Theory of phonon dispersions and piezoelectricity in multilayers of hexagonal boron‐nitride

Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron‐nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long‐wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant e1,11 ( N) as a function of the number of layers N . In agreement with group theory, we find that e1,11 ( N_ g ) = 0 for N_ g even; for an uneven number N_ u of layers we obtain e1,11 ( N_ u ) = 7.31 × 10- 5 \; C\; cm- 2 / N_ u , i.e. the piezoelectric constant decreases as 1/ N_ u .