Nearly-free-electron effective model for conducting nanotubes

We study a nonrelativistic quantum-field-theory model of a many-fermion system on a small cylindrical surface. An attractive contact effective two-body interaction is assumed to permit binding of fermions on the surface. We treat the many-fermion system within mean-field thermodynamics. A self-consistent Hartree-Fock calculation is performed and the total energy, pressure, and chemical potential are investigated in a thermodynamically consistent way. The model is applied to study the electronic properties of metallic single-walled nanotubes (SWNTs). We derive an analytical relation for the single-particle energy separation between two consecutive spikes provoked by Van Hove singularities in the density of states. We also found that the effective electron-electron interaction is necessary to reproduce the experimental fluctuation of the work function as a function of the diameter of SWNTs. The experimental distribution of the work functions with radius presents a nontrivial left-right asymmetry around the peak value that is reproduced by the model. Also, for SWNTs with radius smaller than 2 A, the model gives a work function that increases linearly with 1/R.