Magnetic Properties of Intrinsic London Superconductors

Abstract

We present here a theory of intrinsic London superconductors in the vicinity of the transition point where the transition from the mixed state to the normal state takes place. The equations for local superconductors [i.e., for $\Delta \left(\mathrm{r}\right)$] for impurity-free metal, deduced previously by Gor'kov, are explicitly solved by using the variational function of Abrikosov. Use is made of the results due to Gor'kov concerning the upper critical field of pure superconductors. It is shown that the mixed state in the immediate subcritical region is expressed in terms of ${\kappa }_1$ and ${\kappa }_2$, which coincide at the critical temperature with $\kappa$, the Ginzburg-Landau parameter. The upper critical field is expressed in terms of ${\kappa }_1$, while the slope of the magnetization curve is given in term of ${\kappa }_2$. The explicit calculation of ${\kappa }_1$ and ${\kappa }_2$ shows that ${\kappa }_2$ increases more rapidly than ${\kappa }_1$ as temperature decreases, and diverges at low temperature.