Anderson localization of electron states in graphene in different types of disorder

Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorders in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal disorder all states are localized as predicted by the scaling theory for two-dimensional systems. In the case of OD disorder, the states at the Dirac point (E=0) are shown to be delocalized due to the specific chiral symmetry, although other states (E not equal 0) are still localized. In OD disorder the conductance at E=0 in an MxL rectangular system at the thermodynamical limit is calculated with the transfer-matrix technique for various values of ratio M/L and different types of distribution functions of the OD elements t(nn'). It is found that if all the t(nn)(')'s are positive the conductance is independent of L/M as restricted by two delocalized channels at E=0. If the distribution function includes the sign randomness of elements t(nn)('), the conductivity, rather than the conductance, becomes L/M independent. The calculated value of the conductivity is around 4e(2)/h, in consistence with the experiments.