The Ultra-critical Floquet Non-Fermi Liquid

We demonstrate the existence of a quantum non-equilibrium steady state of periodically driven fermions coupled to a bosonic bath that has no counterpart in equilibrium. This state features multiple sharp Fermi surfaces which are the locus of higher order cusp-like non-analyticities in the momentum occupation, but without an associated jump or quasiparticle residue, therefore making these states non-equilibrium non-fermi liquids. More intriguinly, these non-analyticities survive even when the bath is at finite temperature. This is a property that has no analogue in known equilibrium fermi or non-fermi liquids, because for these equilibrium states temperature invariably acts as a relevant perturbation which smears out the sharpness of the jump or the non-analyticities of the occupation function and endows the fluid with a finite correlation length, beyond which it behaves classically. We discuss how monocromatic radiation in the microwave range impinging in high quality electronic systems is a promising regime to detect these states in experiments.