Nonlinear transport and localization in single-walled carbon nanotubes

We have measured the electrical transport properties of mats of single-walled carbon nanotubes (SWNT) as a function of applied electric and magnetic fields. We find that at low temperatures the resistance as a function of temperature R(T) follows the Mott variable range hopping (VRH) formula for hopping in three dimensions. Measurement of the electric field dependence of the resistance R(E) allows for the determination of the Bohr radius of a localized state a = 700nm. The magnetoresistance (MR) of SWNT mat samples is large and negative at all temperatures and fields studied. The low field negative MR is proportional to H-2, in agreement with variable range hopping in two or three dimensions. 3D VRH indicates good intertube contacts, implying that the localization is due to the disorder experienced by the individual tubes, The 3D localization radius gives a measure of the 1D localization length on the individual tubes, which we estimate to be >700 nm. Implications for the electron-phonon mean free path are discussed.