Energy Anomaly and Polarizability of Carbon Nanotubes*

Electron properties of carbon nanotubes can change qualitatively by applying a strong perpendicular electric field. In metallic tubes the sign of Fermi velocity can be reversed by a sufficiently strong field, while in semiconducting tubes the effective mass can change sign. Changes in the spectrum manifest themselves in a breakup of the Fermi surface and in the energy gap suppression, respectively. The effect is controlled by the field inside the tube which is screened due to the polarization induced on the tube. The theory of screening is linked to the chiral anomaly for 1D fermions that reveals universality and scale invariance of the response dominated by $\pi$ electrons. [Phys. Rev. Lett. {\bf 96}, 036402 (2006)]