$W=0\mathrm{}$ pairing in $\mathrm{}(N,N)\mathrm{}$ 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 $\mathrm{}(N,N)\mathrm{}$ nanotubes. A detailed symmetry analysis shows that the model allows $W=0\mathrm{}$ pairs which we define as two-body singlet eigenstates of H with vanishing on-site repulsion. By means of a nonperturbative canonical transformation we calculate the effective interaction between the electrons of a $W=0\mathrm{}$ pair added to the interacting ground state. We show that the dressed $W=0\mathrm{}$ pair is a bound state for a reasonable parameter values away from half filling. Exact diagonalization results for the (1,1) nanotube confirm the expectations. For $\mathrm{}(N,N)\mathrm{}$ nanotubes of length l, the binding energy of the pair depends strongly on the filling and decreases towards a small but nonzero value as $\overrightarrow{l}\infty .$ 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.