Superconductivity of quasi-one- and quasi-two-dimensional tight-binding electrons in a magnetic field

The upper critical field H-c2(T) of tight-binding electrons in a three-dimensional lattice is investigated. The electrons form Cooper pairs between eigenstates with the same energy in a strong magnetic field. The transition lines in the quasi-one-dimensional case are shown to deviate from the previously obtained results when the hopping matrix elements along the magnetic field are neglected. In the absence of Pauli pair breaking the transition temperature T-c(H) of the quasi-two-dimensional electrons is found to increase in an oscillatory manner as the magnetic field becomes large and to reach T-c(0) in the strong field, as in the quasi-one-dimensional case.