The spectral properties of Schrödinger operators for periodic systems (crystals) are well-understood, thanks to Bloch-Floquet theory. When such periodic systems are cut in half, an "edge spectrum" can appear. This spectrum describes physical properties appearing at the boundary of the system. In this talk, we present a general framework to study this edge spectrum. We make the connection with topological insulators (and bulk-edge correspondence), and we also prove that, for any material cut with an irrational angle, its edge spectrum fills all the bulk gaps.
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