Ultra-critical Fermi Surfaces, Quantum Oscillations, and Bosonic Metals in Floquet Quantum Fluids

Periodically driven quantum systems exhibit rich non-equilibrium phenomena that transcend equilibrium paradigms. We demonstrate the emergence of novel Fermi surface physics in particle-number-conserved fermionic and bosonic systems coupled to heat baths. In the fermionic case, we uncover "ultra-critical" Floquet non-Fermi liquid states characterized by persistent non-analyticities in momentum space occupation that remarkably retain their sharpness at finite temperature - a phenomenon without equilibrium analogues. These non-equilibrium Fermi surfaces manifest in quantum oscillation signatures and display power-law correlations immune to the finite-temperature bath. Extending beyond fermions, we discover analogous Fermi surface physics in bosonic systems, pointing to universal features in driven quantum systems that transcend particle statistics. Our findings open new avenues for realization of exotic non-equilibrium phases in driven quantum materials.