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We propose a new type of instanton interference effect in two-dimensionalhigher-order topological insulators. The intercorner tunneling consists of theinstanton and the anti-instanton pairs that travel through the boundary of thehigher-order topological insulator. The Berry phase difference between theinstanton pairs causes the interference of the tunneling. This topologicaleffect leads to the gate-tunable oscillation of the energy splitting betweenthe corner states, where the oscillatory nodes signal the perfect suppressionof the tunneling. We suggest this phenomenon as a unique feature of thetopological corner states that differentiate from trivial bound states. In theview of experimental realization, we exemplify twisted bilayer graphene, as apromising candidate of a two-dimensional higher-order topological insulator.The oscillation can be readily observed through the transport experiment thatwe propose. Thus, our work provides a feasible route to identify higher-ordertopological materials.

Higher-Order Topological Instanton Tunneling Oscillation