Crystallization for a Brenner-like Potential

Brittan Farmer, Selim Esedoḡlu, Peter Smereka

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11 Scopus citations


Graphene is a carbon molecule with the structure of a honeycomb lattice. We show how this structure can arise in two dimensions as the minimizer of an interaction energy with two-body and three-body terms. In the engineering literature, the Brenner potential is commonly used to describe the interactions between carbon atoms. We consider a potential of Stillinger–Weber type that incorporates certain characteristics of the Brenner potential: the preferred bond angles are 180 and all interactions have finite range. We show that the thermodynamic limit of the ground state energy per particle is the same as that of a honeycomb lattice. We also prove that, subject to periodic boundary conditions, the minimizers are translated versions of the honeycomb lattice.

Original languageEnglish (US)
Pages (from-to)1029-1061
Number of pages33
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Feb 1 2017

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© 2016, Springer-Verlag Berlin Heidelberg.


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