Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"

TL;DR

This paper critiques a recent comparison between the Kubo model and quantum field theory for graphene conductivity, emphasizing that the proposed modification violates gauge invariance and leads to nonphysical results.

Contribution

It clarifies that the original quantum field theoretical approach remains physically justified, countering claims of inconsistencies in the nonlocal case.

Findings

Original quantum field theory results are physically sound.

Modified conductivity expressions violate gauge invariance.

Claims of inconsistencies are unfounded when proper gauge invariance is maintained.

Abstract

Recently, Rodriguez-Lopez, Wang, and Antezza [Phys. Rev. B v.111, 115428 (2025)] compared the theoretical descriptions of electric conductivity of graphene given by the Kubo model and quantum field theory in terms of the polarization tensor. According to this article, in the spatially nonlocal case, the quantum field theoretical description contains ``hard inconsistencies". By modifying the equality, which relates the conductivity and polarization expressions, the predictions of quantum field theory were revised and brought in agreement with those following from the nonrelativistic Kubo model. Here, it is shown that this modification violates the requirement of gauge invariance and, thus, is unacceptable. By comparing both theoretical approaches, we demonstrate that all the results obtained within quantum field theory are physically well justified whereas an application of the modified expression for the conductivity of graphene leads to the consequences of nonphysical character.