Discovery of High Dimensional Band Topology in Twisted Bilayer Graphene.

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 and unconventional superconducting behavior. Besides the apparent significance of band flatness, band topology may be another critical element in strongly correlated twistronics yet receives much less attention. Here we report the discovery of nontrivial high dimensional band topology in t-BLG moiru0027e bands through a systematic nonlocal transport study, in conjunction with an examination rooted in $K$-theory. The moiru0027e 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 high dimensional $Z_2$ invariants characterize the topology of the moiru0027e Dirac bands, validating the topological 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.