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Lattice field theory simulations of graphene

Joaquín E. Drut and Timo A. Lähde
Phys. Rev. B 79, 165425 – Published 20 April 2009
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Abstract

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

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  • Received 12 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.165425

©2009 American Physical Society

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Pauling’s dreams for graphene

Published 20 April 2009

Graphene, believed to be a semimetal so far, might actually be an insulator when suspended freely.

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Authors & Affiliations

Joaquín E. Drut1 and Timo A. Lähde2

  • 1Department of Physics, The Ohio State University, Columbus, Ohio 43210-1117, USA
  • 2Department of Physics, University of Washington, Seattle, Washington, 98195-1560, USA

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Issue

Vol. 79, Iss. 16 — 15 April 2009

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