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For interacting 2D electrons in the presence of magnetic field at halffilling, the system forms a `composite Fermi liquid(CFL)' with emergent Fermisurface and exhibits metallic behavior, based on the standard Halperin, Lee,and Read(HLR) field theory. Recently, Son introduces a composite Dirac theoryas the low energy effective description of Half-filled Landau Level. Suchtheory exhibits particle-hole symmetry and the underlying composite Fermisurface displays a robust $\pi$ Berry phase. In this paper, we start from thebilayer Half-filled Landau Level system where the two composite Fermi surfaceacquires interlayer coherence and forms bonding/anti-bonding composite fermisea. The corresponding interlayer coherent composite Fermi liquid(ICCFL) phaseprovides a straightforward landscape to verify the Dirac nature in Son's theoryand extract the hidden Berry phase structure of the composite Fermi surface.The ICCFL phase contains two Fermi surfaces which are detached in most regionsbut adhesive at two hot spots. Such nematic structure is a consequence of theBerry phase encoded in the Dirac Fermi surface which is absent in HLR theory.Due to the nematicity in ICCFL, the system supports half-quantum vortex withdeconfined $\frac{\pi}{2}$ gauge flux and the phase transition toward ICCFLcontains a Lifshitz criticality with $z=3$ dynamical exponent. In addition, theexciton order parameter carries topological spin number so the ICCFL contains aunique Wen-Zee term which connects EM response with the background geometrycurvature.

Interlayer coherent composite Fermi liquid in Half-filled Landau Level bilayers, a window toward the hidden $\pi$ Berry phase