Localization and one-parameter scaling in hydrogenated graphene

One-parameter scaling at the dirac point in graphene.

We numerically calculate the conductivity sigma of an undoped graphene sheet (size L) in the limit of a vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function beta(sigma)=dlnsigma/dlnL. Contrary to a recent prediction, the scaling flow has no fixed point (beta>0) for conductivities up to and beyond the symplecti...

Single parameter scaling in one-dimensional localization revisited

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained ar...

Scaling of the energy gap in pattern-hydrogenated graphene.

Recent experiments show that a substantial energy gap in graphene can be induced via patterned hydrogenation on an iridium substrate. Here, we show that the energy gap is roughly proportional to N(H)(1/2)/N(C) when disorder is accounted for, where N(H) and N(C) denote concentrations of hydrogen and carbon atoms, respectively. The dispersion relation, obtained through calculation of the momentum...

Single-parameter scaling in one-dimensional Anderson localization: Exact analytical solution

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of single-parameter scaling in this model. According to this criterion, states with energies within the conduction band of the underlying nonrandom system satisfy sin...

Scaling of the energy gap in pattern-hydrogenated graphene: Supporting Information