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Graphene ground states

Name: Graphene ground states
Keywords: 101028 Mathematical modelling, Periodicity, FOS: Physical sciences, Condensed Matter - Soft Condensed Matter, Nonflatness, Mathematics - Analysis of PDEs, SYSTEMS, CONFIGURATIONS, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Mathematics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 22 May 2018Embargo end date: 01 Jan 2018 Italy, Austria, Italy Publisher:Springer Science and Business Media LLCJournal:Zeitschrift für angewandte Mathematik und Physik, volume 69 (issn: 0044-2275, eissn: 1420-9039,

Authors: M Friedrich; U Stefanelli;

doi: 10.1007/s00033-018-0965-2 , 10.48550/arxiv.1802.05049

arXiv: http://arxiv.org/abs/1802.05049

handle: 20.500.14243/350113

Graphene ground states

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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.

Countries

Italy, Austria, Italy

Related Organizations

University of Vienna
Austria
National Research Council
Italy
Istituto di Matematica Applicata e Tecnologie Informatiche
Italy

Keywords

101028 Mathematical modelling, Periodicity, FOS: Physical sciences, Condensed Matter - Soft Condensed Matter, Nonflatness, Mathematics - Analysis of PDEs, SYSTEMS, CONFIGURATIONS, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Mathematics, 101012 Kombinatorik, Mathematical Physics, Condensed Matter - Materials Science, Condensed Matter - Mesoscale and Nanoscale Physics, ORDER, Materials Science (cond-mat.mtrl-sci), 101012 Combinatorics, Mathematical Physics (math-ph), Ground states, 2 DIMENSIONS, Three-dimensional structures, 101028 Mathematische Modellierung, Soft Condensed Matter (cond-mat.soft), CRYSTALLIZATION, Graphene, Analysis of PDEs (math.AP)

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FWF| Variational Structures in Thermomechanics of Solids, FWF| Global variational methods for nonlinear evolution