Nonequilibrium hysteretic phase transitions in periodically light-driven superconductors

We find nonequilibrium phase transitions accompanied by multiple (nested) hysteresis behaviors in superconductors under a time-periodic light driving and coupled to baths. The presence of those transitions is demonstrated by establishing a full phase diagram in the domain of the driving amplitude and frequency by means of the Floquet many-body theory applied to dissipative superconductors. In the weak driving regime with a frequency smaller than half of the superconducting gap, excited quasiparticles are accumulated around the far edges of the bands, realizing a distribution similar to the one described in 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.