Topological wave insulators: a review

Comptes Rendus. Physique, Volume 21 (2020) no. 4-5, pp. 467-499.

Part of the special issue: Metamaterials 1

Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other insulator, electronic TIs exhibit an excessively high resistance to the flow of mobile charges, prohibiting metallic conduction. On their surface, however, they support one-way conductive states with inherent protection against certain types of disorder and defects, defying the common physical wisdom of electronic transport in presence of impurities. When transposed to classical waves, TIs open a wealth of exciting engineering-oriented applications, such as robust routing, lasing, signal processing, switching, etc., with unprecedented robustness against various classes of defects. In this article, we first review the basic concept of topological order applied to classical waves, starting from the simple one-dimensional example of the Su–Schrieffer–Heeger (SSH) model. We then move on to two-dimensional wave TIs, discussing classical wave analogues of Chern, quantum Hall, spin-Hall, Valley-Hall, and Floquet TIs. Finally, we review the most recent developments in the field, including Weyl and nodal semimetals, higher-order topological insulators, and self-induced non-linear topological states.

Découverte à l’origine en matière condensée, la notion d’isolant topologique (IT) a été étendue à divers domaines de la physique des ondes classiques, notamment la photonique, la phononique, l’acoustique, la mécanique et les micro-ondes. Dans leur volume, comme tout autre isolant, les IT électroniques présentent une résistance excessivement élevée à l’écoulement des charges, interdisant la conduction métallique. Sur leur surface, cependant, ils présentent des états conducteurs unidirectionnels avec une protection inhérente contre certains types de défauts, au-delà de ce que pouvait laisser présager la physique du transport électronique en présence d’impuretés. Transposés aux ondes classiques, les IT ouvrent une multitude d’applications passionnantes en ingénierie, comme le routage, les lasers, le traitement du signal, les commutations, etc. avec une robustesse sans précédent face à différentes classes de défauts. Dans cet article, nous passons d’abord en revue le concept de base des IT appliqué aux ondes classiques, à partir de l’exemple simple et monodimensionnel du modèle Su–Schrieffer–Heeger (SSH). Nous passons ensuite aux IT à ondes bidimensionnelles, en discutant des analogues pour les ondes classiques des IT de Chern, d’effet Hall quantique, de spin-Hall, de Valley-Hall, et de Floquet. Enfin, nous passons en revue les développements les plus récents dans le domaine, y compris les semi-métaux de Weyl et nodaux, les isolants topologiques d’ordre supérieur et les états topologiques non linéaires auto-induits.

Published online:

DOI:
10.5802/crphys.3

Keywords: Condensed matter, Photonics, Phononics, Acoustics, Mechanics, Microwaves

Author's affiliations:

Keywords: Condensed matter, Photonics, Phononics, Acoustics, Mechanics, Microwaves

Author's affiliations:

Farzad Zangeneh-Nejad ^{1};
Andrea Alù ^{2};
Romain Fleury ^{1}

Farzad Zangeneh-Nejad; Andrea Alù; Romain Fleury. Topological wave insulators: a review. Comptes Rendus. Physique, Volume 21 (2020) no. 4-5, pp. 467-499. doi : 10.5802/crphys.3. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.3/

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