Dielectric screening for carbon nanotubes in a gating electric field

We use the sp³ tight-binding model to calculate electronic structures of single-walled carbon nanotubes. All the π and σ electrons would take part in charge screening. As a result of the cylindrical symmetry, the momentum (q) and angular momentum transfer (L) are conserved in the electron-electron Coulomb interactions. The static dielectric function ε (q,L), which determines the charge screening ability, is evaluated from the random-phase approximation. ε of L = 1 at long wavelength limit ( q → 0) is very important in understanding the dielectric screening in the presence of a uniform transverse electric field E_⊥. ε ( q = 0, L = 1) hardly depends on the chiral angle, and the dependence on the nanotube radius is weak. It quickly grows as the Fermi level increases, that is, the screening response is largely enhanced by the increasing free carriers.