_______ ______  _       ______       _     _
(_______|____  \| |     / _____)  _  | |   | |
 _       ____)  ) |    | /  ___ _| |_| |   | |
| |     |  __  (| |    | | (___|_   _) |   | |
| |_____| |__)  ) |____| \____/| |_| | |___| |
 \______)______/|_______)_____/       \______|

This repository contains a MATLAB code for solving a Bistritzer-MacDonald Hamiltonian + Hartree interactions and Hubbard U atomic interactions for twisted bilayer graphene. Four magnetic orderings can be selected, namely modulated anti‐ferromagnetic (MAFM), Nodal anti-ferromagnetic (NAFM), hexagonal anti‐ferromagnetic (HAFM) and ferromagnetic (FM).

In publications arising from the use of this code

Please cite:

1. Jimeno-Pozo, A., Goodwin, Z.A.H., Pantaleón, P.A., Vitale, V., Klebl, L., Kennes, D.M., Mostofi, A.A., Lischner, J. and Guinea, F. (2023), Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene. Adv. Phys. Res., 2: 2300048.

@article{jimenopozo2023short,
  author = {Jimeno-Pozo, Alejandro and Goodwin, Zachary A. H. and Pantaleón, Pierre A. and Vitale, Valerio and Klebl, Lennart and Kennes, Dante M. and Mostofi, Arash A. and Lischner, Johannes and Guinea, Francisco},
  title = {Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene},
  journal = {Advanced Physics Research},
  volume = {2},
  number = {12},
  pages = {2300048},
  doi = {https://doi.org/10.1002/apxr.202300048},
  year = {2023}
}

Ref.

1. R. Bistritzer,and A. MacDonald, PNAS 108 (30) 12233-12237 (2011)
2. T. Cea, N. R. Walet, and F. Guinea, PRB 100, 205113 (2019)
3. A. Jimeno-Pozo, Z.A.H. Goodwin, V. Vitale, et al. Adv. Phys. Res., 2:2300048 (2023)
4. https://github.com/stcarr/kp_tblg
5. S. Carr, S. Fang et al. Phys. Rev. Research 1, 013001 (2019)
6. S. Fang, S. Carr et al. arXiv:1908.00058 (2019)

Funding:

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 101067977

Contributors:

• Z. A. H. Goodwin
• C. T. S. Cheung