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

Arkadiy Davydov1*, Kenny Choo1*, Mark H. Fischer1*, Titus Neupert1*

1 Department of Physics, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland

* Corresponding authors emails: adavydov@physik.uzh.ch, choo@physik.uzh.ch, mark.fischer@uzh.ch, titus.neupert@uzh.ch
DOI10.24435/materialscloud:y6-dy [version v1]

Publication date: Dec 22, 2020

How to cite this record

Arkadiy Davydov, Kenny Choo, Mark H. Fischer, Titus Neupert, Four- and twelve-band low-energy symmetric Hamiltonians and Hubbard parameters for twisted bilayer graphene using ab-initio input, Materials Cloud Archive 2020.167 (2020), doi: 10.24435/materialscloud:y6-dy.


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.

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File name Size Description
131.6 MiB This archive contains two custom-build codes used in the work: TBX code, which is the tight-binding solver with all ingredients necessary to study twisted bilayer graphene, and Wannier90 code copy, which was slightly modified with respect to the original one (version 3.1.0) to include time-reversal symmetry constraint
120.9 MiB The 'data' archive contains all the input and most of the output data for construction the low-energy four- and twelve-band TB models for twisted bilayer graphene with corresponding Hubbard parameters. Hubbard parameters are evaluated as matrix elements of the cRPA (Constrained Random Phase Approximation) -screened Coulomb interaction. The computational workflow is described in the README files inside this archive


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International. TBX is released under GNU GPL v3; the modified version of Wannier90 is released under GNU GPL v2; check the "LICENSE" files inside "codes.tar.gz" for more information.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

A. Davydov, K. Choo, M. H. Fischer, T. Neupert, arXiv (in preparation)


MARVEL/DD6 ERC twisted bilayer graphene magic angle tight-binding 2D materials Hubbard parameters cRPA Wannierization Slater-Koster

Version history:

2020.167 (version v1) [This version] Dec 22, 2020 DOI10.24435/materialscloud:y6-dy