Composite Bogoliubov Fermi liquid in a half-filled Chern band

Abstract: The composite Fermi liquid (CFL) 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 {\it the composite Bogoliubov Fermi liquid (CBFL)}. This phase has a number of remarkable 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, non-quantized thermal conductance, Landau damping of density fluctuations, and a non-analytic $|\mathbf{q}|^3$ contribution to the equal-time structure factor $S(\mathbf{q})$. We also briefly discuss vortex physics and possible 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 that go beyond the conventional Landau level paradigm.