LAUSR

We study the intrinsic superconductivity in a dissipative Floquet electronic system in the presence of attractive interactions. Based on the functional Keldysh theory beyond the mean-field treatment, we find that the system shows a time-periodic bosonic condensation and reaches an intrinsic dissipative Floquet superconducting (SC) phase. Due to the interplay between dissipations and periodic modulations, the Floquet SC gap becomes "soft" and contains the diffusive fermionic modes with finite lifetime. However, the bosonic modes are still propagating even in the presence of dissipation. Our results also provides a simple and realistic system where the U(1) symmetry is broken spontaneously with dissipative environment.