W=0 Pairing in $(N,N)$ Carbon Nanotubes away from Half Filling

Abstract

We use the Hubbard Hamiltonian $H$ on the honeycomb lattice to represent the valence bands of carbon single-wall $(N,N)$ nanotubes. A detailed symmetry analysis shows that the model allows W=0 pairs which we define as two-body singlet eigenstates of $H$ with vanishing on-site repulsion. By means of a non-perturbative canonical transformation we calculate the effective interaction between the electrons of a W=0 pair added to the interacting ground state. We show that the dressed W=0 pair is a bound state for resonable parameter values away from half filling. Exact diagonalization results for the (1,1) nanotube confirm the expectations. For $(N,N)$ nanotubes of length $l$, the binding energy of the pair depends strongly on the filling and decreases towards a small but nonzero value as $l\to \infty$. We observe the existence of an optimal doping when the number of electrons per C atom is in the range 1.2$÷$1.3, and the binding energy is of the order of 0.1 $÷$ 1 meV.

16 pages, 6 figures

References in corpus (2)

• On superconductivity in armchair carbon nanotubes
• Crossover from marginal Fermi liquid to Luttinger liquid behavior in carbon nanotubes

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