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Recent experiments in graphene heterostructures have observed Cherninsulators - integer and fractional Quantum Hall states made possible by aperiodic substrate potential. Here we study theoretically the competitionbetween different Chern insulators, which can be tuned by the amplitude of theperiodic potential, leads to a new family of quantum critical points describedby QED$_3$-Chern-Simons theory. At these critical points, $N_f$ flavors ofDirac fermions interact through an emergent U$(1)$ gauge theory at Chern-Simonslevel $K$, and remarkably, the entire family (with any $N_f$ or $K$) can berealized at special values of the external magnetic field. Transitions betweenparticle-hole conjugate Jain states realize "pure" QED$_3$ in which multipleflavors of Dirac fermion interact with a Maxwell U$(1)$ gauge field. Themulti-flavor nature of the critical point leads to an emergent SU$(N_f)$symmetry. Specifically, at the transition from a $\nu=$1/3 to 2/3 quantum Hallstate, the emergent SU(3) symmetry predicts an octet of charge density waveswith enhanced susceptibilities, which is verified by DMRG numerical simulationson microscopic models applicable to graphene heterostructures. We proposeexperiments on Chern insulators that could resolve open questions in the studyof 2+1 dimensional conformal field theories and test recent duality inspiredconjectures.

Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures