Scattering theory of higher order topological insulators

Intrinsic higher order topological insulators (HOTIs) have edge states protected by the global symmetry of the sample. We advance the understanding of HOTIs by developing a theory of scattering topological invariants. Because our approach utilizes the global symmetry properties, it establishes the bulk-edge correspondence. This allows researchers to study intrinsic HOTIs in the presence of disoder as well as quasi-crystalline and amorphous HOTIs. In addition, the scattering approach enables analysis of network models, where Hamiltonian topological invariants are insufficient. In this talk, I will demonstrate the logic behind the general approach by using the BBH model as an example.