Interference and Interaction in multi-wall carbon nanotubes
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We report equilibrium electric resistance R and tunneling spectroscopy (dI/dV)measurements obtained on single multi-wall nanotubes contacted by four metallic Au fingers from above. At low temperature quantum interference phenomena dominate the magnetoresistance. The phase-coherence (lφ)and elastic-scattering lengths (le)are deduced. Because le is of order of the circumference of the nanotubes, transport is quasi-ballistic. This result is supported by a dI/dV spectrum which is in good agreement with the density of states (DOS) due to the one-dimensional subbands expected for a perfect single-wall tube. As a function of temperature T the resistance increases on decreasing T and saturates at ≈1–10 Kfor all measured nanotubes. R(T) cannot be related to the energy-dependent DOS of graphene but is mainly caused by interaction and interference effects. On a relatively small voltage scale of the order ≈10 meV, a pseudogap is observed in dI/dV which agrees with Luttinger-liquid theories for nanotubes. Because we have used quantum diffusion based on Fermi-liquid as well as Luttinger-liquid theory in trying to understand our results, a large fraction of this paper is devoted to a careful discussion of all our results.
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