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Article
Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field
Journal of Mathematical Physics (2010)
  • Andrei Ludu, Embry Riddle Aeronautical University
Abstract
We solve the linear Ginzburg–Landau 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 formalism are constructed as expansions in the linear 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
Winter 2010
Citation Information
Andrei Ludu. "Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field" Journal of Mathematical Physics Vol. 51 Iss. 1 (2010)
Available at: http://works.bepress.com/andrei_ludu/3/