Emergent QED$_3$ from half-filled flat Chern bands

Abstract

In recent years, two-dimensional Dirac materials patterned with a superlattice structure have emerged as a rich platform for exploring correlated and topological quantum matter. In this work, we propose that by subjecting Dirac electrons to a periodic magnetic field with triangular lattice symmetry it is possible to realize a quantum critical phase of N f = 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 particlehole 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.