Efros-Shklovskii variable-range hopping in reduced graphene oxide sheets of varying carbon sp~2 fraction

摘要

We investigate the low-temperature electron transport properties of chemically reduced graphene oxide (RGO) sheets with different carbon sp~2 fractions of 55% to 80%. We show that in the low-bias (Ohmic) regime, the temperature (T) dependent resistance (R) of all the devices follow Efros-Shklovskii variable range hopping (ES-VRH) R ~ exp[(T_(ES)/T)~(1/2)] with (T_(ES) decreasing from 3.1 × 10~4 to 0.42 × 10~4 K and electron localization length increasing from 0.46 to 3.21 nm with increasing sp~2 fraction. From our data, we predict that for the temperature range used in our study, Mott-VRH may not be observed even at 100% sp~2 fraction samples due to residual topological defects and structural disorders. From the localization length, we calculate a band-gap variation of our RGO from 1.43 to 0.21 eV with increasing sp~2 fraction from 55 to 80%, which agrees remarkably well with theoretical predictions. We also show that, in the high bias non-Ohmic regime at low temperature, the hopping is field driven and the data follow R ~ exp[(E_0/E)~(1/2)] providing further evidence of ES-VRH.