对“石墨烯电导率：Kubo模型与非局部量子场论模型”的评论的回复 (ArXiv:2506.10792v2)
Reply to "Comment on "Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model"" (ArXiv:2506.10792v2)
AI总结：
本文针对Bordag等人对石墨烯电导率理论描述的评论进行回复，澄清Kubo公式与量子场论结果的差异，并纠正评论中关于电导率推导和 gauge 不变性的误解。
摘要：
在Bordag等人[Phys. Rev. B 113, 207401 (2026)和ArXiv:2506.10792]的评论中，对[Phys. Rev. B 111, 115428 (2025)]中Kubo公式和量子场论通过极化张量得到的石墨烯电导率理论描述的有效性提出了质疑。在本回复中，我们表明这些担忧源于对Phys. Rev. B 111, 115428 (2025)的误解，其中的结果要么被不准确地表示，要么被应用于模型的有效性范围之外。我们讨论了关于从Kubo公式推导电导率Luttinger公式的问题，并澄清为什么Phys. Rev. B 111, 115428 (2025)的结果不能任意扩展以做出关于gauge不变性的声明。我们进一步证明我们的发现与评论中引用的已建立且广泛接受的文献完全一致。我们确认Phys. Rev. B 111, 115428 (2025)中讨论的电导率模型正确预测了在没有外部电场时电电流为零，这符合物理要求，与评论作者所倡导的模型相反。我们还表明电介电常数在$ω$中不表现出双极，这与评论中的说法相矛盾。最后，我们强调在研究材料的输运性质，包括石墨烯时，包括损耗是标准且已建立的方法，并借此机会纠正Phys. Rev. B 111, 115428 (2025)中的几个小的拼写错误。我们证明并维护Phys. Rev. B 111, 115428 (2025)中得出的所有结果都是完全有效和正确的。
英文摘要：
In the Comment by Bordag et al. [Phys. Rev. B 113, 207401 (2026) and ArXiv:2506.10792], concerns are raised regarding the validity of the results presented in [Phys. Rev. B 111, 115428 (2025)], where the theoretical descriptions of the electric conductivity of graphene obtained from the Kubo formula and from quantum field theory via the polarization tensor are compared. In this Reply, we show that these concerns arise from misinterpretations of Phys. Rev. B 111, 115428 (2025), in which the results are either inaccurately represented or applied outside the domain of validity of the model. We address the comments concerning the derivation of the Luttinger formula for the electric conductivity from the Kubo formula and clarify why the results of Phys. Rev. B 111, 115428 (2025) cannot be arbitrarily extended to make claims on the gauge invariance. We further demonstrate that our findings are fully consistent with the established and widely accepted literature cited in the Comment. We confirm that the model for electric conductivity discussed in Phys. Rev. B 111, 115428 (2025) correctly predicts a vanishing electric current in the absence of an external electric field, as physically required, and in contrast with the model advocated by the Authors of the Comment. We also show that the electric permittivity does not exhibit a double pole in $ω$, contrary to the claim made in the Comment. Finally, we emphasize that the inclusion of losses is a standard and well-established approach in the study of transport properties of materials, including graphene, and we take the opportunity to correct a few minor typographical errors in Phys. Rev. B 111, 115428 (2025). We show and maintain that all results derived in Phys. Rev. B 111, 115428 (2025) are fully valid and correct.
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