Strongly interacting Luttinger liquid states as those inherent in carbon nanotubes

The electronic transport properties of single-walled nanotubes (SWNTs) are characterized by the critical exponent $\Theta$, describing the behavior of the single-particle spectral function near the Fermi energy as $\rho \left(\omega \right)\propto {\mid \omega \mid }^{\Theta }$. Experimentally obtained $\Theta$ values have been reported in the range of 0.43–0.48 for metallic SWNTs. However, these values are much larger than the theoretical upper limit of the exponent, ${\Theta }_{\max }=1∕8$, for the Hubbard model. Here, we show that the observed electronic transport properties can be explained by taking into account a specific hard-core Coulomb interaction. For a many-body system with a hard-core potential, we analytically calculate the critical exponents using the Bethe ansatz and conformal field theory. We find strongly interacting Luttinger liquid states that are characterized by large $\Theta$ values, consistent with the empirical results, suggesting that these states are actually realized in metallic SWNTs and organic conductors.

Figure 1

Dispersion of fermion subbands as a function of the wave vector.

Figure 2

Exponent $K_{\rho }$ as a function of a total density of fermions in the case of a weak interaction and $v=0$, $u=0.2$, and $w=0.1$; solid and dotted curves correspond to the $\chi =\pm 1$ subband.

Figure 3

Critical exponent $\Theta$ at $v=0$, $u=0.2$, and $w=0.1$ in the case of a weak interaction, similar conditions for Fig. 2.

Figure 4

Critical exponent $\Theta$ at $v=0$, $u=2$, and $w=0.5$ in the case of a strong interaction.

Figure 5

Exponent $K_{\rho }$ at $v=0$, $u=2$, and $w=0.5$ in the case of a strong interaction.