Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moire superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.

Automated summary

We propose chiral decomposition rules for twisted N + M multilayer graphene configurations, which include arbitrary stacking order and mutual twist. In the chiral limit at the magic angle, the low-energy bands of these systems consist of chiral pseudospin doublets energetically entangled with two flat bands per valley induced by the moire superlattice potential. Numerical calculations based on realistic parametrization support the analytic construction. We also demonstrate that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, allowing the flat bands to carry nonzero valley Chern numbers. These findings provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.