{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/derivation-of-wannier-orbitals-and-minimal","title":"Derivation of Wannier orbitals and minimal-basis tight-binding hamiltonians for twisted bilayer graphene: a first-principles approach","arxiv_id":"1907.06282","date":"2019-07-14","proceeding":null,"authors":["Stephen Carr","Shiang Fang","Hoi Chun Po","Ashvin Vishwanath","Efthimios Kaxiras"],"abstract":"Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies around the Fermi level, quite challenging. Our goal here is to provide a convenient and physically motivated picture of single-particle physics in TBLG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of \\textit{ab-initio} tight-binding models, including the effects of atomic relaxations. Furthermore, we obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBLG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between $1.3^\\circ$ and $0.6^\\circ$. The models are created using a multi-step Wannier projection technique starting with appropriate $\\textit{ab initio}$ $k \\cdot p$ continuum hamiltonians. Our procedure can also readily capture the perturbative effects of substrates and external displacement fields while offering a significant reduction in complexity for studying electron-electron correlation phenomena in realistic situations.","url_abs":"https://arxiv.org/abs/1907.06282v1","url_pdf":"https://arxiv.org/pdf/1907.06282v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"derivation-of-wannier-orbitals-and-minimal","repo_url":"https://github.com/stcarr/kp_tblg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}