Variable range hopping in graphene with atomic impurities: anomalous magnetic field effects

GONZALO USAJ

Chemnitz

Conferencia; Graphene Week 2013; 2013

Motivated by a recent experiment on diluted fluorinated graphene [1] we study the magnetic field dependence of the localization length in graphene in the presence of atomic impurities. The experimental data of Ref. [1] showed that the presence of F atoms causes the systems to present strong localization effects, being the electron transport at low doping thermally activated (variable range hopping). In this regime, the system presents a strong negative magnetoresistance, which results from a reduction of the Mott activation temperature. The authors attributed the latter to an increase of the localization length induced by the magnetic field, although the underlying mechanism for such increase was unclear. Here, we model the atomic impurities as resonant scatters and use exact analytical expressions for the Green functions of the clean graphene sheet (in the continuous limit) to calculate the spatial decay of the full Green function using an essentially exact numerical method. After averaging over the impurities configuration we can obtain the localization length as a function of the magnetic field for realistic values of the impurity concentration---a comparison with other methods such as the Kernel polynomial expansions is discussed. Our results show that this simple model is able to account for the observed increase of the localization length (by roughly a factor 4). We discuss the physical origin of this effect in terms of the particular structure of the low energy Landau levels in graphene and the symmetry of the honeycomb lattice. References: [1] X. Hong S.-H. Cheng, C. Herding, and J. Zhu, Phys. Rev. B 83 (2011) 085410.