{"paper":{"title":"Periodic Behavior of Topology in Graphene with Nanohole Array","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Topology in graphene with nanohole arrays repeats periodically with supercell size m, every two steps for triangular arrays and every six for honeycomb.","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Xiao Hu, Xing-Xiang Wang, Yong-Cheng Jiang","submitted_at":"2026-05-14T06:32:11Z","abstract_excerpt":"We derive a way to diagnose band topology for graphene with triangular and/or honeycomb array of nanoholes directly from the lattice constant of superstructure $m\\sqrt{3}\\times m\\sqrt{3}$ with integer $m$. Taking into account the $C_{6v}$ crystalline symmetry respected by nanoholes and their array, we demonstrate that nontrivial topology appears periodically with $m$ with period two (six) for triangular (honeycomb) array. These behaviors are verified by Wyckoff positions of Wannier centers and parity index of valence bands at high-symmetry points in Brillouin zone. The results provide a conven"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"nontrivial topology appears periodically with m with period two (six) for triangular (honeycomb) array","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The nanoholes and their array respect the full C_{6v} crystalline symmetry, allowing direct diagnosis of topology solely from the lattice constant of the m√3×m√3 superstructure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Nontrivial band topology in graphene with nanohole arrays appears periodically with superstructure size m (period 2 for triangular arrays, period 6 for honeycomb arrays).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Topology in graphene with nanohole arrays repeats periodically with supercell size m, every two steps for triangular arrays and every six for honeycomb.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6e88eff6f92c5d7f65e05190f21590e637cd1f023314270a29ac2b7ee1015cf7"},"source":{"id":"2605.14436","kind":"arxiv","version":1},"verdict":{"id":"0f0b9c41-8c3c-4a1a-8c2c-9c8ca9317f1a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:34:34.036515Z","strongest_claim":"nontrivial topology appears periodically with m with period two (six) for triangular (honeycomb) array","one_line_summary":"Nontrivial band topology in graphene with nanohole arrays appears periodically with superstructure size m (period 2 for triangular arrays, period 6 for honeycomb arrays).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The nanoholes and their array respect the full C_{6v} crystalline symmetry, allowing direct diagnosis of topology solely from the lattice constant of the m√3×m√3 superstructure.","pith_extraction_headline":"Topology in graphene with nanohole arrays repeats periodically with supercell size m, every two steps for triangular arrays and every six for honeycomb."},"references":{"count":60,"sample":[{"doi":"","year":1980,"title":"K. 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Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, a","work_id":"9a19f4ed-6ea6-4ece-a3c4-b6a04516f761","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":60,"snapshot_sha256":"518ccdd57008916cd35d744767d3d7eaf593f411cc3d734044fed2409c4acbd6","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"}