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.
- Received 12 January 2009
DOI:https://doi.org/10.1103/PhysRevB.79.165425
©2009 American Physical Society
Viewpoint
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.
See more in Physics