Delocalization of disordered massless Dirac fermions in graphene

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. Motivated by recent graphene transport experiments, we have undertaken a numerical study of the conductivity of disordered two-dimensional massless Dirac fermions. The beta function of the Dirac hamiltonian subject to a random scalar potential is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing the dimensionless conductance. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of states of the massless Dirac Hamiltonian can be localized. K. Nomura, M. Koshino, S. Ryu, Phys. Rev. Lett. 99, 146806 (2007).