Efros-Shklovskii variable range hopping in reduced graphene oxide sheets of varying carbon sp2 fraction

Abstract: We investigate the low temperature electron transport properties of chemically reduced graphene oxide (RGO) sheets with different carbon sp2 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 30976 to 4225 K and electron localization length increasing from 0.46 to 3.21 nm with increasing sp2 fraction. From our data, we predict that for the temperature range used in our study, Mott-VRH may not be observed even at 100 % sp2 fraction samples due to residual topological defects and structural disorders. From the localization length, we calculate a bandgap variation of our RGO from 1.43 to 0.21 eV with increasing sp2 fraction from 55 to 80 % which agrees remarkably well with theoretical prediction. We also show that, in the high bias regime, the hopping is field driven and the data follow R ~ exp[(E(0)/E)^1/2] providing further evidence of ES-VRH.