Publication 15-CNA-024

Wulff Shape Emergence in Graphene

Elisa Davoli
Department of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Vienna, Austria
elisa.davoli@univie.ac.at

Paolo Piovano
Faculty of Mathematics
University of Vienna
Oskar-Morgenstern
A-1090 Vienna, Austria
paolo.piovano@univie.ac.at

Ulisse Stefanelli
Faculty of Mathematics
University of Vienna
Oskar-Morgenstern
A-1090 Vienna, Austria
ulisse.stefanelli@univie.ac.at

Abstract: Graphene samples are identifed as minimizers of congurational 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 $n \rightarrow \infty$. 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.

Get the paper in its entirety as  15-CNA-024.pdf

---

«   Back to CNA Publications