The magnetic properties of superconducting alloys I

Abstract

The general Ginzburg - Landau equation valid for all temperatures is derived from the microscopic theory for superconducting alloys where the electronic mean free path 1 is much shorter than the coherence length ${\ensuremath{\xi}}_{0}$.Using this equation the magnetic properties of Abrikosov's mixed state as well as the temperature dependence of the upper critical field ${\mathrm{H}}_{\mathrm{c}\phantom{\rule{0.25em}{0ex}}2}$ are discussed. It is shown that the Abrikosov structure in the vicinity of the transition point is completely characterized by two parameters ${\ensuremath{\kappa}}_{1}(\mathrm{T})$ and ${\ensuremath{\kappa}}_{2}(\mathrm{T})$, both of which coincide at the critical temperature with $\ensuremath{\kappa}$, the Ginzburg-Landau parameter. A peculiar deviation in the thermodynamical behavior at lower temperatures from Abrikosov's theory is found for superconductors with $\ensuremath{\kappa}\ensuremath{\simeq}1/\sqrt{2}$.