{"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/spin-resolved-topology-and-partial-axion","title":"Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators","arxiv_id":"2207.10099","date":"2022-07-20","proceeding":null,"authors":["Kuan-Sen Lin","Giandomenico Palumbo","Zhaopeng Guo","Yoonseok Hwang","Jeremy Blackburn","Daniel P. Shoemaker","Fahad Mahmood","Zhijun Wang","Gregory A. Fiete","Benjamin J. Wieder","Barry Bradlyn"],"abstract":"Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\\mathcal{T}$-) invariant (helical) 3D TCI$\\unicode{x2014}$termed higher-order TCIs (HOTIs)$\\unicode{x2014}$the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), \"spin-Weyl\" semimetals, and $\\mathcal{T}$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that $\\beta$-MoTe$_2$ realizes a spin-Weyl state and that $\\alpha$-BiBr hosts both 3D QSHI and T-DAXI regimes.","url_abs":"https://arxiv.org/abs/2207.10099v3","url_pdf":"https://arxiv.org/pdf/2207.10099v3.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":"spin-resolved-topology-and-partial-axion","repo_url":"https://github.com/kuansenlin/nested_and_spin_resolved_wilson_loop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}