Theoretical study of work function of conducting single-walled carbon nanotubes by a non-relativistic field theory approach

We study a non-relativistic many-fermion system on a small cylindrical surface. The interaction between the fermions is modeled as an attractive two-body contact effective potential, which allows binding of fermions on the cylinder surface. The N-fermion model is solved in a self-consistent Hartree–Fock (HF) approximation, and is applied to study the electronic properties of metallic single-walled carbon nanotubes (SWCNT). The many-fermion HF approach with contact interactions is known to mimic a first order density functional theory. We derive an analytic form of the SWCNT work function (WF), that is parameterized by the Fermi kinetic energy, and reproduces the graphene work function for large radius (R). This model allows us to understand theoretically the small experimental WF fluctuations and the non-trivial left–right asymmetry of the graphene WF distribution found experimentally in a large set of SWCNT with radius above 5 Å. By extending our model for SWCNT with very small radius, we found a WF that increases linearly with 1/R.