  We combine ab initio, tight-binding methods and analytical theory to study
piezoelectric effect of boron nitride nanotubes. We find that piezoelectricity
of a heteropolar nanotube depends on its chirality and diameter and can be
understood starting from the piezoelectric response of an isolated planar
sheet, along with a structure specific mapping from the sheet onto the tube
surface. We demonstrate that coupling between the uniaxial and shear
deformation are only allowed in the nanotubes with lower chiral symmetry. Our
study shows that piezoelectricity of nanotubes is fundamentally different from
its counterpart in three dimensional (3D) bulk materials.
