Graphene ripples as a realization of a two-dimensional Ising model: A scanning tunneling microscope study

J. K. Schoelz, P. Xu, V. Meunier, P. Kumar, M. Neek-Amal, P. M. Thibado, F. M. Peeters

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

Ripples in pristine freestanding graphene naturally orient themselves in an array that is alternately curved-up and curved-down; maintaining an average height of zero. Using scanning tunneling microscopy (STM) to apply a local force, the graphene sheet will reversibly rise and fall in height until the height reaches 60%-70% of its maximum at which point a sudden, permanent jump occurs. We successfully model the ripples as a spin-half Ising magnetic system, where the height of the graphene plays the role of the spin. The permanent jump in height, controlled by the tunneling current, is found to be equivalent to an antiferromagnetic-to-ferromagnetic phase transition. The thermal load underneath the STM tip alters the local tension and is identified as the responsible mechanism for the phase transition. Four universal critical exponents are measured from our STM data, and the model provides insight into the statistical role of graphene's unusual negative thermal expansion coefficient.

Original languageEnglish (US)
Article number045413
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number4
DOIs
StatePublished - Jan 12 2015

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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