  We characterize the response of isolated single- (SWNT) and multi-wall (MWNT)
carbon nanotubes and bundles to static electric fields using first-principles
calculations and density-functional theory. The longitudinal polarizability of
SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles
it is given by the sum of the polarizabilities of the constituent tubes. The
transverse polarizability of SWNTs is insensitive to band gaps and chiralities
and is proportional to the square of the effective radius; in MWNTs the outer
layers dominate the response. The transverse response is intermediate between
metallic and insulating, and a simple electrostatic model based on a
scale-invariance relation captures accurately the first-principles results.
Dielectric response of non-chiral SWNTs in both directions remains linear up to
very high values of applied field.
