Broken Translational and Time-Reversal Symmetry in Unconventional Superconducting Films

We demonstrate that films of an unconventional (d-wave) superconductor at temperatures T less than or similar to 0.43T(c) can exhibit unusual superconducting phases. The new ground states beside the broken gauge and the point group symmetries can spontaneously break (i) continuous translational symmetry and form periodic order parameter structures in the plane of the film, or (ii) time-reversal symmetry and develop a supercurrent flowing along the film. These states are the result of the strong transverse inhomogeneity present in films with a thickness of several coherence lengths. We show a natural similarity between the formation of these states and the Fulde-Ferrell-Larkin-Ovchinnikov state.