{"paper":{"title":"Valley Spin Sum Rule for Dirac Fermions: Topological Argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Jun Goryo","submitted_at":"2010-10-01T06:10:51Z","abstract_excerpt":"We consider a two-dimensional bipartite lattice system. In such a system, the Bloch band spectrum can have some valley points, around which Dirac fermions appear as the low-energy excitations. Each valley point has a valley spin +1 or -1. In such a system, there are two topological numbers counting vortices and merons in the Brillouin zone, respectively. These numbers are equivalent, and this fact leads to a sum rule which states that the total sum of the valley spins is absent even in a system without time-reversal and parity symmetries. We can see some similarity between the valley spin and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0071","kind":"arxiv","version":3},"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"}