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

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

2007-12-29

arxiv.org/abs/0801.0027v1

Phys. Rev. B, 76, 214204 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 12 figures

Scientific paper

10.1103/PhysRevB.76.214204

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 $t_{nn'}$. It is found that if all the $t_{nn'}$'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 $t_{nn'}$, the conductivity, rather than the conductance, becomes $L/M$ independent. The calculated value of the conductivity is around $\frac{4e^2}{h}$, in consistence with the experiments.

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