Abnormal Hopping Conduction In Semiconducting Polycrystalline Graphene

We report the observation of an abnormal carrier transport phenomenon in polycrystalline semiconducting graphene grown by solid carbon source molecular beam epitaxy. At the lowest temperatures in samples with small grain size, the conduction does not obey the two-dimensional Mott- type variable-range hopping (VRH) conduction often reported in semiconducting graphene. The hopping exponent p is found to deviate from the 1/3 value expected for Mott VRH with several samples exhibiting a p = 2/5 dependence. We also show that the maximum energy difference between hopping sites is larger than the activation energy for nearest-neighbor hopping, violating the assumptions of the Mott model. The 2/5 dependence more closely agrees with the quasi-one-dimensional VRH model proposed by Fogler, Teber, and Shklovskii (FTS). In the FTS model, conduction occurs by tunneling between neighboring metallic wires. We suggest that metallic edge states and conductive grain boundaries play the role of the metallic wires in the FTS model.