Fermi surface effect on spontaneous breaking of time-reversal symmetry in unconventional superconducting films

We propose a mechanism that helps stabilize a superconducting state with broken time-reversal symmetry, which was predicted to realize in a d-wave superconducting film [A. B. Vorontsov, Phys. Rev. Lett. 102, 177001 (2009)]. In this superconducting phase, the time-reversal symmetry breaking is accompanied by spontaneous breaking of the translation symmetry along the film surface. We examine how the normal-superconducting phase boundary in the thickness-temperature phase diagram of the film is modified depending on the Fermi surface shape. In particular, the nonuniform superconducting phase is found to substantially extend to a smaller thickness region in the phase diagram when the Fermi surface satisfies a nesting condition. We demonstrate this Fermi surface effect using a square-lattice tight-binding model.