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Title: Modeling of Electronic Dynamics in Twisted Bilayer Graphene
We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-- MacDonald PDE model, which is periodic with respect to the bilayer's moir\'e pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes--Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer--MacDonald model.  more » « less
Award ID(s):
1922165 2406981
PAR ID:
10561572
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
SIAM
Date Published:
Journal Name:
SIAM Journal on Applied Mathematics
Volume:
84
Issue:
3
ISSN:
0036-1399
Page Range / eLocation ID:
1011 to 1038
Subject(s) / Keyword(s):
partial differential equations, electronic properties of materials, 2D materials, moir\'e materials, numerical analysis, twisted bilayer graphene
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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    Abstract Magic angles in the chiral model of twisted bilayer graphene are parameters for which the chiral version of the Bistritzer–MacDonald Hamiltonian exhibits a flat band at energy zero. We compute the sums over powers of (complex) magic angles and use that to show that the set of magic angles is infinite. We also provide a new proof of the existence of the first real magic angle, showing also that the corresponding flat band has minimal multiplicity for the simplest possible choice of potentials satisfying all symmetries. These results indicate (though do not prove) a hidden integrability of the chiral model. 
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  2. ; ; (, Multiscale Modeling & Simulation)
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  3. ; ; ; (, Electronic Structure)
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  4. ; ; ; ; ; ; ; ; ; (, Proceedings of the National Academy of Sciences)
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