Vortex Patterns Beyond Hypergeometric

“…where Ψ( r) is the order parameter, q, m are the Cooper pairs charge and mass, and α < 0, β > 0 are the second-order phase transition coefficients. If we investigate the order parameter in a region smaller than the penetrating length λ, yet comparable to the coherence length ξ, we can neglect the contribution to the free-energy of the term responsible by the expulsion of magnetic flux from the superconductor [4,9,31]. The singularity of the magnetic field consists in an infinitesimal magnetic dipole of relative strength μ = μ magn /μ 0 placed at the origin and directed along the z axis.…”

“…Following the standard numerical procedure for minimization, [4,9,21,27,28,31,32], we plug the test function equation (30) in the functional equation 31and look for minima. With the notations…”

“…Three-dimensional superconducting structures allow interesting physical properties such as giant vortices or multi-vortex states, or even (for larger size) a combination of the two states. The traditional approach relies on the Ginzburg-Landau (GL) free-energy minimization procedure, performed on a basis of linear combinations of solutions of the corresponding linearized GL equation [9,21,28]. While finite mesoscopic superconductor samples (size comparable to coherence length ξ, and penetration depth λ) of different geometries, subjected to external uniform magnetic field, have been theoretically investigated [4,9,17,21,27,28,31,32], there are no exact theoretical models proving that vortex states are possible in unbounded space.…”

Unconventional Vortex States in Nanoscale Superconductors Due to Shape-Induced Resonances in the Inhomogeneous Cooper-pair Condensate

“…Another system where effects of quantum confinement on vortex matter can be probed systematically are the optically trapped cold gases [40], which are nowadays extremely controllable. Further investigations will address the rich physics in the quantum limit, and show the effects of our findings in the 3D-confined case [41][42][43] and multicondensate samples [44], but where also barriers for vortex motion across the oscillating landscape can be investigated for possible use as Q bits or other vortex devices [45].…”

Physical Properties, Charge Carrier Mobility, and Photovoltaic Performance of Dendritic Oligothiophene Bearing Naphthalene Bis(dicarboximide) Groups

“…The problem is more complicated due to its explicitly expressed three-dimensional (3D) character, and it is necessary to take into account bending of vortices due to the effect of the boundary. The vortex state of mesoscopic spherical superconductors was determined using a minimization procedure of the Ginzburg-Landau free energy [23], in which the authors have proposed an interesting new method based on the analogy between the 3D lattice of inclusions and 3D lattice of mesoscopic superconductors. The authors of [23] have calculated that the vortex lines are naturally curved due to strong surface effects and that the giant vortex structure can break up into some smaller giant vortices or singly quantized vortices.…”