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          Abstract

          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.

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          Intrinsic Piezoelectricity in Two-Dimensional Materials

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            Nanotube Piezoelectricity

            E. Mele, Na Sai (2003)
            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.
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              Piezoelectricity in planar boron nitride via a geometric phase

              Due to their low surface mass density, two-dimensional materials with a strong piezoelectric response are interesting for nanoelectromechanical systems with high force sensitivity. Unlike graphene, the two sublattices in a monolayer of hexagonal boron nitride (hBN) are occupied by different elements, which breaks inversion symmetry and allows for piezoelectricity. This has been confirmed with density functional theory calculations of the piezoelectric constant of hBN. Here, we formulate an entirely analytical derivation of the electronic contribution to the piezoelectric response in this system based on the concepts of strain-induced pseudomagnetic vector potential and the modern theory of polarization that relates the polar moment to the Berry curvature. Our findings agree with the symmetry restrictions expected for the hBN lattice and reproduce well the magnitude of the piezoelectric effect previously obtained ab-initio.
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                Author and article information

                Journal
                01 August 2017
                Article
                1708.00384
                da268c98-fec4-44d5-84fb-885a56d69eec

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                cond-mat.mes-hall

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