Ginzburg-Landau equations for a three-dimensional superconductor in a strong magnetic field

Melvin Glenn Royer, Purdue University

Abstract

Physicists know that, even at very low temperatures, a strong externally applied magnetic field will prevent a pottlntially superconducting material from actually entering the superconducting state. If the field strength is then reduced, superconductivity first forms near the surface of the sample before spreading to the interior. Furthermore, in type II superconductors, vortex filaments of normal (nonsuperconducting) material will persist in the interior at still lower fields. From a mathematically rigorous analysis of the Ginzburg-Landau model, we investigate this behavior for a three-dimensional ball of type II material in a uniform magnetic field of strength h. We show that there exists a finite set ${\cal H}$ of critical fields, depending on the radius of the ball and the Ginzburg-Landau parameter k, such that the normal stable if $h > {\rm max}{\cal H}$ and unstable if $h < {\rm min}{\cal H}.$ Furthermore, varying h as a parameter, we show that a superconducting state bifurcates from the normal state at each field in ${\cal H}$ and that the bifurcating states exhibit the anticipated surface superconductivity and vortex phenomena.

Degree

Ph.D.

Advisors

Bauman, Purdue University.

Subject Area

Mathematics|Condensation

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