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Physical Review B

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

Igor N. Karnaukhov, Cees G. H. Diks

Published Dec 19, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physrevb.74.235432

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The electronic transport properties of single-walled nanotubes (SWNTs) are characterized by the critical exponent $\ensuremath{\Theta}$, describing the behavior of the single-particle spectral function near the Fermi energy as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}}^{\ensuremath{\Theta}}$. Experimentally obtained $\ensuremath{\Theta}$ 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, ${\ensuremath{\Theta}}_{\mathrm{max}}=1∕8$, 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 $\ensuremath{\Theta}$ values, consistent with the empirical results, suggesting that these states are actually realized in metallic SWNTs and organic conductors.
We study quantum optical properties of the single-walled carbon nanotube (SWCNT) by introducing the effective interaction between the quantized electromagnetic field and the confined electrons in the SWCNT. Our purpose is to explore the quantum natures of electron transport in the SWCNT by probing its various quantum optical properties relevant to quantum coherence, such as the interference of the scattered and emitted photons, and the bunching and anti-bunching of photons which are characterized by the higher order coherence functions. In the strong field limit, we study the interband Rabi oscillation of electrons driven by a classical light. We also investigate the possible lasing mechanism in superradiation of coherent electrons in a SWCNT driven by a light pump or electron injection, which generate electron population inversion in the higher energy-band of SWCNT.
As a model for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors, a two-band Hubbard model is proposed. When the Coulomb interactions are introduced between the \ensuremath{\alpha} and \ensuremath{\beta} orbitals, an effective attraction of carriers in the \ensuremath{\beta} (doped) band is shown to arise in an appropriate condition. The quantum Monte Carlo method is used to confirm the occurrence of Cooper pairing in finite two-band Hubbard systems. The attraction, which also appears in the density-density correlation, enhances the on-site singlet Cooper pair-pair correlation in the \ensuremath{\beta} band and suppresses the antiferromagnetic spin-spin correlation in the \ensuremath{\alpha} band. The criterion for the pairing and the nature of the pairing are discussed. Thus we provide a mechanism of superconductivity specific to strongly correlated two-band systems.