Correlated Electrons in Carbon Nanotubes

TL;DR

This paper reviews the many-body effects and electron correlations in single-wall carbon nanotubes, deriving an effective model and analyzing their low-energy properties, including Mott insulator phases and transport phenomena.

Contribution

It derives a universal phase Hamiltonian for conducting nanotubes with arbitrary chirality and studies their low-energy electron correlation effects beyond the Luttinger liquid model.

Findings

Weak dependence of Hamiltonian parameters on chiral angle

Localization effects prevent coexistence of intra- and inter-valley scattering at low energies

Mott-like insulating phase with energy gaps up to 0.1 eV at half filling

Abstract

Single-wall carbon nanotubes are almost ideal systems for the investigation of exotic many-body effects due to non-Fermi liquid behavior of interacting electrons in one dimension. Recent theoretical and experimental results are reviewed with a focus on electron correlations. Starting from a microscopic lattice model we derive an effective phase Hamiltonian for conducting single-wall nanotubes with arbitrary chirality. The parameters of the Hamiltonian show very weak dependence on the chiral angle, which makes the low-energy physics of conducting nanotubes universal. The temperature-dependent resistivity and frequency-dependent optical conductivity of nanotubes with impurities are evaluated within the Luttinger-like model. Localization effects are studied. In particular, we found that intra-valley and inter-valley electron scattering can not coexist at low energies. Low-energy properties of clean nanotubes are studied beyond the Luttinger liquid approximation. The strongest Mott-like electron instability occurs at half filling. In the Mott insulating phase electrons at different atomic sublattices form characteristic bound states. The energy gaps of $0.01-0.1$ eV occur in all modes of elementary excitations. We finally discuss observability of the Mott insulating phase in transport experiments. The accent is made on the charge transfer from external electrodes which results in a deviation of the electron density from half-filling.