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Shapiro Steps at the Sliding of Charge Density Waves: Oscillations, Frequency Mixing, and Features in High Electric Fields

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Recent results on the synchronization of the sliding of charge density waves with a radio-frequency electric field, which is manifested in the appearance of Shapiro steps on current–voltage characteristics have been reviewed. Oscillations of the widths of Shapiro steps depending on the amplitude of the radio-frequency field have been studied experimentally and the periodicity of oscillations in the displacement of a charge density wave in the half-cycle of the radio-frequency field has been demonstrated. It has been shown that the width of Shapiro steps can be related to the position of the return point of the charge density wave with respect to the periodic pinning potential. It has been demonstrated how the proposed approach allows one to obtain the form of a current–voltage characteristic measured under the application of the radio-frequency field and to describe Shapiro steps at the frequency mixing on the charge density wave. An original experiment has been described to determine the amplitude of oscillations of the charge density wave in the periodic pinning potential using a radio-frequency lock-in detector. The comparison of the experimental result with the calculation has revealed the effect of the periodic pinning potential on the amplitude of oscillations in the synchronization regime when the action of the periodic pinning potential is not averaged. The synchronization of the charge density wave in high electric fields when its sliding can be characterized by a certain mobility has also been considered. An analogy of the found relations with similar relations for a Josephson junction and a si-ngle-channel quantum wire has been demonstrated.

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Notes

  1. In some cases, e.g., in the case of the commensurability of the CDW and the lattice or in the model from [3], the period of the pinning potential can differ from the period of the CDW. This does not limit the generality of the further consideration if λ is treated as the period of the pinning potential.

  2. The magnitude of a Shapiro step can be defined as the width, height, or area of a feature on the dV/dI(I) curve. One of the variant was presented in [9]. A particular definition is of no matter in this work.

  3. This effect was also noticeable in our measurements at frequencies of about 500 kHz: the charge determined from the data from the EG&G 5302 lock-in detector was slightly smaller than the value calculated from the CVC without the RF field, and a fitting factor of ~1 was used to compare the experiment and calculation.

  4. Instantaneous electric fields determined by both Edc and Erf are implied.

  5. Strictly speaking, oscillations do not become periodic because their amplitude decreases with increasing number.

REFERENCES

  1. H. Fröhlich, Proc. R. Soc. A 223, 296 (1954).

    ADS  Google Scholar 

  2. P. Monceau, Adv. Phys. 61, 325 (2012).

    Article  ADS  CAS  Google Scholar 

  3. S. E. Barnes and A. Zawadowski, Phys. Rev. Lett. 51, 1003 (1983).

    Article  ADS  Google Scholar 

  4. S. Brown and A. Zettl, in Charge Density Waves in Solids, Ed. by L. P. Gor’kov and G. Grüner (North-Holland, Elsevier, Amsterdam, 1989), Vol. 25, p. 223.

    Google Scholar 

  5. A. Zettl and G. Gruner, Solid State Commun. 46, 501 (1983).

    Article  ADS  CAS  Google Scholar 

  6. A. Zettl and G. Gruner, Phys. Rev. B 29, 755 (1984).

    Article  ADS  CAS  Google Scholar 

  7. R. E. Thorne, W. G. Lyons, J. W. Lyding, J. R. Tucker, and J. Bardeen, Phys. Rev. B 35, 6360 (1987).

    Article  ADS  CAS  Google Scholar 

  8. S. G. Zybtsev, V. Ya. Pokrovskii, V. F. Nasretdinova, et al., Phys. Rev. B 95, 035110 (2017).

  9. S. G. Zybtsev, S. A. Nikonov, V. Ya. Pokrovskii, V. V. Pavlovskiy, and D. Staresinic, Phys. Rev. B 101, 115425 (2020).

  10. S. G. Zybtsev and V. Ya. Pokrovskii, Phys. Rev. B 88, 125144 (2013).

  11. M. F. Hundley and A. Zettl, Phys. Rev. B 39, 3026 (1989).

    Article  ADS  CAS  Google Scholar 

  12. R. E. Thorne, J. Phys. IV (France) 131, 89 (2005).

    Article  CAS  Google Scholar 

  13. Y. Funami and K. Aoyama, Phys. Rev. B 108, L100508 (2023).

  14. S. Sridhar, D. Reagor, and G. Grüner, Phys. Rev. Lett. 55, 11 (1985).

    Article  Google Scholar 

  15. S. A. Nikonov, S. G. Zybtsev, A. A. Maizlakh, and V. Ya. Pokrovskii, Appl. Phys. Lett. 118, 213106 (2021).

  16. S. A. Nikonov, S. G. Zybtsev, and V. Ya. Pokrovskii, Appl. Phys. Lett. 118, 253108 (2021).

  17. V. V. Shirotov and Yu. Ya. Divin, Tech. Phys. Lett. 30, 522 (2004).

    Article  ADS  CAS  Google Scholar 

  18. M. V. Nikitin, S. G. Zybtsev, and V. Ya. Pokrovskii, in Proceedings of the 3rd International Conference on Physics of Condensed States PCS-2023, Chernogolovka, May 29–June 2, 2023, Ed. by B. B. Straumal, p. 218.

