{"paper":{"title":"Breakdown of optical phonons' splitting in two-dimensional materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Francesco Mauri, Marco Gibertini, Matteo Calandra, Nicola Marzari, Thibault Sohier","submitted_at":"2016-12-21T15:36:46Z","abstract_excerpt":"We investigate the long-wavelength dispersion of longitudinal and transverse optical phonon modes in polar two-dimensional materials, multilayers, and their heterostructures. Using analytical models and density-functional perturbation theory in a two-dimensional framework, we show that, at variance with the three-dimensional case, these modes are degenerate at the zone center but the macroscopic electric field associated with the longitudinal-optical modes gives rise to a finite slope at the zone center in their corresponding phonon dispersions. This slope increases linearly with the number of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07191","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"}