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We consider fractional quantum Hall states in systems where two flat Chernnumber $C=\pm 1$ bands are labeled by an approximately conserved 'valley' indexand interchanged by time reversal symmetry. At filling factor $\nu=1$ thissetting admits an unusual hierarchy of correlated phases of excitons, neutralparticle-hole pair excitations of a fully valley-polarized `orbitalferromagnet' parent state where all electrons occupy a single valley. Excitonsexperience an effective magnetic field due to the Chern numbers of theunderlying bands. This obstructs their condensation in favor of a variety ofcrystalline orders and gapped and gapless liquid states. All these have thesame quantized charge Hall response and are electrically incompressible, butdiffer in their edge structure, orbital magnetization, and hence valley andthermal responses. We explore the relevance of this scenario for Moir\'eheterostructures of bilayer graphene on a hexagonal boron nitride substrate.

Excitonic fractional quantum Hall hierarchy in Moir\'e heterostructures