{"paper":{"title":"Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP","physics.optics"],"primary_cat":"math-ph","authors_text":"J. P. Lee-Thorp, M. I. Weinstein, Y. Zhu","submitted_at":"2017-10-10T03:48:10Z","abstract_excerpt":"Consider electromagnetic waves in two-dimensional {\\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\\LA=-\\nabla_\\bx\\cdot A(\\bx) \\nabla_\\bx$, where $A(\\bx)$ is $\\Lambda_h-$ periodic ($\\Lambda_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, $A(\\bx)$ is $\\mathcal{P}\\mathcal{C}-$ invariant ($A(\\bx)=\\overline{A(-\\bx)}$) and $120^\\circ$ rotationally invariant ($A(R^*\\bx)=R^*A(\\bx)R$, where $R$ is a $120^\\circ$ rotation in the plane)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03389","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"}