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Berry-Chern monopoles and spectral flows

Pierre Delplace

SciPost Phys. Lect. Notes 39 (2022) · published 10 March 2022

Abstract

This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers associated to degeneracy points. The notions of topological indices (Chern numbers, analytical indices) are introduced for non specialists with a wave physics or condensed matter background. The correspondence is detailed with several examples, including the Dirac equations in two dimensions, Weyl fermions in three dimensions, the shallow water model in fluid dynamics and other generalizations.

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