Higher-Order Topological Corner State Tunneling in Twisted Bilayer Graphene

Higher-order topological insulator is a newly discovered topological material, characterized by the topological corner states. In this work, we propose quantum oscillation that identifies the two-dimensional higher-order topological phase in twisted bilayer graphene systems. We use an instanton approach to argue that the tunneling of electrons between the topological corner states of the higher-order topological insulator generally causes the gate-tunable oscillation in the energy spectra. The oscillatory nodes signal the perfect suppression of the tunneling, which features the topological nature of the corner states. In the view of experimental realization, we propose the transport experiment that can readily observe the oscillation. Our work provides a feasible route to identify higher-order topological materials in twisted bilayer graphenes.