{"paper":{"title":"Nontrivial topological states on a M\\\"obius band","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"cond-mat.mes-hall","authors_text":"A. Quelle, C. Morais Smith, W. Beugeling","submitted_at":"2014-03-27T12:33:33Z","abstract_excerpt":"In the field of topological insulators, the topological properties of quantum states in samples with simple geometries, such as a cylinder or a ribbon, have been classified and understood during the last decade. Here, we extend these studies to a M\\\"obius band, and argue that its lack of orientability prevents a smooth global definition of parity-odd quantities such as pseudovectors. In particular, the Chern number, the topological invariant for the quantum Hall effect, lies in this class. The definition of spin on the M\\\"obius band translates into the idea of the orientable double cover, an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6998","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}