Impurity State and Variable Range Hopping Conduction in Graphene

Abstract

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

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• Fluorine absorption on single and bilayer graphene: Role of sublattice and layer decoupling
• Defect-enhanced Rashba spin-polarized currents in carbon nanotubes
• Anomalous exchange interaction between intrinsic spins in conducting graphene systems
• Partial preservation of chiral symmetry and colossal magnetoresistance in adatom doped graphene
• Probing divacancy defects in a zigzag graphene nanoribbon through RKKY exchange interaction