Abstract
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 moiré 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.
Original language | English (US) |
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Pages (from-to) | 1011-1038 |
Number of pages | 28 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 84 |
Issue number | 3 |
DOIs | |
State | Published - May 2024 |
Bibliographical note
Publisher Copyright:© 2024 Society for Industrial and Applied Mathematics.
Keywords
- 2D materials
- electronic properties of materials
- moiré materials
- numerical analysis
- partial differential equations
- twisted bilayer graphene