The elastic constant $C_{11}$ and piezoelectric stress constant $e_{1,11}$ of two-dimensional (2D) dielectric materials comprising h-BN, $2H\text{−}{\mathrm{MoS}}_2$, and other transition-metal dichalcogenides and dioxides are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained with ab initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows us to express the inner-strain contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h-BN and ${\mathrm{MoS}}_2$. Trends in the different microscopic quantities as functions of atomic composition are discussed.

• Received 25 October 2016
• Revised 26 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.125415