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

TL;DR

This paper investigates Anderson localization in graphene, revealing that diagonal disorder localizes all states, while off-diagonal disorder preserves delocalized states at the Dirac point due to chiral symmetry, with conductance around 4e^2/h.

Contribution

It demonstrates the contrasting effects of diagonal and off-diagonal disorder on electron localization in graphene, highlighting the role of chiral symmetry in delocalization at the Dirac point.

Findings

Diagonal disorder localizes all electron states in graphene.

Off-diagonal disorder preserves delocalized states at the Dirac point.

Conductivity at E=0 is approximately 4e^2/h, matching experimental results.

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 $t_{nn'}$. 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.