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Graphene ground states

Zeitschrift für angewandte Mathematik und Physik volume 69, Article number: 70 (2018) Cite this article

Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Manuel Friedrich & Ulisse Stefanelli

  2. Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, v. Ferrata 1, 27100, Pavia, Italy

    Ulisse Stefanelli

Authors
  1. Manuel Friedrich
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  2. Ulisse Stefanelli
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Correspondence to Ulisse Stefanelli.

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Friedrich, M., Stefanelli, U. Graphene ground states. Z. Angew. Math. Phys. 69, 70 (2018). https://doi.org/10.1007/s00033-018-0965-2

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  • DOI: https://doi.org/10.1007/s00033-018-0965-2

Mathematics Subject Classification

  • 70F45
  • 82D80

Keywords

  • Graphene
  • Ground states
  • Nonflatness
  • Three-dimensional structures
  • Periodicity