Composite Bogoliubov Fermi Liquid in a Half-Filled Chern Band

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 |q|^{3} contribution to the equal-time structure factor S(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.