A note on transversal flexoelectricity in two-dimensional systems

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.