Excitonic quantum criticality: from bilayer graphene to narrow Chern bands

We study a family of excitonic quantum phase transitions describing the evolution of a bilayer metallic state to an inter-layer coherent state where excitons condense. We argue that such transitions can be continuous and exhibit a non-Fermi liquid counterflow response ρcounterflow(ω)~ω2/z that directly encodes the dynamical critical exponent z. This physics is relevant to any system with spin, valley, or layer degrees of freedom. We consider two contexts for excitonic quantum criticality: (1) a weakly interacting graphene bilayer, and (2) a system of two narrow, half-filled Chern bands at zero external magnetic field, with total Chern number Cₜₒₜ=0, which may soon be realizable in moir\'{e} fractional quantum anomalous Hall systems. The latter system hosts a time-reversed pair of composite Fermi liquid states, and the condensation of excitons of the composite fermions leads to an exotic exciton insulator* state with a charge neutral Fermi surface. Our work sheds new light on the physics of inter-layer coherence transitions in 2D materials, and it constitutes the first unambiguous example of quantum critical transport in a clean non-Fermi liquid metal.