W=0 pairing in (N,N) carbon nanotubes away from half filling

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→∞. 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.