Bulk Solution of Ginzburg-Landau Equations for Type II Superconductors: Upper Critical Field Region

Bose-Einstein condensates in fast rotation

“…One first defines the coarse-grain averagen(x, y) of the spatial density n(x, y) = N|ψ(x, y)| 2 , in order to smooth the rapid variations at the vortex cores. The energy functional (15) can be written in terms ofn instead of n, provided the interaction parameter G is renormalized to bG, where b ≃ 1.16 is the so-called Abrikosov parameter [68]. This parameter arises from the discreteness of the vortex distribution: since the wave function ψ(x, y) must vanish at the vortex location, the average value of |ψ| 4 over the unit cell, hence the interaction energy, is larger than the result obtained if |ψ| was quasi-uniform over the cell.…”

Periodic solutions to the self-dual Ginzburg–Landau equations

“…Our method of proof is based on an iterative scheme which proves to be very useful in §3. Linear bifurcation analysis [3,1,2] finds the periodic superconducting solution which bifurcates from the normal state (ψ = 0), shows that the area of the unit cell at the bifurcation is given by l x l y = 2πM/κ 2 . Odeh [5] proved, in addition, that periodic weak solutions exist whenever l x l y > 2πM/κ 2 .…”

“…A linear bifurcation analysis of different periodic structures was performed by Kleiner et al [2], who found their solution to be energetically preferable to that of Abrikosov [1]. Chapman [3] studied the linear bifurcation of several other periodic structures together with the linear stability of Abrikosov's [1] solution, which was found unstable, and of the solution in Kleiner et al [2], which was found stable to several different modes of perturbations.…”

“…Chapman [3] studied the linear bifurcation of several other periodic structures together with the linear stability of Abrikosov's [1] solution, which was found unstable, and of the solution in Kleiner et al [2], which was found stable to several different modes of perturbations. The periodic structure in [2] has also been observed experimentally [4].…”

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].…”