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We examine the possibility of creating the Moore-Read Pfaffian in the lowestLandau level when the multicomponent Halperin 331 state (believed to describequantum Hall bilayers and wide quantum wells at the filling factor $\nu=1/2$)is destroyed by the increase of tunneling. Using exact diagonalization of thebilayer Hamiltonian with short-range and long-range (Coulomb) interactions inspherical and periodic rectangular geometries, we establish that tunneling is aperturbation that drives the 331 state into a compressible composite Fermiliquid, with the possibility for an intermediate critical state that possessessome properties of the Moore-Read Pfaffian. These results are interpreted inthe two-component BCS model for Cauchy pairing with a tunneling constraint. Wecomment on the conditions to be imposed on a system with fluctuating density inorder to achieve the stable Pfaffian phase.

Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases