Kekul’e-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of $m sim 100text{meV}$. We show that twisted bilayer graphene in which one or both layers have Kekul’e-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekul’e-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle $theta approx 0.7^circ$ and Dirac mass $m approx 100text{meV}$. When both layers have Kekul’e-O order, there is a large parameter regime around $thetaapprox 1^circ$ and $mgtrsim 100text{meV}$ in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases of matter.
Published : "arXiv Mesoscale and Nanoscale Physics".