Optical lattice vibrations in monolayer hexagonal boron nitride from macroscopic equations

Abstract

Using two pairs of macroscopic equations deduced from a dipole lattice model including electronic polarization (EP) of ions and local field effects (LFEs) self-consistently, optical lattice vibrations in monolayer hexagonal boron nitride (BN) are studied theoretically for both in-plane and out-of-plane motions. Longitudinal and transverse optical (LO and TO) modes and out-of-plane (ZO) modes are derived, and explicit expressions are obtained for phonon dispersion, group velocity and density of states. The analytical phonon dispersion relations describe previous numerical results very well; the LO phonon dispersion is identical to the analytical expression of Sohier et al, which shows the degeneracy of the LO and TO modes at and the splitting at finite wavevectors due to the long-range macroscopic field. Whilst relating to microscopic quantities, the linear coefficients of the lattice equations are determined by first-principles calculated quantities (such as macroscopic susceptibilities). Therefore the EP and LFEs on the vibrational properties are studied. With no EP or LFEs, all the phonon frequencies are overestimated significantly. Including EP, the LFEs increase (decrease) the in-plane (out-of-plane) dielectric susceptibility by a factor of 2.5–3.5. Both ionic EP and LFEs should be included to obtain an accurate description of the lattice dynamics.