Abstract
Previous works on nodal d-wave superconductors have shown that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like modulated superconducting (SC) state can be realized with no magnetic field when quasiparticles acquire an additional linear term in the wavevector in their dispersion. In the present work, stability of such a novel modulated SC state in an artificial film against an applied magnetic field is studied. As a reflection of the presence of the two different FFLO states, one close to zero field and the other at the high field end, in a single field v.s. temperature phase diagram of thin films, the conventional uniform SC state generally tends to appear as a reentrant ordered phase bounded by the normal phase in {\it lower} fields.
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