Photo-induced superconductivity at integer filling = activated discrete time crystal?

Parametric resonance has been widely discussed as a mechanism of both photo-induced superconductivity and discrete time crystal. we reveal a possible connection between the two seemingly different phenomena. We show that a parametrically driven system with global U(1) symmetry has an intrinsically nonequilibrium steady state, which spontaneously breaks both the discrete time translation symmetry and the U(1) symmetry. The U(1)-breaking order parameter oscillates at half of the drive frequency, resembling a parametrically-driven oscillator. When coupling to electromagnetic field, this nonequilibrium phase exhibits perfect conductivity and Meissner effect, even though the time average of the order parameter is zero.