Modeling of electronic dynamics in twisted bilayer graphene

TL;DR

This paper proves that the quantum dynamics of electrons in incommensurate twisted bilayer graphene can be approximated on finite domains and validates the Bistritzer-MacDonald model through extensive numerical analysis.

Contribution

It establishes a rigorous approximation method for incommensurate twisted bilayer graphene dynamics and assesses the Bistritzer-MacDonald model's validity.

Findings

Finite domain approximation of tight-binding model dynamics.

Validation range of the Bistritzer-MacDonald PDE model.

Speed of propagation estimates for quantum dynamics.

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.