Luttinger Liquid Behavior in Metallic Carbon Nanotubes

Coulomb interaction effects have pronounced consequences in carbon nanotubes due to their 1D nature. In particular, correlations imply the breakdown of Fermi liquid theory and typically lead to Luttinger liquid behavior characterized by pronounced power-law suppression of the transport current and the density of states, and spin-charge separation. This paper provides a review of the current understanding of non-Fermi liquid effects in metallic single-wall nanotubes (SWNTs). We provide a self-contained theoretical discussion of electron-electron interaction effects and show that the tunneling density of states exhibits power-law behavior. The power-law exponent depends on the interaction strength parameter g and on the geometry of the setup. We then show that these features are observed experimentally by measuring the tunneling conductance of SWNTs as a function of temperature and voltage. These tunneling experiments are obtained by contacting metallic SWNTs to two nanofabricated gold electrodes. Electrostatic force microscopy (EFM) measurements show that the measured resistance is due to the contact resistance from the transport barrier formed at the electrode/nanotube junction. These EFM measurements show also the ballistic nature of transport in these SWNTs. While charge transport can be nicely attributed to Luttinger liquid behavior, spin-charge separation has not been observed so far. We briefly describe a transport experiment that could provide direct evidence for spin-charge separation.