Nonequilibrium phononic first-order phase transition in a driven fermion chain

We study the direct laser drive of infrared-active phonons that are quadratically coupled to a spinless fermion chain. Feedback is incorporated by phonon dressing of the electronic dispersion, which enables effective non-linearities in the phonon dynamics. We uncover a first-order phase transition in the phononic steady state in which hysteretic effects allow either large or small phonon occupation depending on the drive protocol. We discuss the implications of these findings for probing phase transitions in real driven materials.