On type-II superconductors with a first-order transition at the lower critical field

The free energy of a superconductor in the mixed state is obtained to first order in 1–(T/T _c) and – in terms of the solutions of the Ginzburg-Landau equations for = . The circular cell approximation is used to evaluate the lower critical field and the discontinuity in the magnetization at this field for those type-II materials displaying a first-order transition at the field of first flux penetration; the cases of both singly quantized and doubly quantized vortices are considered. The main result of the numerical calculations is that the critical value of for a first-order transition is identical to the critical value of for an attractive interaction between widely separated vortices.Supported in part by the National Research Council of Canada.