Half-filled Landau level in a honeycomb lattice: Chern insulator of composite fermions

The study of electronic correlations in half-filled Landau level presents a challenge due to the massive degeneracy in the single-particle spectrum. The most successful description of this exotic state has been in terms of field theory of composite fermions: either the Halperin-Lee-Read (HLR) version where the composite fermions are the original electrons bound to some fluxes; or the Dirac composite fermion which exploits the duality of the field strength and density. In this work we demonstrate the construction of a lattice version of the long-wavelength field theories. We show that for a honeycomb lattice, a HLR type construction of composite fermions leads to a Chern insulator which reduces to the Haldane model at half-filling. As a result, the K and K’ points are gapped out which can be measured in tunneling experiments.