Emergent QED3 from half-filled flat Chern bands

Recently, two-dimensional Dirac materials patterned with a superlattice structure have emerged as a rich platform for exploring correlated and topological quantum matter. In this paper, we propose that by subjecting Dirac electrons on a particle-hole symmetric topological insulator (TI) surface to a periodic magnetic field with triangular lattice symmetry, it is possible to realize a quantum critical phase of Nf=3 Dirac fermion species strongly coupled to an emergent gauge field, or 2+1-D quantum electrodynamics (QED3). We demonstrate explicitly that the QED3 phase naturally arises from a Dirac composite fermion (CF) picture, where the periodic magnetic field manifests as a periodic CF potential and transforms the CF Fermi surface into gapless Fermi points. We further show that by breaking the particle-hole symmetry of the TI surface - either by doping or by introducing a periodic electrostatic potential with zero mean - our quantum critical phase gives way to a sequence of fractional Chern insulator phases. Our theory illustrates the rich menagerie of quantum phases possible around half filling of a flat Chern band.