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

Shi-Jie Xiong; Ye Xiong

doi:10.1103/PhysRevB.76.214204

paper

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

arXiv:0801.0027 · doi:10.1103/PhysRevB.76.214204

Abstract

Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder 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 ( $E \neq = 0$ ) are still localized. In OD disorder the conductance at E=0 in an $M \times L$ 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 $t_{n n^{'}}$ . It is found that if all the $t_{n n^{'}}$ 's are positive the conductance is independent of $L / M$ as restricted by 2 delocalized channels at E=0. If the distribution function includes the sign randomness of elements $t_{n n^{'}}$ , 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.

arXiv comment24 pages, 12 figures

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

Abstract

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