Twisted bilayer graphene from first-principles: structural and electronic properties

TL;DR

This study uses first-principles density functional theory to analyze the structural and electronic properties of twisted bilayer graphene across various angles, providing detailed atomic and electronic insights.

Contribution

It offers the first comprehensive ab initio analysis of tBLG, including relaxed structures and electronic properties, aligning well with continuum models and serving as a reference for future many-body studies.

Findings

Lattice relaxation agrees with continuum elastic models.

Electronic structure calculations match plane-wave DFT results.

Fermi velocity and band width depend on twist angle with a small offset.

Abstract

We present a comprehensive first-principles study of twisted bilayer graphene (tBLG) for a wide range of twist angles, with a focus on structural and electronic properties. By employing density functional theory (DFT) with an optimized local basis set, we simulate tBLG, obtaining fully relaxed commensurate structures for twist angles down to 0.987{\deg}. For all angles the lattice relaxation agrees well with continuum elastic models. For angles accessible to plane-wave DFT (VASP), we provide a detailed comparison with our local basis DFT (SIESTA) calculations, demonstrating excellent agreement in both the atomic and electronic structure. The dependence of the Fermi velocity and band width on the twist angle shows qualitative agreement with results from an `exact' $\mathbf{k \cdot p}$ continuum model, but reveals a small twist angle offset. Additionally, we provide details of the low-energy wavefunction character, band inversion and symmetries. Our results provide an ab initio reference point for the microscopic structure and electronic properties of tBLG which will serve as the foundation for future studies incorporating many-body effects.