The Breakdown of Superconductivity Due to Strong Fields for the Ginzburg--Landau Model

Abstract

We study the behavior of a superconducting material subjected to a constant applied magnetic field, $\bH_a=h\bee$ with $|\bee|=1$, using the Ginzburg--Landau theory. We analytically show the existence of a critical field $\oh,$ for which when $h>\oh,$ the normal states are the only solutions to the Ginzburg--Landau equations. We estimate $\oh$. As $\k\downarrow 0$ we derive $\oh=O(1)$, while as $\k\to\infty$ we obtain $\oh=O(\k)$.