Luttinger-liquid behaviour in carbon nanotubes

Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level E(F) are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations, The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts(1). For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires(2,3) have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained, Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour(4,5), but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states(6). Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires(7-10) that may exhibit Luttinger-liquid behaviour(11,12). Here we present measurements of the conductance of bundles ('ropes') of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.