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Title:
Magnetic oscillations in a model of (twisted bilayer) graphene
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Abstract:
We consider the simplest model for graphene in a magnetic field given by a hexagonal quantum graphs. Using semiclassical methods (with the strength of the magnetic field as the small parameter) we obtain a geometric description of the density of states showing asymmetry seen in physical experiments but not in commonly used perfect cone approximations. That density of states can then be used to see magnetic oscillations such as the de Haas--van Alphen effect. We then discuss extensions of this result close to every rational flux which implies results on the Hausdorff dimension of the spectrum and recent results for twisted bilayer graphene. Joint work with M Zworski, R Han, R Kim and X Zhu.
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