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arxiv: 2506.10792 · v2 · pith:36QNFLLLnew · submitted 2025-06-12 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci· quant-ph

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

M.Bordag , N.Khusnutdinov , G.L.Klimchitskaya , V.M.Mostepanenko This is my paper

Pith reviewed 2026-05-22 00:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sciquant-ph
keywords graphene conductivityKubo modelquantum field theorypolarization tensorgauge invariancenonlocal effects
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0 comments X

The pith

A modification reconciling Kubo and quantum field theory conductivity in graphene violates gauge invariance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper critiques a recent comparison of graphene electric conductivity models that found hard inconsistencies in the quantum field theory approach for spatially nonlocal cases. To resolve apparent disagreements with the Kubo model, the authors of the commented paper altered the relation between conductivity and the polarization tensor. This comment demonstrates that the alteration breaks exact gauge invariance, rendering it physically unacceptable. The original quantum field theory results are shown to respect all required symmetries and to avoid nonphysical outcomes that appear when the modified expressions are used instead.

Core claim

The modification of the equality relating the conductivity and polarization expressions violates the requirement of gauge invariance and is therefore unacceptable. All 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.

What carries the argument

Gauge invariance, the symmetry that any valid conductivity expression for graphene must preserve exactly.

If this is right

  • Quantum field theory descriptions of graphene conductivity remain valid in both local and nonlocal regimes without needing adjustment.
  • The modified conductivity expressions yield nonphysical predictions that conflict with fundamental symmetries.
  • Direct comparisons between Kubo and quantum field theory models must retain the original relation between conductivity and polarization tensor.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Gauge invariance checks could serve as a quick test for proposed adjustments to conductivity formulas in other two-dimensional materials.
  • Reconciling the two models may require revisiting the definition of conductivity itself rather than altering the polarization relation.

Load-bearing premise

Any valid expression for conductivity in graphene must preserve gauge invariance exactly.

What would settle it

A calculation or measurement showing that the modified conductivity formula produces observable nonphysical effects, such as violation of current conservation or unphysical response to electromagnetic fields, that the unmodified quantum field theory formula does not.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. This manuscript is a comment on Rodriguez-Lopez, Wang, and Antezza (Phys. Rev. B 111, 115428, 2025). It argues that the modification they proposed to the relation equating conductivity and polarization expressions in the spatially nonlocal regime violates the gauge-invariance requirement of quantum field theory. The authors compare the Kubo and QFT approaches and conclude that the original QFT results remain physically justified while the modified expressions produce nonphysical consequences.

Significance. If the central argument holds, the comment is significant for the mesoscopic physics of graphene because it upholds a standard symmetry principle that must be preserved in electromagnetic response functions. The work merits explicit credit for invoking gauge invariance without introducing free parameters, ad-hoc adjustments, or circular self-references, thereby providing a clean, falsifiable test of model validity.

minor comments (1)
  1. Abstract: the phrase 'consequences of nonphysical character' is vague; a single concrete example (e.g., a sign change in a response function or violation of a sum rule) would improve immediate readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript, the positive assessment of its significance, and the recommendation to accept. The referee's summary correctly identifies the central claim that the proposed modification to the conductivity-polarization relation violates gauge invariance.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim rests on the external, standard requirement of gauge invariance in electromagnetic response functions, which is invoked to reject the proposed modification to the conductivity-polarization relation. This principle is not constructed from the paper's own inputs, fitted parameters, or self-citations; it is a pre-existing symmetry constraint from QED. The comparison between the Kubo model and QFT polarization tensor is presented as revealing nonphysical consequences in the modified case, without any step that reduces by definition or statistical forcing to the paper's own assumptions. No self-definitional loops, ansatz smuggling, or renaming of known results occur. The derivation chain is therefore independent and self-contained against external physical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim depends on the standard domain assumption of gauge invariance in electromagnetic field theory applied to condensed-matter systems; no free parameters or new entities are introduced.

axioms (1)
  • domain assumption Gauge invariance must be preserved in any physically acceptable expression relating conductivity to the polarization tensor.
    Invoked directly to reject the modification proposed in the commented paper.

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discussion (0)

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Reference graph

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