Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes

We argue that long-range Coulomb forces convert an isolated $(N,N)$ armchair carbon nanotube into a strongly renormalized Luttinger liquid. At high temperatures, we find anomalous temperature dependences for the interaction and impurity contributions to the resistivity, and similar power-law dependences for the local tunneling density of states. At low temperatures, the nanotube exhibits spin-charge separation, visible as an extra energy scale in the discrete tunneling density of states (for which we give an analytic form), signaling a departure from the orthodox theory of Coulomb blockade.