Lattice field theory simulations of graphene

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.

14 pages, 7 figures. Published version freely available if accessed via http://physics.aps.org/articles/v2/30

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• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two Dimensional Atomic Crystals
• Ultrahigh electron mobility in suspended graphene
• The structure of suspended graphene sheets
• Temperature dependent transport in suspended graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Modeling disorder in graphene
• Is graphene in vacuum an insulator?
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Cited by in corpus (5)

• Supercritical Coulomb center and excitonic instability in graphene
• Coulomb interaction in graphene: Relaxation rates and transport
• Magnetic field driven instability of charged center in graphene
• Artifical atoms in interacting graphene quantum dots
• Four-dimensional Yang-Mills theory with a three-dimensional fermion membrane