  We study Anderson localization in graphene with short-range disorder using
the real-space Kubo-Greenwood method implemented on graphics processing units.
Two models of short-range disorder, namely, the Anderson on-site disorder model
and the vacancy defect model, are considered. For graphene with Anderson
disorder, localization lengths of quasi-one-dimensional systems with various
disorder strengths, edge symmetries, and boundary conditions are calculated
using the real-space Kubo-Greenwood formalism, showing excellent agreement with
independent transfer matrix calculations and superior computational efficiency.
Using these data, we demonstrate the applicability of the one-parameter scaling
theory of localization length and propose an analytical expression for the
scaling function, which provides a reliable method of computing the
two-dimensional localization length. This method is found to be consistent with
another widely used method which relates the two-dimensional localization
length to the elastic mean free path and the semiclassical conductivity.
Abnormal behavior at the charge neutrality point is identified and interpreted
to be caused by finite-size effects when the system width is comparable to or
smaller than the elastic mean free path. We also demonstrate the finite-size
effect when calculating the two-dimensional conductivity in the localized
regime and show that a renormalization group beta function consistent with the
one-parameter scaling theory can be extracted numerically. For graphene with
vacancy disorder, we show that the proposed scaling function of localization
length also applies. Lastly, we discuss some ambiguities in calculating the
semiclassical conductivity around the charge neutrality point due to the
presence of resonant states.
