Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3470767· OSTI ID:21476539

Ludu, A ^[1]; Van Deun, J; Cuyt, A ^[2]; Milosevic, M V; Peeters, F M ^[1]

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1. Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)
2. Departement Wiskunde-Informatica, Universiteit Antwerpen, Middelheimlaan 1, B-2020 Antwerpen (Belgium)

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.

• OSTI ID: 21476539
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3470767; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CONTINUED FRACTIONS
EIGENFUNCTIONS
EIGENVALUES
FREE ENERGY
GINZBURG-LANDAU THEORY
HYPERGEOMETRIC FUNCTIONS
MAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
SCHROEDINGER EQUATION
SUPERCONDUCTIVITY
SUPERCONDUCTORS
VORTICES
DIFFERENTIAL EQUATIONS
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
WAVE EQUATIONS