  The observation of delicate correlated phases in twisted heterostructures of
graphene and transition metal dichalcogenides suggests an inherent resilience
of moir\'e flat bands against certain types of disorder. We investigate the
robustness of moir\'e flat bands in the chiral limit of the Bistrizer-MacDonald
model, applicable to both platforms in certain limits. We show a drastic
difference between the protection of the first magic angle and higher magic
angles to chiral symmetric disorder such as random higher moir\'e potential
harmonics arising, for instance, from lattice relaxation. We find that the
first magic angle is topologically protected by a topological index theorem,
similar to the protection of the zeroth Landau level of Dirac fermions, whose
flatness withstands any chiral symmetric perturbation such as non-uniform
magnetic fields. Focusing on the first magic angle of twisted bilayer graphene,
our analysis reveals a hidden non-local constant of motion that permits the
decomposition of the non-abelian gauge field induced by inter-layer tunnelings
into two decoupled abelian ones, underscoring a topological mechanism for band
flatness. Through numerical simulations, we further show the strikingly
different robustness of flat bands across protected (first) and unprotected
(higher) magic angles in the presence of various types of disorder and identify
the scattering processes that are enhanced or suppressed in the chiral limit.
Interestingly, we find that the suppression of disorder broadening persists
away from the chiral limit and is further accentuated by isolating a single
sublattice polarized flat band in energy. Our analysis suggests the Berry
curvature hotspot at the top of the K and K' valence band in the transition
metal dichalcogenide monolayers is essential for the stability of its moir\'e
flat bands and their correlated states.
