Maurer, S. M. and Yeh, N.-C. and Tombrello, T. A. (1998) Numerical calculation of the vortex-columnar-defect interaction and critical currents in extreme type-II superconductors - a two-dimensional model based on the Ginzburg-Landau approximation. Journal of Physics: Condensed Matter, 10 (33). pp. 7429-7443. ISSN 0953-8984. http://resolver.caltech.edu/CaltechAUTHORS:20090918-133518043
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We extend our previous one-dimensional Ginzburg-Landau calculations of the pinning energy of vortices to two dimensions, in order to achieve an understanding of the pinning forces exerted on vortices by defects. By minimizing the free energy using a relaxation scheme, we obtain the spatial variation of the order parameter and supercurrents for a vortex in the vicinity of a cylindrical defect in an extreme type-II superconductor. The resulting two-dimensional field distributions provide a direct mapping of the spatial dependence of the vortex-defect pinning potential, thereby yielding the pinning force and depinning current as a function of the defect size and magnetic field. We also use periodic boundary conditions in the two-dimensional Ginzburg-Landau equations to solve for the known vortex-vortex interaction, in order to verify the resolution and accuracy of our approach for extreme type-II superconductors. Our direct numerical derivation of the pinning force per vortex is shown to be applicable to a wide range of magnetic fields and columnar-defect densities, and the calculated results are consistent with experimental observation.
|Additional Information:||Copyright © Institute of Physics and IOP Publishing Limited 1998. Received 16 April 1998, in final form 3 June 1998. Print publication: Issue 33 (24 August 1998). SM would like to acknowledge support from Caltech’s Ph11 and the Summer Undergraduate Research (SURF) programs that made his participation possible. SM also thanks Brian D’Urso for helpful discussions on the numerical algorithms. The work was supported in part by the National Science Foundation (Grants DMR94-01315 and DMR93-18931), the Office of Naval Research (Grant N00014-91-J-1556), and the David and Lucile Packard Foundation.|
|Official Citation:||Numerical calculation of the vortex-columnar-defect interaction and critical currents in extreme type-II superconductors - a two-dimensional model based on the Ginzburg-Landau approximation S M Maurer, N-C Yeh and T A Tombrello 1998 J. Phys.: Condens. Matter 10 7429-7443 doi: 10.1088/0953-8984/10/33/012|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||George Porter|
|Deposited On:||05 Oct 2009 18:02|
|Last Modified:||26 Dec 2012 11:24|
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