Escaping the Composite Fermi Sea: An Incompressible State at Half Filling in Graphene's Lowest Landau Level

Recent experiments in monolayer and trilayer graphene have observed incompressible even-denominator fractional quantum Hall states within narrow regions of parameter space associated with crossings of zeroth Landau levels. This is surprising because at half filling the Coulomb interaction in the zeroth Landau level is expected to favour a compressible composite Fermi liquid. Here we provide the first quantitative energetic study of the candidate incompressible phases and of the microscopic mechanisms that can stabilise them near such Landau-level crossings. Using exact diagonalization and infinite density-matrix renormalisation group, we first study ultra-short-range corrections to the Coulomb interaction arising from finite layer separation, lattice-scale effects, and electron-phonon coupling. We find that a sufficiently strong attractive short-range interaction drives the composite Fermi liquid first into a weakly paired d-wave pseudospin-singlet state and subsequently into a strongly paired state. However, microscopic estimates of these short-range corrections are far too small to stabilise either incompressible phase. We then incorporate Landau-level mixing through screening within the random-phase approximation. Screening substantially reshapes the effective interaction, suppresses the weak-pairing regime, and strongly enhances the tendency toward strong pairing. For a realistic range of microscopic parameters, the strongly paired phase is stabilised over a substantial fraction of that range. Our results identify the interplay of Landau-level mixing and ultra-short-range interactions as a plausible microscopic mechanism for the experimentally observed incompressible states in monolayer and trilayer graphene and point toward a strongly paired composite-fermion phase as their candidate ground state.