Comment on “Piezoelectricity in planar boron nitride via a geometric phase”

Using the strain-dependent effective Hamiltonian and the geometric phase, Droth et al. [Phys. Rev. B 94, 075404 (2016)] obtain an analytical expression for the electronic contribution to the piezoelectricity of planar hexagonal boron nitride ($h$-BN). Their analytical results of piezoelectric constants for $h$-BN are invalid because of the mistakes in constructing the adiabatic process of the piezoelectricity. In this Comment, we reconstruct a proper adiabatic process for piezoelectricity and formulate a general Berry phase expression for the piezoelectric coefficients of two-dimensional piezoelectric crystals by means of the modern theory of polarization. The corrected analytical results of the piezoelectric constants are in complete consistency with the first-principles calculations and hence manifest the validity and generality of the Berry phase expression of piezoelectric coefficients.