Critical FieldsHc2(T)andHc3(T)in Strong-Coupling Superconductors

The Ginsburg-Landau (G-L) equations are developed for a superconducting system with strongly retarded electron-phonon interactions. The resultant equations are then solved for two choices of phonon spectrum, the first being a simple Einstein one and the second being that of two Lorentzians. For comparison with experiment, parameters are chosen appropriate to the strong-coupling element Pb. Solutions are obtained with the aid of a computer for the critical field $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ close to the critical temperature $T_c$ for both the clean and dirty cases. Results are then compared with experiment. An immediate corollary of our G-L equations is that the ratio of the critical field $H_{c3\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$, associated with nucleation in a surface layer, to $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ is 1.7, the same as for weak-coupling superconductors.