Superconductivity of Quasi-Two-Dimensional Tight-Binding Electrons in a Strong Magnetic Field

We have investigated the transition temperature $T_{\mathrm{c}}(H)$ of superconductiv ity in quasi-two-dimensional (Q2D) tight-binding electrons in a strong magnetic field. When the magnetic field is parallel to 2D conducting plane, $T_{\mathrm{c}}(H)$ of the Q2D superconductor is shown to increase in an oscillatory manner as the magnetic field becomes large and to reach $T_{\rm c}(0)$ in a strong magnetic f ield limit for the spin-triplet superconductor. We consider the cases of on-site and nearest sites attractive interaction, and calculate the magnetic field depe ndences of the transition temperature for various types of symmetry. The first o rder transition from $p_y$-wave to $p_x$-wave is shown to occur at $H\sim 35$T w hen the magnetic field is parallel to the $y$ direction, which will be observed in a triplet superconductor, Sr${}_2$RuO${}_4$.