{"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/angle-dependent-it-ab-initio-low-energy","title":"Angle-Dependent {\\it Ab initio} Low-Energy Hamiltonians for a Relaxed Twisted Bilayer Graphene Heterostructure","arxiv_id":"1908.00058","date":"2019-07-31","proceeding":null,"authors":["Shiang Fang","Stephen Carr","Ziyan Zhu","Daniel Massatt","Efthimios Kaxiras"],"abstract":"We present efficient angle-dependent low-energy Hamiltonians to describe the properties of the twisted bilayer graphene (tBLG) heterostructure, based on {\\it ab initio} calculations of mechanical relxation and electronic structure. The angle-dependent relaxed atomic geometry is determined by continuum elasticity theory, which induces both in-plane and out-of-plane deformations in the stacked graphene layers. The electronic properties corresponding to the deformed geometry are derived from a Wannier transformation to local interactions obtained from Density Functional Theory calculations. With these {\\it ab initio} tight-binding Hamiltonians of the relaxed heterostructure, the low-energy effective theories are derived from the projections near Dirac cones at K valleys. For twist angles ranging from 0.7$^\\circ$ to 4$^\\circ$, we extract both the intra-layer pseudo-gauge fields and the inter-layer coupling terms in the low-energy Hamiltonians, which extend the conventional low-energy continuum models. We further include the momentum dependent inter-layer scattering terms which give rise to the particle-hole asymmetric features of the electronic structure. Our model Hamiltonians can serve as a starting point for formulating physically meaningful, accurate interacting electron theories.","url_abs":"https://arxiv.org/abs/1908.00058v1","url_pdf":"https://arxiv.org/pdf/1908.00058v1.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":"angle-dependent-it-ab-initio-low-energy","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":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}