Ubiquity of conical points in topological insulators

Drouot, Alexis

doi:10.5802/jep.152

Ubiquity of conical points in topological insulators
[Omniprésence des points de Dirac dans les isolants topologiques]

Drouot, Alexis ¹

¹ Padelford Hall, University of Washington W Stevens Way NE, Seattle, WA 98105, USA

Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 507-532.

Résumé
Abstract

Nous montrons que les valeurs propres dégénérées de matrices dépendant de trois paramètres possèdent généralement une structure conique. Nous appliquons ce résultat à l’étude des phases topologiques de systèmes quantiques. Nous montrons que les déformations adiabatiques entre deux isolants topologiques distincts ont une conductivité globale égale au nombre chiral de points de Dirac.

We show that generically, the degeneracies of a family of Hermitian matrices depending on three parameters have a conical structure. Our result applies to the study of topological phases of matter. It suggests that adiabatic deformations of two-dimensional topological insulators come generically with Dirac-like propagating currents, whose total conductivity equals the chiral number of conical points.

Reçu le : 2020-05-14
Accepté le : 2021-02-08
Publié le : 2021-02-23

DOI : 10.5802/jep.152

Classification : 47A13, 81Q10, 81Q05
Keywords: Dirac cones, topological insulators, Chern numbers
Mot clés : Point de Dirac, isolants topologiques, nombres de Chern

Affiliations des auteurs :

Drouot, Alexis ¹

¹ Padelford Hall, University of Washington W Stevens Way NE, Seattle, WA 98105, USA

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Drouot, Alexis. Ubiquity of conical points in topological insulators. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 507-532. doi : 10.5802/jep.152. http://www.numdam.org/articles/10.5802/jep.152/

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