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On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

by O. Cépas, P. Quémerais

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Submission summary

Authors (as registered SciPost users): Olivier Cépas
Submission information
Preprint Link:  (pdf)
Date submitted: 2022-04-04 08:12
Submitted by: Cépas, Olivier
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? A nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever, allows to address this issue beyond perturbation theory. For some special parameters of the model, at integrable points, it has exact solutions: the wave is cnoidal rather than simply harmonic but its envelope function remains continuous. As a consequence, the charge-density wave may slide over the lattice potential at no energy cost, in agreement with the Fr\"ohlich's argument. When the integrability is broken, however, the envelope function may be discontinuous, electrons tend to form some stronger distinct chemical bonds, i.e. local dimers or oligomers. The wave is intrinsically pinned by the lattice. We argue that an Aubry transition from the sliding phase to the insulating pinned phase occurs when the nonlinearities become strong.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2022-8-31 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2204.00278v1, delivered 2022-08-31, doi: 10.21468/SciPost.Report.5610


1- Pedagogical course on commensurate/incommensurate one-dimensional systems and on the corresponding work of Brazovskii et al.
2- Scientific global reliance.
3- New numerical results allowing the determination of a phase diagram, which is the real interest of the article.
4- Clarity of the text (except for some details to be modified).
5- The subject is acknowledging a revival so this article may have some visibility if it is published.


1- Unusual balance between recalled results already well-established and new ones.
2- Irregularity of style, mixing colloquial expressions and pompous ones, telegraphic style and long sentences.
3- Too many repetitions at all orders (inside paragraphs, inside sections and in the whole text).
4- A few points to be clarified, on the mathematical (or physical) plan. Some details must simply be discarded.
5- The length of the article may discourage some readers.


See file rap-CepasQuemerais.pdf

Requested changes

See corrCepasQuemerais.pdf, which link is at the end of rap-CepasQuemerais.pdf. SciPost recommends not to use annotations but, seeing the amount of problems I have found no other method (in particular, I have estimated the time needed to type these annotations to 40 hours). A contradictory injonction for referees is to be constructive, which I have been as much as possible.


  • validity: good
  • significance: low
  • originality: low
  • clarity: good
  • formatting: mediocre
  • grammar: mediocre

Author:  Olivier Cépas  on 2022-10-12  [id 2917]

(in reply to Report 2 on 2022-08-31)

See attached file.



Anonymous Report 1 on 2022-6-27 (Invited Report)


Pedagogical presentation of the state of the art about charge density wave pinning in various models for one-dimension lattice


Difficult to identify novelties among the quantity of results that are listed from the long history of charge density wave.


I propose to accept the publication on the condition presented below.

Requested changes

The authors must clarify their breakthrough in the field of charge density waves in their abstract and introduction.


  • validity: high
  • significance: high
  • originality: ok
  • clarity: top
  • formatting: reasonable
  • grammar: perfect

Author:  Olivier Cépas  on 2022-10-12  [id 2916]

(in reply to Report 1 on 2022-06-27)

We would like to thank the referee for his very positive report and careful reading.

Regarding the weakness pointed out, we have tried to improve the
manuscript by rewritting part of the abstract and introduction. We
emphasize that the paper is not a review in that it includes new
arguments about the old solution of Brazovskii et al. and a thorough study
of a new model which is the perturbed BDK model. This leads
to an Aubry transition, not discussed earlier in this context.

We are grateful to the referee for recognizing the pedagogical
character of the paper, which took us some time to develop and which we hope to be useful.

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