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arXiv · 1908.01377

Edge states in ordinary differential equations for dislocations

David Gontier
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Abstract

In this article, we study Schrödinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with the dislocation parameter. We introduce several integer-valued indices, including Chern number for bulk indices, and various spectral flows for edge indices. We prove that all these indices coincide, providing a proof a bulk-edge correspondence in this case. The study is also made for dislocations in Dirac models on the real line. We prove that 0 is always an eigenvalue of such operators.

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David Gontier. 2019-08-04. Edge states in ordinary differential equations for dislocations. https://doi.org/10.1063/1.5128886

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