Z2 topology and edge states of twisted bilayer graphene*

Recently twisted bilayer graphene (tBLG) emerges as a new platform of strongly correlated electrons near a magic twist angle, which hosts many exciting phenomena such as the Mott-like insulating phase, unconventional superconducting behavior, and emergent Chern ferromagnetism. Besides the apparent significance of band flatness, band topology may be another critical element responsible for the strongly correlated phenomena (like in the fractional quantum Hall effect) yet receives much less attention. We demonstrate that, while an unusual symmetry of tBLG trivializes the Berry curvature, two Z2 invariants characterize the topology of the moiré Dirac bands. We further show that subtle gapless edge states can survive in the electron and hole superlattice gaps of tBLG and mediate universal nonlocal transport that are robust to the interlayer electric field, twist angle, and edge termination.