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The variable range hopping theory, as formulated for exponentially localizedimpurity states, does not necessarily apply in the case of graphene withcovalently attached impurities. We analyze the localization of impurity statesin graphene using the nearest-neighbor, tight-binding model of anadatom-graphene system with Green's function perturbation methods. Theamplitude of the impurity state wave function is determined to decay as a powerlaw with exponents depending on sublattice, direction, and the impurityspecies. We revisit the variable range hopping theory in view of this resultand find that the conductivity depends as a power law of the temperature withan exponent related to the localization of the wave function. We show that thistemperature dependence is in agreement with available experimental results.

Impurity State and Variable Range Hopping Conduction in Graphene