Abstract
We analyze the splitting of exact flat bands in the chiral model of the twisted bilayer graphene (TBG) when the AA′/BB′ coupling of the full Bistritzer–MacDonald model is taken into account. The first-order perturbation caused by the AA′/BB′ potential is the same for both bands and satisfies interesting symmetries, in particular it vanishes on the line defined by the K points. The splitting of the flat bands is governed by the quadratic term which vanishes at the K points.
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