Nonequilibrium hysteretic phase transitions in periodically light-driven superconductors

We find nonequilibrium phase transitions accompanied by multiple (nested) hysteresis behaviors in superconductors coupled to baths under a time-periodic light driving. The transitions are demonstrated with a full phase diagram in the domain of the driving amplitude and frequency by means of the Floquet many-body theory. In the weak-driving regime with a frequency smaller than half of the superconducting gap, excited quasiparticles are accumulated at the far edges of the bands, realizing a distribution reminiscent of the Eliashberg effect, which suddenly becomes unstable in the strong-driving regime due to multiphoton-assisted tunneling across the gap mediated by the in-gap Floquet sidebands. We also show that superconductivity is enhanced in the weak-driving regime without effective cooling, which is attributed to the modulation of the spectrum due to Floquet sidebands.