Nonuniform superconducting states caused by odd-frequency Cooper pairs

Abstract: We discuss the origin of a nonuniform superconducting state in which Cooper pairs have a finite center of mass momentum. The instability to such a nonuniform superconducting state is analyzed by a pole of the pair fluctuation propagator for weak coupling superconductors. The results show that odd(even)-frequency Cooper pairs stabilize a nonuniform (uniform) superconducting phase below the transition temperature. We provide a theoretical framework that explains the reasons for appearing the nonuniform superconducting states.