The composite Fermi liquid in the half-filled Landau level is a cornerstone of the quantum Hall phase diagram. Recent experiments and numerics indicate that an anomalous composite Fermi liquid (ACFL) can also arise at half filling of a Chern band without any external magnetic field, opening new possibilities for paired states of composite fermions beyond the fully gapped Pfaffian phase. We argue that, in inversion-asymmetric Chern bands with lattice rotational symmetry reduced to $C_3$, as realized in experimental platforms where signatures of the ACFL have been observed, composite fermions can form a superconductor with neutral gapless Bogoliubov Fermi surfaces. We term the resulting electronic state the composite Bogoliubov Fermi liquid. This phase has a number of properties that make it distinct from both the ACFL and the fully gapped Pfaffian. For instance, it is incompressible, has quantized Hall conductance, shows no quantum oscillations as a function of magnetic field or doping, and has topological ground state degeneracy on a torus despite the presence of gapless quasiparticles. At the same time, the neutral Bogoliubov Fermi surface yields metallic $T$-linear specific heat, nonquantized thermal conductance, Landau damping of density fluctuations, and a nonanalytic $|\mathit{q}{|}^3$ contribution to the equal-time structure factor $S(\mathit{q})$. We also discuss vortices and fractionalized daughter states induced by doping or external magnetic fields. Our results pave the way for a broader understanding of gapless topological phases arising from paired composite fermions in Chern bands beyond the conventional Landau level paradigm.

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• Chern insulators
• Composite fermions
• Fractional quantum Hall effect
• Fractionalization
• Topological phases of matter
• Chern-Simons gauge theory
• Landau-Ginzburg theory