Temperature Dependence of the Critical Thickness of d-Wave Superconducting Films

We report a theoretical study of the critical thickness for a broken time-reversal state that may arise in d-wave superconducting films. By examining the effect of the Fermi surface shape on the critical thickness on the basis of a square lattice tight-binding model, we found that a substantial reduction of the critical thickness occurs near the half-filled limit. This result indicates that the Fermi surface nesting causes the area of the broken time-reversal superconducting phase to extend to a smaller thickness region in the thickness-temperature phase diagram.