First-principles calculation of electronic polarization of III-V   nanotubes
  A first-principles study of the electronic polarization of BN and AlN nanotubes and their graphitic sheets under an external electric field has been performed. We found that the polarization per atom of zigzag nanotubes increases with decreasing diameter while that of armchair nanotubes decreases. The variation of the polarization is related to the exterior angle of the bonds around the B or Al atoms rather than that around the N atoms. The increase in the polarization of the zigzag nanotubes with decreasing diameter is caused by the large variation of the exterior angle when they are wrapped into the tubular form. On the other hand, the decrease in the bond length results in the weak polarization of thin armchair nanotubes. 
Jun Otsuka, Tomoya Ono, and Kikuji Hirose