A THEORETICAL-STUDY FOR THE SUPERCONDUCTIVITY UNDER THE ULTRA-HIGH MAGNETIC-FIELD IN THE STRONG-COUPLING

The formulation of strong coupling theory for superconductivity in the ultra-high magnetic field is made in the expression of Dyson's equati on for the case where electrons are confined only in a few Landau leve ls. The set of self-consistent equations is proposed in the procedure of Eliashberg theory. Further, results of numerical calculation for th e 2-dimensional system performed by the use of Frolich-type potential are discussed. In the dependence of the critical temperature T(c) on t he field, the convex-structures appear whose peaks correspond to the h alf-filling in Landau levels. For the ultra-high field where electrons occupy only the ground Landau level, T(c) increases with increasing t he field. However, it has the tendency to be suppressed by the effect of the retardation for the interaction. On the contrary, the renormali zation coefficient increases more abruptly. These behaviors are charac teristic features shown clearly in the present calculation.