Luttinger Liquid Behavior in Metallic Carbon Nanotubes

Abstract

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.

Electron Spin in Single Wall Carbon Nanotubes

“…Another surprising observation is, that it can be observed also in multi wall carbon nanotubes, in spite of the much weaker 1-dimensionality there [18]. The observation of the Luttinger liquid effect confirm ancient theories [17], however we would still like to see other consequences of this new liquid and understand why, for instance, the odd-even behaviour, described above, is not affected. No semiclassical and intuitive picture of the Luttinger liquid exists.…”

Conductance of one-dimensional quantum wires

“…TLL with finite g (long-range interaction cut off by the finite length of the sample and the width of the tube) without screening gate is indeed realized in a SWNT [21]. The boundary condition which ensures Q + Q TLL = 0 with no reference to the metallic gate is, in fact,…”

Landau damping in a two-dimensional electron gas with imposed quantum grid

“…Choosing according to Refs. 7,3 v ≈ 8 · 10 7 cm/sec and a ≈ 20 nm, one finds that characteristic plasmon frequencies lie in far infrared region ω ∼ 10 14 sec −1 , while characteristic wave vectors are estimated as q ∼ 10 6 cm −1 .…”

“…A single wire is characterized by its radius r 0 , length L, and LL interaction parameter g. The minimal nanotube radius is r 0 ≈ 0.35 nm, 13 maximal nanotube length is L ≈ 1 mm, and the LL parameter is estimated as g ≈ 0.3. 7 In experimentally realizable setups 3 the QCB is a cross-structure of suspended single-wall carbon nanotubes lying in two parallel planes separated by an interplane distance d, placed on a dielectric or semiconductor substrate (see Fig.1). Nevertheless, some generic properties of QCB may be described under the assumption that QCB is a genuine 2D system.…”

“…A constituent element of QCB (quantum wire or nanotube) possesses the LL-like spectrum. 6,7 A single array of parallel quantum wires is still a LL-like system qualified as a sliding phase 8 provided only the electrostatic interaction between adjacent wires is taken into account. If tunneling is suppressed and the two arrays are coupled only by electrostatic interaction in the crosses, the system possesses the LL zero energy fixed point, and besides, a rich Bosetype excitation spectrum (plasmon modes) arises at finite energies in the 2D Brillouin zone (BZ).…”