Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of a massive phason in a charge-density-wave insulator

Nature Materials (2023)Cite this article

Subjects

Abstract

The lowest-lying fundamental excitation of an incommensurate charge-density-wave material is believed to be a massless phason—a collective modulation of the phase of the charge-density-wave order parameter. However, long-range Coulomb interactions should push the phason energy up to the plasma energy of the charge-density-wave condensate, resulting in a massive phason and fully gapped spectrum1. Using time-domain terahertz emission spectroscopy, we investigate this issue in (TaSe4)2I, a quasi-one-dimensional charge-density-wave insulator. On transient photoexcitation at low temperatures, we find the material strikingly emits coherent, narrowband terahertz radiation. The frequency, polarization and temperature dependences of the emitted radiation imply the existence of a phason that acquires mass by coupling to long-range Coulomb interactions. Our observations underscore the role of long-range interactions in determining the nature of collective excitations in materials with modulated charge or spin order.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Collective modes of an incommensurate CDW phase.
Fig. 2: THz emission from (TaSe4)2I.
Fig. 3: Temperature (T) and pump fluence (F) dependence of the 0.23 THz mode.
Fig. 4: Model of a radiating massive phason coupled to a non-radiating acoustic phonon.

Data availability

Source data are provided with this paper. Additional data are available from the corresponding author upon reasonable request.

References

  1. Lee, P. A. & Fukuyama, H. Dynamics of the charge-density wave. II. Long-range Coulomb effects in an array of chains. Phys. Rev. B 17, 542–548 (1978).

    Article  CAS  Google Scholar 

  2. Schwartz, M. D. Quantum Field Theory and the Standard Model (Cambridge Univ. Press, 2013).

  3. Fradkin, E. Field Theories of Condensed Matter Physics (Cambridge Univ. Press, 2013).

  4. Anderson, P. W. Plasmons, gauge invariance, and mass. Phys. Rev. 130, 439–442 (1963).

    Article  Google Scholar 

  5. Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).

    Article  Google Scholar 

  6. Lee, P. A., Rice, T. M. & Anderson, P. W. Fluctuation effects at a Peierls transition. Phys. Rev. Lett. 31, 462–465 (1973).

    Article  CAS  Google Scholar 

  7. Wong, K. Y. M. & Takada, S. Effects of quasiparticle screening on collective modes: incommensurate charge-density-wave systems. Phys. Rev. B 36, 5476–5492 (1987).

    Article  CAS  Google Scholar 

  8. Virosztek, A. & Maki, K. Collective modes in charge-density waves and long-range Coulomb interactions. Phys. Rev. B 48, 1368–1372 (1993).

    Article  CAS  Google Scholar 

  9. Wang, Z. et al. Charge density wave transport in (TaSe4)2I. Solid State Commun. 46, 325–328 (1983).

    Article  CAS  Google Scholar 

  10. Maki, M., Kaiser, M., Zettl, A. & Grüner, G. Charge density wave transport in a novel inorganic chain compound (TaSe4)2I. Solid State Commun. 46, 497–500 (1983).

    Article  CAS  Google Scholar 

  11. Fujishita, H., Sato, M. & Hoshino, S. Incommensurate superlattice reflections in quasi one dimensional conductors (MSe4)2I (M=Ta and Nb). Solid State Commun. 49, 313–316 (1984).

    Article  CAS  Google Scholar 

  12. Donovan, S., Kim, Y., Alavi, B., Degiori, L. & Gruner, G. The optical spectrum of charge density wave condensates. Solid State Commun. 75, 721–724 (1990).

    Article  CAS  Google Scholar 

  13. Degiorgi, L. & Grüner, G. Pinned and bound collective-mode state in charge-density-wave condensates. Phys. Rev. B 44, 7820–7827 (1991).

    Article  CAS  Google Scholar 

  14. Gooth, J. et al. Axionic charge-density wave in the Weyl semimetal (TaSe4)2I. Nature 575, 315–319 (2019).

    Article  CAS  Google Scholar 

  15. Sakai, K. (ed) Terahertz Optoelectronics (Springer, 2005).

  16. Rees, D. et al. Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi. Sci. Adv. 6, 29 (2020).

    Article  Google Scholar 

  17. Gao, Y. et al. Chiral terahertz wave emission from the Weyl semimetal TaAs. Nat. Commun. 11, 720 (2020).

    Article  CAS  Google Scholar 

  18. Luo, L. et al. A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe5. Nat. Mater. 20, 329–334 (2021).

    Article  CAS  Google Scholar 

  19. Dekorsy, T., Auer, H., Bakker, H. J., Roskos, H. G. & Kurz, H. THz electromagnetic emission by coherent infrared-active phonons. Phys. Rev. B 53, 4005–4014 (1996).

    Article  CAS  Google Scholar 

  20. Schaefer, H. et al. Dynamics of charge density wave order in the quasi one dimensional conductor (TaSe4)2I probed by femtosecond optical spectroscopy. Eur. Phys. J. Spec. Top. 222, 1005–1016 (2013).

    Article  Google Scholar 

  21. Lorenzo, J. E., Currat, R., Monceau, P., Hennion, B. & Levy, F. Neutron investigation of optic-phonon branches in the quasi-one-dimensional compound (TaSe4)2I. Phys. Rev. B 47, 10116–10121 (1993).

