Second-order topological insulator in twisted bilayer graphene with small twist angles

In recent years, the study of higher-order topological states and their material realizations has become a research frontier in topological condensed matter physics. We demonstrate that twisted bilayer graphene with small twist angles behaves as a second-order topological insulator possessing topological corner charges. Using a tight-binding model, we compute the topological band indices and corner states of finite-sized twisted bilayer graphene flakes. It is found that for any small twist angle, whether commensurate or incommensurate, the gaps both below and above the flat bands are associated with nontrivial topological indices. Our results not only extend the concept of second-order band topology to arbitrary small twist angles but also confirm the existence of corner states at acute-angle corners.