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


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.

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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.


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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).

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Authors and Affiliations



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.

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Correspondence to Fahad Mahmood.

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

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Kim, S., Lv, Y., Sun, XQ. et al. Observation of a massive phason in a charge-density-wave insulator. Nat. Mater. (2023).

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