Anomalous screening in narrow-gap carbon nanotubes

The screening of Coulomb interaction controls many-body physics in carbon nanotubes, as it tunes the range and strength force that acts on charge carriers binds electron-hole pairs into excitons. In doped tubes, effective drives competition between Luttinger liquid Wigner crystal, whereas undoped narrow-gap tubes dictates Mott or excitonic nature correlated insulator observed at low temperature. Here, by computing dielectric function selected narrow- zero-gap from first principles, we show standard effective-mass model systematically underestimates long wavelength, hence missing binding low-energy reason is critically lacks full three-dimensional topology tube, being adapted graphene theory. As ab inito calculations are limited to small develop a two-band based plane-wave expansion Bloch states exact truncated cutoff technique. We demonstrate our -- computationally cheap approach provides correct for any size chirality. A striking result screened remains long-ranged even gapless an effect microscopic local fields generated electrons moving curved tube surface. application, electron-electron felt distances relevant quantum transport experiments super Coulombic.