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

Xue-Yang Song; Hart Goldman; Liang Fu

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arXiv · 2302.10169

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

Xue-Yang Song·Hart Goldman·Liang Fu

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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.

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Xue-Yang Song, Hart Goldman, Liang Fu. 2023-02-20. Emergent QED$_3$ from half-filled flat Chern bands. https://arxiv.org/abs/2302.10169

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