Twistronics of Kekule Graphene: Honeycomb and Kagome Flat Bands

Kekule-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of m similar to 100 meV. We show that twisted bilayer graphene in which one or both layers have Kekule-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekule-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 approximate to 0.7 degrees andDiracmass m approximate to 100 meV. When both layers have Kekule-O order, there is a large parameter regime around theta approximate to 1 degrees and m greater than or similar to 100 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.