The electronic properties of carbon nanotubes are very rich. Over the past few years they have allowed to study many nanoscale transport properties in a single material class, e.g., superconductivity, Kondo effect, Luttinger liquid behavior, Altshuler Aronov anomalies, and spin transport. In this talk, after a broad introduction into the relevant concepts and results, two exemplary topics will be presented:
(1) The interplay of disorder and electron-electron interactions can be described by field theory. Results for the crossover from the Luttinger liquid into the diffusive Altshuler-Aronov-dominated phase (as the disorder is increased) will be given, using the conductivity and the tunneling density of states as concrete examples.
(2) The linear conductance is even in a magnetic field B because of the fundamental Onsager symmetry. However, there are nonlinear terms in the I(U) characteristics that are linear in B and even in U. Such terms have attracted much attention recently, as they give direct clues about interactions and the chirality (handedness) of the medium. I discuss this question in the context of chiral nanotubes.