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

Abstract

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 $(E\ensuremath{\ne}0)$ are still localized. In OD disorder the conductance at $E=0$ in an $M\ifmmode\times\else\texttimes\fi{}L$ 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 ${t}_{n{n}^{\ensuremath{'}}}$. It is found that if all the ${t}_{n{n}^{\ensuremath{'}}}$'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 ${t}_{n{n}^{\ensuremath{'}}}$, the conductivity, rather than the conductance, becomes $L∕M$ independent. The calculated value of the conductivity is around $\frac{4{e}^{2}}{h}$, in consistence with the experiments.