Piezoelectricity and valley chern number in inhomogeneous hexagonal 2D crystals

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 k·p model Hamiltonians. An analytical expression for the piezoelectric constant is obtained in terms of topological quantities, such as the 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 MoS₂. We further generalize 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 ≳10¹¹cm⁻² can be induced by realistic inhomogeneous strains, ϵ ≈ 0.01–0.03.