Composite fermions have played a seminal role in understanding the quantum Hall effect, particularly the formation of a compressible `composite Fermi liquid (CFL) at filling factor nu = 1/2. Here we suggest that in multi-layer systems interlayer Coulomb repulsion can similarly generate `metallic behavior of composite fermions between layers, even if the electrons remain insulating. Specifically, we propose that a quantum Hall bilayer with nu = 1/2 per layer at intermediate layer separation may host such an interlayer coherent CFL, driven by exciton condensation of composite fermions. This phase has a number of remarkable properties: the presence of `bonding and `antibonding composite Fermi seas, compressible behavior with respect to symmetric currents, and fractional quantum Hall behavior in the counterflow channel. Quantum oscillations associated with the Fermi seas give rise to a new series of incompressible states at fillings nu = p/[2(p pm 1)] per layer (p an integer), which is a bilayer analogue of the Jain sequence.
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