Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field

A. Ludu; J. Van Deun; M. V. Milošević; A. Cuyt; F. M. Peeters

doi:10.1063/1.3470767

Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field

A. Ludu, J. Van Deun, M. V. Milošević, A. Cuyt, F. M. Peeters

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Journal of Mathematical Physics
Volume	51
DOIs	https://doi.org/10.1063/1.3470767
State	Published - Aug 2010
Externally published	Yes

Keywords

mesoscopic superconductivity
vortex states
axial magnetic field
Ginzburg-Landau

Disciplines

Condensed Matter Physics
Non-linear Dynamics
Partial Differential Equations

Access to Document

10.1063/1.3470767License: Unspecified

Cite this

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title = "Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field",

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",

author = "A. Ludu and {Van Deun}, J. and Milo{\v s}evi{\'c}, {M. V.} and A. Cuyt and Peeters, {F. M.}",

year = "2010",

month = aug,

doi = "10.1063/1.3470767",

language = "American English",

volume = "51",

journal = "Journal of Mathematical Physics",

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TY - JOUR

T1 - Analytic Treatment of Vortex States in Cylindrical Superconductors in Applied Axial Magnetic Field

AU - Ludu, A.

AU - Van Deun, J.

AU - Milošević, M. V.

AU - Cuyt, A.

AU - Peeters, F. M.

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

KW - mesoscopic superconductivity

KW - vortex states

KW - axial magnetic field

KW - Ginzburg-Landau

U2 - 10.1063/1.3470767

DO - 10.1063/1.3470767

M3 - Article

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

ER -