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Predicting topologically protected interface state with high-frequency homogenization
[Calcul par homogénéisation haute-fréquence d’un mode d’interface protégé topologiquement]
Marie Touboul1 orcid  ; Bruno Lombard2 orcid ; Antonin Coutant2 orcid
1POEMS, CNRS, INRIA, Institut Polytechnique de Paris, 91120, Palaiseau, France
2Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 269-291

When two semi-infinite periodic media are joined together, a localized interface mode may exist, whose frequency belongs to their common band gap. Moreover, if certain spatial symmetries are satisfied, this mode is topologically protected and thus is robust to defects. A method has recently been proposed to identify the existence and the frequency of this mode, based on the computation of surface impedances at all the frequencies in the gap. In this work, we approximate the surface impedances thanks to high-frequency effective models, and therefore get a prediction of topologically protected interface states while only computing the solution of an eigenvalue problem at the edges of the bandgaps. We also show that the nearby eigenvalues high-frequency effective models give rise to a better approximation of the surface impedance.

Quand deux milieux périodiques semi-infinis sont accolés, un mode localisé à l’interface peut exister. Sa fréquence appartient à l’intersection des bandes de fréquences interdites de chacun des deux milieux. De plus, si certaines symétries matérielles sont satisfaites, alors ce mode est protégé topologiquement et est donc robuste aux imperfections. Une méthode a récemment été proposée pour identifier l’existence et la fréquence de ce mode, basée sur le calcul des impédances de surface des deux milieux, et ce à toutes les fréquences à l’intérieur des bandes interdites. Ici, nous approchons les impédances de surface par des modèles effectifs déduits de l’homogénéisation haute-fréquence. La détermination du mode d’interface protégé topologiquement revient alors simplement à calculer un seul problème aux valeurs propres aux frontières des bandes interdites. On montre aussi que le modèle effectif reposant sur l’hypothèse de valeurs propres voisines donne une meilleure approximation des impédances de surface.

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DOI : 10.5802/crmeca.358
Keywords: periodic media, high-frequency homogenization, topologically protected interface modes, surface impedance, Floquet–Bloch theory
Mots-clés : milieux périodiques, homogénéisation haute-frequence, modes d’interface topologiquement protégés, impédance de surface, théorie de Floquet–Bloch

Marie Touboul  1   ; Bruno Lombard  2   ; Antonin Coutant  2

1 POEMS, CNRS, INRIA, Institut Polytechnique de Paris, 91120, Palaiseau, France
2 Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Marie Touboul; Bruno Lombard; Antonin Coutant. Predicting topologically protected interface state with high-frequency homogenization. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 269-291. doi: 10.5802/crmeca.358
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