Composite Fermion Insulator in Opposite-Fields Quantum Hall Bilayers

We consider a quantum Hall bilayers from opposite magnetic fields close to the filling 1/2 + 1/2 . We add inter-layer repulsive interaction starting from two decoupled Composite Fermion Liquids (CFL) with opposite chiralities. In this case physical exciton is frustrated from condensation, unlike the conventional quantum Hall bilayers. We argue that more natural phases are the exciton condensates between composite fermions or between slave bosons. The resulting states are insulators with neutral Fermi surfaces coupled to an emergent U(1) gauge field without Chern-Simons term. This insulating state is a generalization of the well-known CFL state. We also comment on the possibility of a topological superconductor in this system. Finally we give experimental proposals to simulate this novel system in a graphene moire system consisting of two nearly flat bands with opposite Chern numbers 1 and -1.