Optical topological chiral modes flowing between non-topological materials
Marco Marciani (Labo de Physique de l'ENS Lyon)
The most remarkable feature of the so-called "topological crystals" is the presence of states flowing at their edge that are robust against disorder. A beautiful mathematical theory allows to predict the properties of such states directly from the topological invariants (e.g. the Chern numbers) of the bulk bands. Given the great success of this theory in terms of theoretical impact and technological advance, in recent years much effort has been put to make the extension from the field electronics to other fields and from crystals to various non-crystaline systems such as quasi-crystals and amorphous materials. In this talk I will show how deal with continuous systems governed by linear Maxwell's equations. Even though bands Chern numbers cannot be defined and optical materials are non-topological, we discover that interface Chern numbers can always be defined by means of the theory of spectral flows. These invariants correctly describe chiral modes as we verified numerically on interfaces between different gyrotropic materials.  S. Raghu and F. D. M. Haldane, Phys. Rev. A78, 033834 (2008).  M. G. Silveirinha, Phys. Rev. B92, 125153 (2015).  M. Marciani and P. Delplace, arXiv:1906.09057 (2019).