Activated hopping transport in nematic conducting aerogel at low temperatures

The transport properties of nematic aerogels, which consist of highly oriented Al$_2$O$_3\cdot$SiO$_2$ nanofibers coated with a graphene shell with a large number of defects, are studied. The temperature dependences of the electrical resistivity in the range of 9-40K strictly follow the formula derived to describe the variable range hopping (VRH) conductivity, in which exponent $α$ changes from 0.4 to 0.9 when the number of layers in the graphene shell decreases from 4-6 to 1-2. The dependence of $α$ on the shell thickness can be explained by a simultaneous change in the dimensionality of hopping transport and the character of the energy dependence of the density of localized states near the Fermi level. The fact that $α$ approaches unity at the minimum graphene shell thickness indicates a gradual transition from VRH transport to nearest neighbor hopping (NNH) transport. The magnetoresistance measured at T = 4.2 K is negative, increases significantly with decreasing graphene shell thickness, and is approximated by a formula for the case of weak localization with a good accuracy. The phase coherence lengths are in a reasonable relation with the graphene grain sizes. The conducting aerogels under study complement the well-known set of materials that exhibit hopping electron transport at low temperatures, which is characteristic of media with strong carrier localization, and also a negative magnetoresistance, which usually manifests itself under weak localization conditions.