Excitonic quantum criticality: From multilayer graphene to narrow Chern bands

We study a family of excitonic quantum phase transitions describing the evolution of a bilayer metallic state to an interlayer coherent state where excitons condense. We argue that such transitions can be continuous and exhibit a non-Fermi liquid counterflow response ${\ensuremath{\rho}}_{\mathrm{counterflow}}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2/z}$ that directly encodes the dynamical critical exponent $z$. Our calculations are performed within a controlled expansion around $z=2$. This physics is relevant to any system with spin, valley, or layer degrees of freedom. We consider two contexts for excitonic quantum criticality: (1) an interacting bilayer of strongly correlated Fermi liquids, 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 materials. 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 interlayer coherence transitions in two-dimensional materials.