Department of Physics and Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev Lett. 2012 Dec 21;109(25):256601. doi: 10.1103/PhysRevLett.109.256601. Epub 2012 Dec 20.
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.
变量范围跳跃理论，如针对指数局域杂质态所建立的理论，不一定适用于共价键合杂质的石墨烯。我们使用相邻近原子-石墨烯系统的近邻、紧束缚模型，结合格林函数微扰方法，来分析杂质态在石墨烯中的局域化。杂质态波函数的幅度确定按幂律衰减，指数取决于子晶格、方向和杂质种类。鉴于这一结果，我们重新审视了变量范围跳跃理论，并发现电导率与温度呈幂律关系，其指数与波函数的局域化有关。我们表明，这种温度依赖性与现有的实验结果是一致的。
