Berry-Chern monopoles and spectral flows
Pierre Delplace
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 and other generalizations.
Topics & Concepts
Degeneracy (biology)Dirac (video compression format)FermionChern classPhysicsTheoretical physicsMagnetic monopoleMathematical physicsMathematicsPure mathematicsQuantum mechanicsBioinformaticsNeutrinoBiologyTopological Materials and PhenomenaQuantum many-body systemsCold Atom Physics and Bose-Einstein Condensates