A note on transversal flexoelectricity in two-dimensional systems

TL;DR

This paper clarifies the relationship between two definitions of flexoelectric coefficients in 2D systems, showing they are consistent but measure different physical quantities, resolving previous discrepancies.

Contribution

It demonstrates that the models in two prior papers are consistent and explains the differences in their definitions of flexoelectric coefficients.

Findings

The model in Ref. [Phys. Rev. Mat. 5, L030801 (2021)] is correct.

Discrepancies are due to different definitions of coefficients.

The coefficients measure different physical effects.

Abstract

In a recent letter [Phys. Rev. Lett. 127, 216801 (2021)], the authors introduced the effective flexoelectric coefficient $\mu^\textrm{2D}$ for quantifying the flexoelectric effect in 2D systems, and reported a disagreement with the flexoelectric coefficient $\mu_\text{T}$ introduced in Ref. [Phys. Rev. Mat. 5, L030801 (2021)], attributed to the neglect of the metric term $\varphi^\text{M}$ -- quadrupolar moment of the unperturbed charge density -- in the formulation of Ref. [Phys. Rev. Mat. 5, L030801 (2021)]. Here, we show that the model in Ref. [Phys. Rev. Mat. 5, L030801 (2021)] is correct and is in agreement with that in Ref. [Phys. Rev. Lett. 127, 216801 (2021)]. The discrepancies in the numerical values of the coefficients arise due to the difference in their definitions: $\mu_\textrm{T}$ measures changes in bending-induced out-of-plane polarization, whereas $\mu^\textrm{2D}$ measures changes in bending-induced voltage drop across the 2D system.