Interference and Interaction in multi-wall carbon nanotubes

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 (l(phi)) and elastic-scattering lengths (l(e)) are deduced. Because l(e) 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 approximate to 1-10 K for 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 approximate to 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.