Ubiquity of conical points in topological insulators
[Omniprésence des points de Dirac dans les isolants topologiques]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021) , pp. 507-532.

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 :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/jep.152
Classification : 47A13,  81Q10,  81Q05
Mots clés : Point de Dirac, isolants topologiques, nombres de Chern
@article{JEP_2021__8__507_0,
     author = {Alexis Drouot},
     title = {Ubiquity of conical points in topological~insulators},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {507--532},
     publisher = {\'Ecole polytechnique},
     volume = {8},
     year = {2021},
     doi = {10.5802/jep.152},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.152/}
}
Alexis Drouot. Ubiquity of conical points in topological insulators. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021) , pp. 507-532. doi : 10.5802/jep.152. https://jep.centre-mersenne.org/articles/10.5802/jep.152/

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