Index theory and bulk-boundary correspondence for inversion-symmetric second-order topological insulators

Abstract

We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped systems. Our method uses extensions of the symbols of some Toeplitz operators on discrete quarter planes and computations of topological equivariant K-theory groups.

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