[Paper Review] Flexoelectricity in two-dimensional materials

Matteo Springolo, Miquel Royo+1 more|arXiv (Cornell University)|Oct 16, 2020

Nonlocal and gradient elasticity in micro/nano structures4 citations

TL;DR

This paper develops a first-principles framework to calculate flexoelectricity in two-dimensional materials by modeling the voltage response to strain gradients within a supercell geometry. It identifies two distinct contributions—electronic and lattice-mediated—with a key role for the quadrupolar moment of the unperturbed charge density, revealing large flexoelectric responses in 2D materials like graphene and phosphorene.

ABSTRACT

Flexoelectricity, the generation of a macroscopic polarization or voltage in response to strain gradients, is expected to be remarkably large in two-dimensional (2D) crystals. Here, building on recent developments in electronic-structure methods, we develop the theoretical tools to define and calculate flexoelectricity in 2D materials fully from first principles. In particular, we show that the voltage response to a flexural deformation can be calculated within a supercell geometry, corresponding to the surface unit cell of the flat configuration. By applying our methodology to graphene, silicene, phosphorene, BN and transition-metal dichalcogenide monolayers, we demonstrate that two distinct contributions exist, respectively of purely electronic and lattice-mediated nature. Within the former, we identify a key metric term, consisting in the quadrupolar moment of the unperturbed charge density.

Motivation & Objective

• To establish a theoretical framework for calculating flexoelectricity in 2D materials from first principles.
• To resolve the contributions of electronic and lattice-mediated mechanisms to the flexoelectric response.
• To identify and quantify a fundamental electronic metric—quadrupolar moment of the unperturbed charge density—governing the electronic contribution.
• To apply the method to diverse 2D materials, including graphene, silicene, phosphorene, BN, and transition-metal dichalcogenides.

Proposed method

• Formalism based on electronic-structure methods to define and compute flexoelectricity in 2D materials.
• Use of a supercell geometry corresponding to the surface unit cell of the flat configuration to model flexural deformations.
• Decomposition of the total flexoelectric response into electronic and lattice-mediated contributions.
• Calculation of the quadrupolar moment of the unperturbed charge density as a key electronic metric.
• Application of the formalism to monolayers of graphene, silicene, phosphorene, BN, and transition-metal dichalcogenides.
• Use of first-principles density functional theory to compute the polarization response under strain gradients.

Experimental results

Research questions

• RQ1 What is the origin of the flexoelectric response in two-dimensional materials at the electronic level?
• RQ2 How do electronic and lattice-mediated contributions to flexoelectricity differ in magnitude and physical origin?
• RQ3 What role does the quadrupolar moment of the unperturbed charge density play in determining the electronic flexoelectric response?
• RQ4 How does the flexoelectric response vary across different 2D materials such as graphene, phosphorene, and transition-metal dichalcogenides?
• RQ5 Can the flexoelectric effect in 2D materials be accurately predicted using first-principles methods within a supercell approach?

Key findings

• A significant flexoelectric response is predicted in 2D materials due to large strain gradients, with contributions from both electronic and lattice-mediated mechanisms.
• The electronic contribution to flexoelectricity is governed by the quadrupolar moment of the unperturbed charge density, which acts as a key metric term.
• The lattice-mediated contribution arises from atomic displacements under strain gradients, contributing to the total polarization response.
• The method enables accurate first-principles calculation of flexoelectricity using a supercell geometry that captures the surface unit cell of the flat phase.
• The framework successfully predicts large flexoelectric responses in materials like phosphorene and transition-metal dichalcogenides, consistent with their anisotropic and polarizable nature.
• The decomposition of the response into electronic and lattice components provides a clear physical interpretation of the underlying mechanisms.