  The electronic and piezoelectric properties of the boron nitride (BN)
nanotubes are investigated with the hybrid density functional (B3LYP) method.
We first study bulk h-BN and BN sheet and find that the B3LYP band structure
and energy gap are consistent with the GW results. The B3LYP band gap is larger
than the LDA one by about 1.8 eV for both zigzag and armchair nanotubes with
various radius. We give an alternative interpretation that the optical
absorption lines at 4.45 eV might be due to the electron transition in small
zigzag BN nanotubes. The piezoelectric constant from the B3LYP method for
zigzag BN nanotubes are substantially larger than those in the PVDF polymer
family, suggesting BN nanotubes as candidates for various nanoelectromechanical
applications.
