Superconductivities of Quasi-One-Dimensional and Quasi-Two-Dimensional Tight-Binding Electrons in Magnetic Field

The superconductivity of the tight binding electrons in a magnetic field is studied. We can treat both cases of quasi-one-dimension and quasi-two-dimension in the same manner. We study a various kind of anisotropic superconductivity with line nodes of the energy gap by taking attractive interaction between electrons in nearest sites along each axis. The magnetic field dependence of the transition temperature is calculated for a various pairing symmetry of superconductivity. When a magnetic field is applied in the conducting plane, the transition temperature is shown to increase as the magnetic field increases. In the strong magnetic field the eigenstates approach to those in the absence of hopping between planes, resulting in no orbital frustration.