Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals

Abstract

Conversion of mechanical forces to electric signal is possible in non-centrosymmetric materials due to linear piezoelectricity. The extraordinary mechanical properties of two-dimensional materials and their high crystallinity make them exceptional platforms to study and exploit the piezoelectric effect. Here, the piezoelectric response of non-centrosymmetric hexagonal two-dimensional crystals is studied using the modern theory of polarization and $\mathbf{k}\cdot \mathbf{p}$ model Hamiltonians. An analytical expression for the piezoelectric constant is obtained in terms of topological quantities such as the {\it valley Chern number}. The theory is applied to semiconducting transition metal dichalcogenides and hexagonal Boron Nitride. We find good agreement with available experimental measurements for MoS${}_2$. We further generalise the theory to study the polarization of samples subjected to inhomogeneous strain (e.g.~nanobubbles). We obtain a simple expression in terms of the strain tensor, and show that charge densities $\gtrsim 10^{11}{\mathrm{cm}}^{-2}$ can be induced by realistic inhomogeneous strains, $\epsilon \approx 0.01-0.03$.

arXiv comment14 pages, 3 figures

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• Comment on "Piezoelectricity in planar boron nitride via a geometric phase"
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