[Paper Review] Four- and twelve-band low-energy symmetric Hamiltonians and Hubbard parameters for twisted bilayer graphene using ab-initio input

Arkadiy Davydov, Kenny Choo+2 more|arXiv (Cornell University)|Dec 22, 2020

Graphene research and applications4 citations

TL;DR

This paper presents a computationally efficient workflow to derive symmetric, purely real four- and twelve-band tight-binding Hamiltonians for twisted bilayer graphene at the first magic angle, using ab-initio data fitted at larger angles and the Wannier90 software with maximum localization. It further computes symmetry-respecting extended Hubbard parameters via cRPA, enabling accurate low-energy models for twisted multilayer systems.

ABSTRACT

A computationally efficient workflow for obtaining low-energy tight-binding Hamiltonians for twisted bilayer graphene, obeying both crystal and time-reversal symmetries is presented in this work. The Hamiltonians at the first magic angle are generated using the Slater-Koster approach with parameters obtained by a fit to ab-initio data at larger angles. Low-energy symmetric four-band and twelve-band Hamiltonians are constructed using the Wannier90 software. The advantage of our scheme is that the low-energy Hamiltonians are purely real and are obtained with the maximum-localization procedure to reduce the spread of the basis functions. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation (cRPA) for screening, which again respect the symmetries. The workflow is straightforwardly transferable to other twisted multi-layer materials.

Motivation & Objective

• To develop a systematic and efficient method for constructing low-energy tight-binding Hamiltonians that respect both crystal and time-reversal symmetries in twisted bilayer graphene.
• To ensure the resulting Hamiltonians are purely real by employing maximum-localization of Wannier functions to minimize basis function spread.
• To compute extended Hubbard parameters consistent with the symmetry of the system using the constrained random phase approximation (cRPA) for screening.
• To create a transferable framework applicable to other twisted multilayer 2D materials.

Proposed method

• Using the Slater-Koster approach, parameters for the low-energy Hamiltonians are fitted to ab-initio data obtained at larger twist angles.
• Employing the Wannier90 software to construct maximally localized Wannier functions, ensuring the resulting Hamiltonians are purely real and symmetric.
• Constructing both four-band and twelve-band low-energy models that preserve the system's crystal and time-reversal symmetries.
• Applying the constrained random phase approximation (cRPA) to compute extended Hubbard parameters that respect the same symmetries.
• Validating the symmetry consistency of both the hopping parameters and the Hubbard interactions in the derived models.
• Designing a workflow that is directly transferable to other twisted multilayer 2D materials with similar symmetry constraints.

Experimental results

Research questions

• RQ1 How can low-energy tight-binding Hamiltonians for twisted bilayer graphene be constructed to strictly preserve both crystal and time-reversal symmetries?
• RQ2 What is the optimal method to ensure the resulting Hamiltonians are purely real while minimizing the spread of Wannier functions?
• RQ3 How can extended Hubbard parameters be computed in a way that respects the same symmetries as the hopping terms?
• RQ4 To what extent can this workflow be generalized to other twisted multilayer 2D materials?
• RQ5 What is the impact of using ab-initio data from larger twist angles as a reference for fitting parameters at the first magic angle?

Key findings

• The derived four- and twelve-band Hamiltonians are purely real and explicitly respect both crystal and time-reversal symmetries.
• The maximum-localization procedure in Wannier90 successfully reduces the spread of the Wannier functions, enhancing the accuracy and interpretability of the low-energy models.
• The extended Hubbard parameters computed via cRPA are consistent with the symmetry of the system, ensuring physical consistency in many-body interactions.
• The workflow is transferable to other twisted multilayer 2D materials, enabling systematic construction of symmetry-preserving low-energy models.
• The use of ab-initio data at larger angles as a fitting reference enables accurate parameterization at the first magic angle, despite the strong correlation effects present there.