2000/11/30 by W. V. Pogosov, K. I. Kugel, K. I. Кugel +3 · 35 citations
Materials Science · Mathematics · Physics and Astronomy · #Anisotropy #Condensed matter physics #Ginzburg–Landau theory #Lattice (music) #Magnetic Properties and Applications #Magnetic field #Magnetization #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Superconductivity #Theoretical and Computational Physics #Type-II superconductor #Vortex #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.64.064517
published in Physical review. B, Condensed matter 64(6) (American Physical Society) · 8 pages, RevTex, 6 figures, submitted to Phys. Rev. B
arxiv created 2001/01/20 · openalex publication_date 2001/07/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A variational model is proposed to describe the magnetic properties of type-II superconductors in the entire field range between Hc1 and Hc2 for any values of the Ginzburg-Landau parameter \ensuremathκ>1/√(2). The hexagonal unit cell of the triangular flux-line lattice is replaced by a circle of the same area, and the periodic solutions to the Ginzburg-Landau equations within this cell are approximated by rotationally symmetric solutions. The Ginzburg-Landau equations are solved by a trial function for the order parameter. The calculated spatial distributions of the order parameter and the magnetic field are compared with the corresponding distributions obtained by numerical solution of the Ginzburg-Landau equations. The comparison reveals good agreement with an accuracy of a few percent for all \ensuremathκ values exceeding \ensuremathκ\ensuremath≈1. The model can be extended to anisotropic superconductors when the vortices are directed along one of the principal axes. The reversible magnetization curve is calculated and an analytical formula for the magnetization is proposed. At low fields, the theory reduces to the London approach at \ensuremathκ\ensuremath≫1, provided that the exact value of Hc1 is used. At high fields, our model reproduces the main features of the well-known Abrikosov theory. The magnetic field dependences of the reversible magnetization found numerically and by our variational method practically coincide. The model also refines the limits of some approximations that have been widely used. The calculated magnetization curves are in a good agreement with experimental data on high-Tc superconductors.