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

TL;DR

This paper proposes a new quantum critical phase in 2D Dirac materials under a periodic magnetic field, leading to emergent QED$_3$ and fractional Chern insulator phases, expanding understanding of correlated topological matter.

Contribution

It introduces a novel realization of QED$_3$ in Dirac materials with a periodic magnetic field, connecting Dirac composite fermions to emergent gauge fields and fractional Chern insulators.

Findings

QED$_3$ phase naturally arises from Dirac composite fermion picture.

Breaking particle-hole symmetry leads to fractional Chern insulator phases.

The theory reveals diverse quantum phases around 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 (QED$_3$). We demonstrate explicitly that the QED$_3$ 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.