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.
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Keywords: Dirac cones, topological insulators, Chern numbers
Mot clés : Point de Dirac, isolants topologiques, nombres de Chern
@article{JEP_2021__8__507_0, author = {Drouot, Alexis}, 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 = {http://www.numdam.org/articles/10.5802/jep.152/} }
TY - JOUR AU - Drouot, Alexis TI - Ubiquity of conical points in topological insulators JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 507 EP - 532 VL - 8 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.152/ DO - 10.5802/jep.152 LA - en ID - JEP_2021__8__507_0 ER -
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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