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 multi-photon-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.