  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.
