• 文献标题:   Wulff shape emergence in graphene
  • 文献类型:   Article
  • 作  者:   DAVOLI E, PIOVANO P, STEFANELLI U
  • 作者关键词:   ground state, hexagonal lattice, isoperimetric inequality, wulff shape
  • 出版物名称:   MATHEMATICAL MODELS METHODS IN APPLIED SCIENCES
  • ISSN:   0218-2025 EI 1793-6314
  • 通讯作者地址:   Univ Vienna
  • 被引频次:   9
  • DOI:   10.1142/S0218202516500536
  • 出版年:   2016

▎ 摘  要

Graphene samples are identified as minimizers of configurational energies featuring both two- and three-body atomic-interaction terms. This variational viewpoint allows for a detailed description of ground-state geometries as connected subsets of a regular hexagonal lattice. We investigate here how these geometries evolve as the number n of carbon atoms in the graphene sample increases. By means of an equivalent characterization of minimality via a discrete isoperimetric inequality, we prove that ground states converge to the ideal hexagonal Wulff shape as n -> infinity. Precisely, ground states deviate from such hexagonal Wulff shape by at most Kn(3/4) + o(n(3/4)) atoms, where both the constant K and the rate n(3/4) are sharp.