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arXiv · 1707.03769

Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals

Habib Rostami·Francisco Guinea·Marco Polini·Rafael Roldán
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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 ${\bm k} \cdot {\bm p}$ 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 $\gtrsim 10^{11} {\rm cm}^{-2}$ can be induced by realistic inhomogeneous strains, $ε\approx 0.01 - 0.03$.

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Habib Rostami, Francisco Guinea, Marco Polini, Rafael Roldán. 2018-07-10. Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals. https://doi.org/10.1038/s41699-018-0061-7

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