Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals

TL;DR

This paper develops a theoretical framework linking piezoelectric response in 2D hexagonal crystals to topological properties like the valley Chern number, and applies it to materials such as MoS2 and h-BN, predicting significant charge densities under strain.

Contribution

It introduces an analytical expression for piezoelectric constants based on topological quantities and extends the theory to inhomogeneous strains in 2D materials.

Findings

Good agreement with experimental data for MoS2

Charge densities up to 10^{11} cm^{-2} predicted under realistic strains

Analytical relation between piezoelectricity and valley Chern number

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, $\epsilon \approx 0.01 - 0.03$.