    Article  CAS  Google Scholar 

  22. Nguyen, Q. L. et al. Ultrafast X-ray scattering from collective modes of the charge density wave in (TaSe4)2I. Preprint at arXiv https://arxiv.org/abs/2210.17483 (2022).

  23. Shi, W. et al. A charge-density-wave topological semimetal. Nat. Phys. 17, 381–387 (2021).

    Article  CAS  Google Scholar 

  24. Sugai, S., Sato, M. & Kurihara, S. Interphonon interactions at the charge-density-wave phase transitions in (TaSe4)2I and (NbSe4)2I. Phys. Rev. B 32, 6809–6818 (1985).

    Article  CAS  Google Scholar 

  25. Lorenzo, J. E. et al. A neutron scattering study of the quasi-one-dimensional conductor. J. Phys.: Condens. Matter 10, 5039–5068 (1998).

    CAS  Google Scholar 

  26. Fujishita, H., Shapiro, S. M., Sato, M. & Hoshino, S. A neutron scattering study of the quasi-one-dimensional conductor (TaSe4)2I. J. Phys. C: Solid State Phys. 19, 3049–3057 (1986).

    Article  CAS  Google Scholar 

  27. Kim, T. W., Donovan, S., Grüner, G. & Philipp, A. Charge-density-wave dynamics in (Ta1–xNbxSe4)2I alloys. Phys. Rev. B 43, 6315–6325 (1991).

    Article  CAS  Google Scholar 

  28. Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).

    Article  CAS  Google Scholar 

  29. Yamamoto, A., Mishina, T., Masumoto, Y. & Nakayama, M. Coherent oscillation of zone-folded phonon modes in GaAs-AlAs superlattices. Phys. Rev. Lett. 73, 740–743 (1994).

    Article  CAS  Google Scholar 

  30. Park, H., Wang, X., Nie, S., Clinite, R. & Cao, J. Mechanism of coherent acoustic phonon generation under nonequilibrium conditions. Phys. Rev. B 72, 100301 (2005).

    Article  Google Scholar 

  31. Sinchenko, A. A., Ballou, R., Lorenzo, J. E., Grenet, T. & Monceau, P. Does (TaSe4)2I really harbor an axionic charge density wave? Appl. Phys. Lett. 120, 063102 (2022).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank P. Abbamonte, P. Armitage, D. Chaudhuri, T.-C. Chiang, L. Cooper, S. Kivelson, A. Kogar, P. Lee, V. Madhavan, D. Torchinsky and B. Wieder for insightful discussions. This work was supported by the Quantum Sensing and Quantum Materials, an Energy Frontier Research Center, funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0021238. F.M. acknowledges support from the EPiQS program of the Gordon and Betty Moore Foundation (grant GBMF11069). R.A.D. acknowledges support from the Bloch Postdoctoral Fellowship in Quantum Science and Engineering of the Stanford University Quantum Fundamentals, Architectures, and Machines initiative (Q-FARM), and from the Karel Urbanek and Marvin Chodorow Postdoctoral Fellowship of the Department of Applied Physics at Stanford University. X.-Q.S. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF8691. We acknowledge the use of the spectroscopic ellipsometry setup at the Institute for Basic Science (IBS) in Korea (grant no. IBS-R009-D1).

Author information

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Soyeun Kim, Yinchuan Lv, Xiao-Qi Sun, Nina Bielinski, Azel Murzabekova, Kejian Qu, Barry Bradlyn & Fahad Mahmood

  2. Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Soyeun Kim, Yinchuan Lv, Chengxi Zhao, Nina Bielinski, Azel Murzabekova, Kejian Qu, Daniel P. Shoemaker & Fahad Mahmood

  3. Materials Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Chengxi Zhao & Daniel P. Shoemaker

  4. Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Ryan A. Duncan, Quynh L. D. Nguyen & Mariano Trigo

  5. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Ryan A. Duncan, Quynh L. D. Nguyen & Mariano Trigo

Authors
  1. Soyeun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yinchuan Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiao-Qi Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengxi Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nina Bielinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Azel Murzabekova
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Kejian Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ryan A. Duncan
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Quynh L. D. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Mariano Trigo
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Daniel P. Shoemaker
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Barry Bradlyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Fahad Mahmood
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.K., Y.L., N.B., A.M. and F.M. performed the THz emission spectroscopy experiments and the corresponding data analysis. X.-Q.S. and B.B. developed the theoretical understanding and modelling. C.Z., K.Q. and D.P.S synthesized and characterized the samples. R.A.D., Q.L.D.N. and M.T. gave crucial insights into the understanding and analysis of the data. S.K., X.-Q.S., B.B. and F.M. wrote the manuscript with input from all the authors. F.M. conceived and supervised this project.

Corresponding author

Correspondence to Fahad Mahmood.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Manfred Fiebig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–9 and discussion.

Source data

Source Data Fig. 2

Source data.

Source Data Fig. 3

Source data.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kim, S., Lv, Y., Sun, XQ. et al. Observation of a massive phason in a charge-density-wave insulator. Nat. Mater. (2023). https://doi.org/10.1038/s41563-023-01504-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41563-023-01504-5

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing