  Recently twisted bilayer graphene (t-BLG) emerges as a new strongly
correlated physical platform near a magic twist angle, which hosts many
exciting phenomena such as the Mott-like insulating phases, unconventional
superconducting behavior and emergent ferromagnetism. Besides the apparent
significance of band flatness, band topology may be another critical element in
determining strongly correlated twistronics yet receives much less attention.
Here we report compelling evidence for nontrivial noninteracting band topology
of t-BLG moir\'e Dirac bands through a systematic nonlocal transport study, in
conjunction with an examination rooted in $K$-theory. The moir\'e band topology
of t-BLG manifests itself as two pronounced nonlocal responses in the electron
and hole superlattice gaps. We further show that the nonlocal responses are
robust to the interlayer electric field, twist angle, and edge termination,
exhibiting a universal scaling law. While an unusual symmetry of t-BLG
trivializes Berry curvature, we elucidate that two $Z_2$ invariants
characterize the topology of the moir\'e Dirac bands, validating the
topological edge origin of the observed nonlocal responses. Our findings not
only provide a new perspective for understanding the emerging strongly
correlated phenomena in twisted van der Waals heterostructures, but also
suggest a potential strategy to achieve topologically nontrivial metamaterials
from topologically trivial quantum materials based on twist engineering.
