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Mathematical results on the chiral model of twisted bilayer graphene (with an appendix by Mengxuan Yang and Zhongkai Tao) (2310.20642v2)

Published 31 Oct 2023 in cond-mat.mes-hall, math-ph, math.AP, and math.MP

Abstract: The study of twisted bilayer graphene (TBG) is a hot topic in condensed matter physics with special focus on {\em magic angles} of twisting at which TBG acquires unusual properties. Mathematically, topologically non-trivial flat bands appear at those special angles. The chiral model of TBG pioneered by Tarnopolsky--Kruchkov--Vishwanath has particularly nice mathematical properties and we survey, and in some cases, clarify, recent rigorous results which exploit them.

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