Microlocal analysis of the bulk-edge correspondence

Abstract

The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It suggests novel perspectives for the analysis of topologically protected transport.

arXiv comment44 pages

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Cited by in corpus (9)

• Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators
• Mathematical theory for topological photonic materials in one dimension
• Asymmetric transport computations in Dirac models of topological insulators
• Wave-packet propagation in a finite topological insulator and the spectral localizer index
• Asymmetric transport for magnetic Dirac equations
• From orbital magnetism to bulk-edge correspondence
• Topological edge states of continuous Hamiltonians
• Scattering theory of topologically protected edge transport
• Topological junctions for one-dimensional systems