  19. J. C. Gill, Solid State Commun. 39, 1203 (1981).

    Article  ADS  CAS  Google Scholar 

  20. E. C. Geil and R. E. Thorne, Phys. Rev. Lett. 114, 016404 (2015).

  21. S. G. Zybtsev, V. Ya. Pokrovskii, O. M. Zhigalina, D. N. Khmelenin, D. Stareshinich, S. Shturm, and E. Chernyshova, J. Exp. Theor. Phys. 124, 665 (2017).

    Article  ADS  CAS  Google Scholar 

  22. S. G. Zybtsev, V. Ya. Pokrovskii, V. F. Nasretdinova, and S. V. Zaitsev-Zotov, J. Commun. Technol. Electron. 63, 1053 (2018).

    Article  Google Scholar 

  23. S. G. Zybtsev, V. Ya. Pokrovskii, S. A. Nikonov, A. A. Maizlakh, and S. V. Zaitsev-Zotov, JETP Lett. 117, 157 (2023).

    Article  ADS  CAS  Google Scholar 

  24. G. Grüner and A. Zettl, Phys. Rep. 119, 117 (1985).

    Article  ADS  Google Scholar 

  25. S. G. Zybtsev and V. Ya. Pokrovskii, Phys. Rev. B 84, 085139 (2011).

  26. P. Monceau, in Electronic Properties of Inorganic Quasi-One-Dimensional Conductors, Ed. by P. Monceau (Reidel, Dortrecht, 1985), p. 139, part 2.

  27. J. Richard, J. Chen, and S. N. Artemenko, Solid State Commun. 85, 605 (1993).

    Article  ADS  CAS  Google Scholar 

  28. K. K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, New York, 1986).

    Google Scholar 

  29. M. Papoular, Phys. Lett. A 76, 430 (1980).

    Article  ADS  Google Scholar 

  30. G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).

    Article  ADS  Google Scholar 

  31. S. G. Zybtsev, V. Ya. Pokrovskii, S. V. Zaitsev-Zotov, and V. F. Nasretdinova, Phys. B (Amsterdam, Neth.) 407, 1696 (2012).

  32. C. W. J. Beenakker and H. van Houten, Phys. Rev. Lett. 66, 3056 (1991).

    Article  ADS  CAS  PubMed  Google Scholar 

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Funding

The electrophysical studies of NbS3 and the analysis of the results were performed by S.G. Zybtsev, V.Ya. Pokrov-skii, A.V. Snezhko, and S.A. Nikonov and were supported by the Russian Science Foundation (project no. 22-12-00319). The growth of the NbS3 crystals and the comparison of the properties of the charge density wave and the Josephson junction were carried out by A.A. Maizlakh, S.V. Zaitsev-Zotov, M.V. Nikitin, and V.V. Pavlovskiy and was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment).

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Authors and Affiliations

  1. Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, 125009, Moscow, Russia

    S. G. Zybtsev, V. Ya. Pokrovskii, S. A. Nikonov, M. V. Nikitin, A. A. Maizlakh, A. V. Snezhko, V. V. Pavlovskiy & S. V. Zaitsev-Zotov

  2. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow region, Russia

    A. V. Snezhko

  3. Faculty of Physics, HSE University, 105066, Moscow, Russia

    V. V. Pavlovskiy & S. V. Zaitsev-Zotov

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  1. S. G. Zybtsev
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  2. V. Ya. Pokrovskii
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  3. S. A. Nikonov
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  4. M. V. Nikitin
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  5. A. A. Maizlakh
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  8. S. V. Zaitsev-Zotov
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Correspondence to V. Ya. Pokrovskii.

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Translated by R. Tyapaev

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Zybtsev, S.G., Pokrovskii, V.Y., Nikonov, S.A. et al. Shapiro Steps at the Sliding of Charge Density Waves: Oscillations, Frequency Mixing, and Features in High Electric Fields. Jetp Lett. 119, 123–135 (2024). https://doi.org/10.1134/S002136402360369X

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