Magic angle conditions for twisted three-dimensional topological insulators

Abstract

When two layers of graphene are stacked at a specific ``magic'' twist angle, the Dirac cones hybridize, forming perfectly flat bands. Can Dirac cones at the interface between two stacked and twisted 3D topological insulators exhibit similar band flattening? Ultimately, the generalization from Dirac cones in sublattice space to spin space is not so simple. The authors derive here the necessary conditions to flatten the anomalous Dirac cones, which has implications for realizing tunable interacting topological phases.