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.

由于线性压电性，在非中心对称材料中可能会将机械力转换为电信号。二维材料的非凡机械性能及其高结晶度使其成为研究和利用压电效应的绝佳平台。在这里，使用现代极化理论和k · p模型哈密顿量，研究了非中心对称六角形二维晶体的压电响应。压电常数的解析表达式是根据拓扑量（例如谷值Chern数）获得的。该理论适用于半导体过渡金属二卤化物和六方氮化硼。我们发现与MoS _2的可用实验测量结果非常吻合。我们进一步推广该理论，以研究经受不均匀应变（例如，纳米气泡）的样品的极化。我们在应变张量的方面获得一个简单的表达，表明电荷密度≳ 10 ¹¹厘米^-2可以通过现实的不均匀应变，来诱导ε 听，说：0.01-0.03。