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(b)

Fig. 19.43. Plots of magnetoresistance vs. magnetic field. The inset shows the arrangements of the four probes for resistivity and Hall effect measurements. The solid lines are calculated from 2D weak localization theory. The arrow shows the field at which the magnetic energy g/J.BH and thermal energy kBT are approximately equal at 2 K. The high-temperature data are presented in (a) and the low-temperature data in (b) [19.134],

Fig. 19.43. Plots of magnetoresistance vs. magnetic field. The inset shows the arrangements of the four probes for resistivity and Hall effect measurements. The solid lines are calculated from 2D weak localization theory. The arrow shows the field at which the magnetic energy g/J.BH and thermal energy kBT are approximately equal at 2 K. The high-temperature data are presented in (a) and the low-temperature data in (b) [19.134], dependent resistivity and the magnetoresistance at low T and H to 2D weak localization theory [19.135], showing a log T dependence for the weak localization contribution to the resistivity and a negative magnetoresistance with its characteristic T and H dependences [19.134], A low-temperature sheet resistance of 5.5 kfl/D at 5 K is obtained from this 2D weak localization analysis, and this value of the sheet resistance is compatible with the diameter of the multiple tubule bundle sample.

Also of interest is that attempts to fit the low-temperature, low-field transport measurements on the tubule bundles give poor agreement with ID weak localization theories [19.134]. Above 65 K, the magnetoresistance was found to be positive, and the conductivity was found to increase linearly with T, which was attributed mainly to an increase in carrier concentration with increasing T [19.134]. This is a reasonable conclusion in view of the low carrier concentration (1019/cm3) and the resultant low Fermi level (<10 meV) of carbon nanotubes. The magnetoresistance behavior for this sample containing multiple tubule bundles shows notable differences relative to the magnetoresistance for pyrocarbons and individual disordered carbon fibers [19.60,136] regarding their T- and //-dependent behaviors. Although at an early stage, these measurements show promise for providing new insights into the electronic structure and transport properties of carbon nanotubes.

Of particular interest to magnetoresistance studies is the recent report of the observation of conductance fluctuations in a single 20-nm-diameter nanotube [19.133] through measurement, using a four probe method, of sample-specific aperiodic structures in the magnetic field dependence of the resistance below 1 K. Referring to Fig. 19.44, we see aperiodic structures in the magnetoresistance at various magnetic field values. These aperiodic structures are independent of temperature in the low-temperature limit. The amplitudes of the two indicated fluctuations are constant in magnitude (AG = 0.2e2/h) at low-temperature (below 0.4 K) but decrease in magnitude above 0.4 K according to a T~a (a ~ 1/2) law [19.133], consistent with the theory for universal conductance fluctuations [19.135,138,139], At T = 0, a particular defect configuration in the sample gives rise to a specific pattern in the magnetoresistance (see Fig. 19.44), which remains

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