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 ${\rho_{\mathrm{counterflow}}(\omega)\sim\omega^{2/z}}$ 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 $C_{\mathrm{tot}}=0$, 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.