{"paper":{"title":"A Geometric Design Principle for $\\mathbb{Z}_2$ Topological Phases in Twisted Triangular-Lattice Bilayers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Hongming Weng, Jiaheng Li, Jiaxuan Liu, Quansheng Wu, Yan Zhang, Zhong Fang","submitted_at":"2026-06-11T07:52:07Z","abstract_excerpt":"Twisted van der Waals bilayers provide a versatile platform for engineering moir\\'{e} electronic states, yet a general design principle for time-reversal-invariant topological moir\\'{e} bands remains elusive. Here, we establish a geometry-driven principle for triangular-lattice bilayers: symmetry-related minima of the stacking-energy landscape are promoted by twist and relaxation into the two sublattices of an emergent honeycomb moir\\'{e} lattice. First-principles calculations for BiTeBr reveal robust $\\Gamma$-valley moir\\'{e} valence bands with a nontrivial $\\mathbb{Z}_2$ index over a range o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13015/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}