The European Physical Journal Special Topics

, Volume 148, Issue 1, pp 83–89 | Cite as

A cosmological model for corrugated graphene sheets

  • A. CortijoEmail author
  • M. A.H. Vozmediano


Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.


Fullerene Graphene Sheet Dirac Equation European Physical Journal Special Topic Cosmic String 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Instituto de Ciencia de Materiales de MadridMadridSpain
  2. 2.Universidad Carlos III de Madrid, Avenida de la Universidad 30MadridSpain

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