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