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Article
Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field
Journal of Mathematical Physics (2010)
  • A. Ludu, Northwestern State University, Louisiana
  • J. Van Deun, Universiteit Antwerpen
  • M. V. Milošević, Universiteit Antwerpen
  • A. Cuyt, Universiteit Antwerpen
  • F. M. Peeters, Universiteit Antwerpen
Abstract
We solve the linear Ginzburg–Landau (GL) equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis and selected by minimization of the free energy. We present examples of vortex states and their energies for different samples in enhancing/suppressing superconductivity surroundings.
Keywords
  • mesoscopic superconductivity,
  • vortex states,
  • axial magnetic field,
  • Ginzburg-Landau
Publication Date
August, 2010
DOI
https://doi.org/10.1063/1.3470767
Citation Information
A. Ludu, J. Van Deun, M. V. Milošević, A. Cuyt, et al.. "Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field" Journal of Mathematical Physics Vol. 51 Iss. 8 (2010) ISSN: 0022-2488
Available at: http://works.bepress.com/andrei_ludu/3/