Modeling of electronic dynamics in twisted bilayer graphene

• URL: http://arxiv.org/abs/2308.10430v2
• Date: Mon, 26 Feb 2024 02:01:09 GMT
• Title: Modeling of electronic dynamics in twisted bilayer graphene
• Authors: Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson
• Abstract summary: We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. We first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. We then provide extensive numerical computations which clarify the range of validity of the Bistritzer-MacDonald model.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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