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

TL;DR

This paper investigates electron pairing mechanisms in $(N,N)$ carbon nanotubes using the Hubbard model, revealing bound pairs away from half filling with potential implications for superconductivity.

Contribution

It introduces the concept of W=0 pairs in the Hubbard model on honeycomb lattices and demonstrates their binding and potential for pairing in carbon nanotubes.

Findings

W=0 pairs are bound states away from half filling.

Optimal doping range identified at 1.2-1.3 electrons per C atom.

Binding energy of pairs is about 0.1 to 1 meV.

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$\div$1.3, and the binding energy is of the order of 0.1 $\div$ 1 meV.