{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T12:08:16Z","timestamp":1790424496221,"version":"4.1.0"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>We investigate the spectrum and the dispersion relation of the Schr\u00f6dinger operator with point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level dispersion bands have conic singularities near Dirac points, which are the vertices of the first Brillouin zone. The existence of such conic dispersion bands plays an important role in various electronic properties of honeycomb-structured materials such as graphene. We then prove that, for a honeycomb lattice, the spectra generated by higher-level dispersion relations are all connected, so the complete spectrum consists of at most three bands. Numerical simulations for dispersion bands with various parameters are also presented.<\/jats:p>","DOI":"10.1137\/14095827x","type":"journal-article","created":{"date-parts":[[2016,4,26]],"date-time":"2016-04-26T13:33:20Z","timestamp":1461677600000},"page":"1459-1488","source":"Crossref","is-referenced-by-count":21,"title":["Dirac Cones for Point Scatterers on a Honeycomb Lattice"],"prefix":"10.1137","volume":"48","author":[{"given":"Minjae","family":"Lee","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,4,26]]},"reference":[{"key":"atypb1","volume-title":"Solvable Models in Quantum Mechanics","author":"Albeverio S.","year":"2005","edition":"2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050771"},{"key":"atypb3","unstructured":"G. Berkolaiko and A. 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