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Abstract |
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[1] 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[2]. 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[3]. These invariants correctly describe chiral modes as
we verified numerically on interfaces between different gyrotropic
materials.
[1] S. Raghu and F. D. M. Haldane, Phys. Rev. A78, 033834 (2008).
[2] M. G. Silveirinha, Phys. Rev. B92, 125153 (2015).
[3] M. Marciani and P. Delplace, arXiv:1906.09057 (2019). |
