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.

Figure 1

The lattice of hBN does not possess an inversion center and hence allows for piezoelectricity. (a) Isotropic strain ($u_{xx}=u_{yy},u_{xy}\equiv u_{yx}=0$) leads to a vanishing pseudomagnetic vector potential $\mathit{A}$ and does not induce a polarization $\mathit{P}$. (b), (c) Realizations of the strain tensor $u_{ij}$ that lift the trigonal symmetry and generate a change in the polarization. The induced polarization and the vector potential are always orthogonal, $\mathit{P}\perp \mathit{A}$.