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arxiv: 2603.19982 · v2 · submitted 2026-03-20 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Reply to "Comment on "Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model"" (ArXiv:2506.10792v2)

Pablo Rodriguez-Lopez , Jian-Sheng Wang , Mauro Antezza This is my paper

Pith reviewed 2026-05-15 08:13 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords graphene conductivityKubo formulapolarization tensorquantum field theoryLuttinger formulaelectric permittivitygauge invariance
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0 comments X

The pith

The Kubo and quantum field theory models for graphene conductivity are fully valid and consistent.

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

This reply defends a 2025 comparison of electric conductivity in graphene obtained from the Kubo formula against results from a nonlocal quantum field theory model using the polarization tensor. It argues that the concerns in the comment arise from misinterpretations of the original derivations or from extending the model beyond its stated domain of validity. The reply clarifies the derivation of the Luttinger formula from the Kubo expression, shows that the conductivity model yields zero current without an external field, and confirms that the permittivity lacks a double pole in frequency. The work maintains consistency with standard literature on transport in graphene and treats the inclusion of losses as a conventional step.

Core claim

All results derived in Phys. Rev. B 111, 115428 (2025) remain fully valid and correct; the comment's concerns stem from inaccurate representations of the model or applications outside its domain, including on gauge invariance, while the conductivity correctly vanishes without external field and the permittivity shows no double pole.

What carries the argument

The direct comparison of conductivity expressions from the Kubo formula (including its reduction to the Luttinger formula) and from the polarization tensor in quantum field theory, with explicit checks for physical requirements such as zero current in the absence of driving field.

If this is right

  • The conductivity model satisfies the physical requirement of vanishing current without an external electric field.
  • The electric permittivity derived from the model does not contain a double pole in frequency.
  • The Kubo and quantum field theory results align with widely accepted literature on graphene transport.
  • Inclusion of losses remains a standard and appropriate step when modeling transport properties.

Where Pith is reading between the lines

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

  • The two models can be treated as interchangeable for conductivity calculations inside their common regime of validity.
  • Future comparisons of semiclassical and field-theoretic approaches in two-dimensional materials will need explicit statements of domain limits to avoid gauge-invariance disputes.
  • The same pattern of defending model consistency may recur when other transport quantities are computed by multiple methods in graphene or related systems.

Load-bearing premise

The concerns in the comment arise only from misinterpretations of the original paper rather than from genuine flaws in its derivations.

What would settle it

A calculation using the original model that produces nonzero current without external field or that shows a double pole in the electric permittivity at frequency omega.

read the original abstract

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 $\omega$, 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.

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 / 2 minor

Summary. This manuscript is a Reply to the Comment by Bordag et al. (Phys. Rev. B 113, 207401 (2026)) on the original work Phys. Rev. B 111, 115428 (2025). It maintains that all results of the original paper remain valid and correct, arguing that the Comment's concerns arise from misinterpretations of the Kubo-to-Luttinger derivation, the restricted domain of validity of the model (preventing arbitrary extension to gauge-invariance claims), and the treatment of losses. The Reply demonstrates consistency with cited literature, verifies that the electric current vanishes when the external field is zero, shows that the permittivity lacks a double pole in ω, and corrects minor typographical errors from the original paper.

Significance. If the clarifications and verifications hold, the Reply strengthens the comparison between the Kubo formula and nonlocal quantum field theory approaches to graphene conductivity, helping to resolve potential confusion in the literature on transport properties of 2D materials. It affirms the physical consistency of the model (J=0 for E_ext=0) and its alignment with established results, which is valuable for ongoing work in mesoscopic physics.

minor comments (2)
  1. The Reply references specific equations and claims from the Comment (e.g., double pole in permittivity) but would benefit from explicitly quoting or numbering the disputed expressions from ArXiv:2506.10792v2 for easier cross-checking by readers.
  2. The correction of typographical errors from Phys. Rev. B 111, 115428 (2025) is noted in the abstract; listing the exact corrections (e.g., equation numbers or page references) in the main text would improve transparency.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our Reply and for the positive recommendation to accept the manuscript. The referee's summary accurately reflects the scope and conclusions of our work.

Circularity Check

0 steps flagged

No significant circularity; reply relies on external literature and model-domain clarifications

full rationale

The reply defends the original Phys. Rev. B 111, 115428 (2025) results by clarifying the Kubo-to-Luttinger derivation, restricting the model's domain to prevent gauge-invariance extensions, verifying J=0 when E_ext=0, confirming no double pole in permittivity, and aligning with established cited literature. These steps reference independent benchmarks and physical requirements rather than reducing claims to self-fitted parameters or unverified self-citations. The central assertion of validity rests on external consistency and explicit checks, not on redefinition or renaming within the reply itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no explicit free parameters, axioms, or invented entities can be extracted. The text invokes standard inclusion of losses as a domain assumption but provides no new ones.

pith-pipeline@v0.9.0 · 5688 in / 1005 out tokens · 47864 ms · 2026-05-15T08:13:24.409226+00:00 · methodology

discussion (0)

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Reference graph

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