Superconducting phase transitions in thin mesoscopic rings with enhanced surface superconductivity

Vortex Patterns Beyond Hypergeometric

“…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…”

“…The resulting expression for F is much simplified because we use for test functions the analytical solutions of the linearized problem. By introduction equation (30) in equation (31), and by using equation (32) and the orthonormality properties of Q ∞1 , we obtain, [4,7], the following values for the two coefficients that minimize the free energy For these value of the coefficients the Gibbs free energy equation (31) becomes…”

“…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. In this case the presence of an external applied magnetic field is un-physical (requests infinite energy) and one needs to generate the magnetic field from a localized source.…”

Vortex States in Nanosized Superconducting Strips with Weak Links Under an External Magnetic Field

“…For example, strong confinement leads to the formation of the giant vortex state [1][2][3][4][5] and multivortex state [6][7][8][9][10][11], which are energetically less favorable in bulk type-II superconductors [12]. An even more exotic vortex state was predicted to exist in nanoscale samples with artificial pinning: the vortex-antivortex state [13][14][15].…”

Finite Element Treatment of Vortex States in 3D Mesoscopic Cylindrical Superconductors in a Tilted Magnetic Field

“…Due to the interaction between vortices and sample boundaries, vortex configurations strongly dependent on the size and geometry of mesoscopic samples whose dimensions are of the order of the penetration depth λ or the coherence length ξ. For example, strong confinement leads to the formation of the giant vortex state [3][4][5][6][7] and multivortex state [8][9][10][11][12][13][14], which are energetically less favorable in bulk type-II superconductors [15]. The vortex-antivortex states are easily stabilized in an inhomogeneous magnetic field [16].…”