Graphene ground states

  • Manuel Friedrich
  • Ulisse StefanelliEmail author


Graphene is locally two-dimensional but not flat. Nanoscale ripples appear in suspended samples and rolling up often occurs when boundaries are not fixed. We address this variety of graphene geometries by classifying all ground-state deformations of the hexagonal lattice with respect to configurational energies including two- and three-body terms. As a consequence, we prove that all ground-state deformations are either periodic in one direction, as in the case of ripples, or rolled up, as in the case of nanotubes.


Graphene Ground states Nonflatness Three-dimensional structures Periodicity 

Mathematics Subject Classification

70F45 82D80 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Istituto di Matematica Applicata e Tecnologie Informatiche E. MagenesPaviaItaly

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