Intervalley-Coupled Twisted Bilayer Graphene from Substrate Commensuration

We show that intervalley coupling can be induced in twisted bilayer graphene (TBG) by aligning the bottom graphene layer with either of two types of commensurate insulating triangular Bravais lattice substrate. The intervalley coupling folds the ±K valleys of TBG to the Γ-point and hybridizes the original TBG flat bands into a four-band model equivalent to the p_{x}-p_{y} orbital honeycomb lattice model, in which the second conduction and valence bands have quadratic band touchings and can become flat due to geometric frustration. The spin-orbit coupling from the substrate opens gaps between the bands, yielding topological bands with spin Chern numbers C up to ±4. For realistic substrate potential strengths, the minimal bandwidths of the hybridized flat bands are still achieved around the TBG magic angle θ_{M}=1.05°, and their quantum metrics are nearly ideal. We identify two candidate substrate materials Sb_{2}Te_{3} and GeSb_{2}Te_{4}, which nearly perfectly realize the commensurate lattice constant ratio of sqrt[3] with graphene. These systems provide a promising platform for exploring strongly correlated topological states driven by geometric frustration.