"Topologically protected flatness in chiral moire heterostructures"
We investigate the robustness of moire flat bands in the chiral limit of the Bistrizer-MacDonald model and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. We understand these differences using a hidden constant of motion that permits the decomposition of the non-abelian gauge field induced by interlayer tunnelings into two decoupled abelian ones. At all magic angles, the resulting effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moire flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation such as non-uniform magnetic fields due to a topological index theorem -- thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. Through numerical simulations, we further study various types of disorder and identify the scattering processes that are enhanced or suppressed in the chiral limit.
