{"paper":{"title":"Fine Structures of Berry Curvature and Unquantized Valley Chern Numbers in Valley Photonic Crystals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Valley Chern numbers in photonic crystals form a continuous spectrum rather than quantizing to half-integers.","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Masaya Notomi, Taiki Yoda, Wei Dai, Yuto Moritake","submitted_at":"2026-03-28T11:35:26Z","abstract_excerpt":"Valley photonics has emerged as a promising platform in topological photonic systems, yet the topological nature of valley-dependent phenomena remains unsettled. Theoretically, inter-valley scattering may occur with structural imperfections, and global Chern numbers vanish due to time-reversal symmetry. As a result, valley-dependent topology is locally defined around K(K') points in the half-Brillouin zone (HBZ). While half-integer valley Chern numbers have been widely assumed, their quantization and topological validity remain controversial. Here, we systematically investigate a continuous sp"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that valley Chern numbers are generically unquantized and instead form a continuous spectrum varying with structural parameters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The numerical computation of Berry curvature over the half-Brillouin zone for a continuous family of structural parameters accurately reflects physical behavior without discretization artifacts or truncation effects that could produce an artificial continuous spectrum.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Valley Chern numbers in photonic crystals form a continuous spectrum rather than being quantized, due to inter- and intra-valley Berry curvature cancellations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Valley Chern numbers in photonic crystals form a continuous spectrum rather than quantizing to half-integers.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"60f3195078ba3adb253fb396048083963b9252113bd82b916b5267fc2f144fc7"},"source":{"id":"2603.27244","kind":"arxiv","version":1},"verdict":{"id":"9c097236-d5a5-44fe-9983-0ce53c5f84a4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:01:36.804624Z","strongest_claim":"We show that valley Chern numbers are generically unquantized and instead form a continuous spectrum varying with structural parameters.","one_line_summary":"Valley Chern numbers in photonic crystals form a continuous spectrum rather than being quantized, due to inter- and intra-valley Berry curvature cancellations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The numerical computation of Berry curvature over the half-Brillouin zone for a continuous family of structural parameters accurately reflects physical behavior without discretization artifacts or truncation effects that could produce an artificial continuous spectrum.","pith_extraction_headline":"Valley Chern numbers in photonic crystals form a continuous spectrum rather than quantizing to half-integers."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.27244/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":36,"sample":[{"doi":"","year":1959,"title":"D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010)","work_id":"51500f40-6a56-4ad1-b178-f5bbc1c605c4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"W. Yao, D. Xiao, and Q. Niu, Valley-dependent optoelec- tronics from inversion symmetry breaking, Phys. Rev. B 77, 235406 (2008)","work_id":"9d92aab5-771a-414f-91a8-5607fdd041d7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys.81, 109 (2009)","work_id":"c63a4a86-b316-4982-bf7d-a376d62fabc4","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Cou- pled spin and valley physics in monolayers of mos 2 and other group-vi dichalcogenides, Phys. Rev. Lett.108, 196802 (2012)","work_id":"fa4554e8-7396-4c25-9284-1f1a685f953c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett.93, 083901 (2004)","work_id":"8e45719c-344f-4259-bec5-95be2087dd15","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"5c188a046f051fb43cd3223523ba3b2e6d800cb308369ff1c59df900632cdcd0","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"56a66773f104755adbb54f398fad2a37f2b0180d3969ead2d5659f97c23a32f1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}