Topological suppression of quantum tunneling

In this talk, we prove that if we bring together two band insulators with different topology, described by arbitrary topological indices, there must exist specific momentum points in the Brillouin zone where the wavefunctions of the two insulators are orthogonal and cannot hybridize. For 2D insulators, this conclusion implies that topology will prohibit tunneling of electrons between the two insulators at this momentum. This conclusion can also be generalized to some strongly-correlated topological systems. Explicit demonstration and proof will be provided for topological band insulators and fractional quantum Hall states.