Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model

作者：Pablo Rodriguez-López, Jian‐Sheng Wang, Mauro Antezza · 发表于：Physical review. B./Physical review. B · 年份：2025 · DOI：10.1103/physrevb.111.115428 · 被引用次数：16 · 研究领域：Graphene research and applications、Quantum and electron transport phenomena、Surface and Thin Film Phenomena

We compare three models of graphene electric conductivity: a nonlocal Kubo model, a local model derived by Falkovsky, and, finally, a nonlocal quantum field theory (QFT) polarization-based model. These models are supposed to provide consistent results since they are derived from the same Hamiltonian. While we confirm that the local model is a proper $\mathbit{q}\ensuremath{\rightarrow}\mathbit{0}$ limit of both the nonlocal Kubo and the nonlocal QFT model (once losses are added to this last model), we find hard inconsistencies in the nonlocal QFT model as derived and currently used in literature. In particular, in the genuine nonlocal region ($\mathbit{q}\ensuremath{\ne}\mathbit{0}$), the available QFT model shows an intrinsic nonphysical plasmalike behavior for the interband transversal electric conductivity at low frequencies (even after introducing the unavoidable losses). The Kubo model, instead, shows the expected behavior, i.e., an almost constant electric conductivity as a function of frequency $\ensuremath{\omega}$ with a gap for frequencies $\ensuremath{\hbar}\ensuremath{\omega}<\sqrt{{(\ensuremath{\hbar}{v}_{F}q)}^{2}+4{m}^{2}}$. We show that the Kubo and QFT models can be expressed using an identical polarization operator ${\mathrm{\ensuremath{\Pi}}}_{\ensuremath{\mu}\ensuremath{\nu}}(\ensuremath{\omega},\mathbit{q})$, but they employ different expressions for the electric conductivity ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\nu}}(\ensuremath{\omega}...