Piezoelectricity and valley chern number in inhomogeneous hexagonal 2D crystals

Habib Rostami,Marco Polini,Rafael Roldán,Francisco Guinea

doi:10.1038/s41699-018-0061-7

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 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.

Highlights

Piezoelectricity is a property of crystals with broken inversion symmetry, which allows conversion of mechanical to electric energy.[1,2] When subjected to an external strain field ε, piezoelectric crystals acquire a polarization P that is described by the third-rank piezoelectric tensor γijk ∂Pi=∂εjkjε
The so-called modern theory of polarization exploits the properties of the Berry connection (BC) of the electronic wave-functions to quantify the change of polarization in an extended system.[3–5]
The BC is obtained in terms of the Bloch orbitals, and the polarization can be calculated as an integral of the BC on whole Brillouin zone

Summary

Introduction

Piezoelectricity is a property of crystals with broken inversion symmetry, which allows conversion of mechanical to electric energy.[1,2] When subjected to an external strain field ε, piezoelectric crystals acquire a polarization P that is described by the third-rank piezoelectric tensor γijk ∂Pi=∂εjkjε!0. This quantum mechanical description of the polarization has been used to calculate the piezoelectric constant of a number of crystals from ab initio[6,7], as well as analytical approaches.[8,9]

Results

Conclusion