Hybridized mechanism of pairing of fermions in single-walled carbon nanotubes

A two-band fermion model with boundary fields describing the band structure of a single-walled carbon nanotube (SWNT) is proposed and solved exactly by the nested Bethe ansatz. The fermions, occupying two degenerate subbands that are shifted relative to each other, interact via inner- and interband on-site Coulomb interactions, and one-particle and correlated on-site hybridizations. The critical exponents of the correlation functions are calculated using the Bethe ansatz solution and conformal field theory. It is found that a two-component electron liquid state, one of which is defined by an attractive effective electron-electron interaction, is realized for strong hybridized interaction. The attractive interaction leads to the formation of a spinless bound state of Cooper-type pairs and dominating correlations of singlet pairs for arbitrary band fillings. We suggest that this electron pairing mechanism may be the key to resolving the nature of superconductivity in SWNT’s.

Figure 1

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

Figure 2

Critical exponents of the correlation functions of the density-density $\left(\nu \right)$ and singlet pairs $\left(\mu \right)$, as a function of the electron density in the case of weak hybridized interaction; solid curves correspond to the subband with $c=U+W$, dotted with $c=U-W$.

Figure 3

The same details as for Fig. 2, for the case of a strong hybridized interaction.