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.

  • Article
  • Published:

Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction

Abstract

We introduce ultrafast low-energy electron diffraction (ULEED) in backscattering for the study of structural dynamics at surfaces. Using a tip-based source of ultrashort electron pulses, we investigate the optically driven transition between charge density wave phases at the surface of 1T-TaS2. The large transfer width of the instrument allows us to employ spot-profile analysis, resolving the phase-ordering kinetics in the nascent incommensurate charge density wave phase. We observe a coarsening that follows a power-law scaling of the correlation length, driven by the annihilation of dislocation-type topological defects of the charge-ordered lattice. Our work opens up the study of a wide class of structural transitions and ordering phenomena at surfaces and in low-dimensional systems.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: ULEED set-up and high-resolution diffraction pattern from 1T-TaS2.
Figure 2: ULEED of the structural phase transition between CDW phases.
Figure 3: Phase-ordering kinetics of IC CDW governed by topological defects.
Figure 4: Numerical simulation of phase-ordering kinetics.

Similar content being viewed by others

References

  1. Lüth, H. Surfaces and Interfaces of Solid Materials (Springer Science & Business Media, 2013).

    MATH  Google Scholar 

  2. Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973).

    ADS  Google Scholar 

  3. Wolf, M. Femtosecond dynamics of electronic excitations at metal surfaces. Surf. Sci. 377, 343–349 (1997).

    ADS  Google Scholar 

  4. Höfer, U. et al. Time-resolved coherent photoelectron spectroscopy of quantized electronic states on metal surfaces. Science 277, 1480–1482 (1997).

    Google Scholar 

  5. Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–310 (2016).

    Google Scholar 

  6. Bovensiepen, U., Petek, H. & Wolf, M. Dynamics at Solid State Surfaces and Interfaces (John Wiley & Sons, 2010).

    Google Scholar 

  7. Rohwer, T. et al. Collapse of long-range charge order tracked by time-resolved photoemission at high momenta. Nature 471, 490–493 (2011).

    ADS  Google Scholar 

  8. Eich, S. et al. Time- and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti:Sapphire lasers. J. Electron Spectrosc. Relat. Phenom. 195, 231–236 (2014).

    Google Scholar 

  9. Sohrt, C., Stange, A., Bauer, M. & Rossnagel, K. How fast can a Peierls–Mott insulator be melted? Faraday Discuss. 171, 243–257 (2014).

    ADS  Google Scholar 

  10. Petek, H. & Ogawa, S. Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals. Prog. Surf. Sci. 56, 239–310 (1997).

    ADS  Google Scholar 

  11. La- O-Vorakiat, C. et al. Ultrafast demagnetization measurements using extreme ultraviolet light: comparison of electronic and magnetic contributions. Phys. Rev. X 2, 011005 (2012).

    Google Scholar 

  12. Elsayed-Ali, H. E. & Herman, J. W. Picosecond time-resolved surface-lattice temperature probe. Appl. Phys. Lett. 57, 1508–1510 (1990).

    ADS  Google Scholar 

  13. Aeschlimann, M. et al. A picosecond electron gun for surface analysis. Rev. Sci. Instrum. 66, 1000–1009 (1995).

    ADS  Google Scholar 

  14. Schäfer, S., Liang, W. & Zewail, A. H. Structural dynamics of surfaces by ultrafast electron crystallography: experimental and multiple scattering theory. J. Chem. Phys. 135, 214201 (2011).

    ADS  Google Scholar 

  15. Hanisch-Blicharski, A. et al. Ultra-fast electron diffraction at surfaces: from nanoscale heat transport to driven phase transitions. Ultramicroscopy 127, 2–8 (2013).

    Google Scholar 

  16. Frigge, T. et al. Optically excited structural transition in atomic wires on surfaces at the quantum limit. Nature 544, 207–211 (2017).

    ADS  Google Scholar 

  17. Becker, R. S., Higashi, G. S. & Golovchenko, J. A. Low-energy electron diffraction during pulsed laser annealing: a time-resolved surface structural study. Phys. Rev. Lett. 52, 307–310 (1984).

    ADS  Google Scholar 

  18. Karrer, R., Neff, H. J., Hengsberger, M., Greber, T. & Osterwalder, J. Design of a miniature picosecond low-energy electron gun for time-resolved scattering experiments. Rev. Sci. Instrum. 72, 4404–4407 (2001).

    ADS  Google Scholar 

  19. Cirelli, C. et al. Direct observation of space charge dynamics by picosecond low-energy electron scattering. Europhys. Lett. 85, 17010 (2009).

    ADS  Google Scholar 

  20. Gulde, M. et al. Ultrafast low-energy electron diffraction in transmission resolves polymer/graphene superstructure dynamics. Science 345, 200–204 (2014).

    ADS  Google Scholar 

  21. Müller, M., Paarmann, A. & Ernstorfer, R. Femtosecond electrons probing currents and atomic structure in nanomaterials. Nat. Commun. 5, 5292 (2014).

    ADS  Google Scholar 

  22. Siwick, B. J., Dwyer, J. R., Jordan, R. E. & Miller, R. J. D. An atomic-level view of melting using femtosecond electron diffraction. Science 302, 1382–1385 (2003).

    ADS  Google Scholar 

  23. Baum, P., Yang, D.-S. & Zewail, A. H. 4D visualization of transitional structures in phase transformations by electron diffraction. Science 318, 788–792 (2007).

    ADS  Google Scholar 

  24. Carbone, F., Kwon, O.-H. & Zewail, A. H. Dynamics of chemical bonding mapped by energy-resolved 4D electron microscopy. Science 325, 181–184 (2009).

    ADS  Google Scholar 

  25. Ernstorfer, R. et al. The formation of warm dense matter: experimental evidence for electronic bond hardening in gold. Science 323, 1033–1037 (2009).

    ADS  Google Scholar 

  26. Eichberger, M. et al. Snapshots of cooperative atomic motions in the optical suppression of charge density waves. Nature 468, 799–802 (2010).

    ADS  Google Scholar 

  27. Mourik, M. W., van Engelen, W. J., Vredenbregt, E. J. D. & Luiten, O. J. Ultrafast electron diffraction using an ultracold source. Struct. Dyn. 1, 034302 (2014).

    Google Scholar 

  28. Haupt, K. et al. Ultrafast metamorphosis of a complex charge-density wave. Phys. Rev. Lett. 116, 016402 (2016).

    ADS  Google Scholar 

  29. King, W. E. et al. Ultrafast electron microscopy in materials science, biology, and chemistry. J. Appl. Phys. 97, 111101 (2005).

    ADS  Google Scholar 

  30. Zewail, A. H. Four-dimensional electron microscopy. Science 328, 187–193 (2010).

    ADS  Google Scholar 

  31. Piazza, L. et al. Design and implementation of a fs-resolved transmission electron microscope based on thermionic gun technology. Chem. Phys. 423, 79–84 (2013).

    Google Scholar 

  32. Feist, A. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200–203 (2015).

    ADS  Google Scholar 

  33. Plemmons, D. A., Suri, P. K. & Flannigan, D. J. Probing structural and electronic dynamics with ultrafast electron microscopy. Chem. Mater. 27, 3178–3192 (2015).

    Google Scholar 

  34. van Oudheusden, T. et al. Compression of subrelativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction. Phys. Rev. Lett. 105, 264801 (2010).

    ADS  Google Scholar 

  35. Chatelain, R. P., Morrison, V. R., Godbout, C. & Siwick, B. J. Ultrafast electron diffraction with radio-frequency compressed electron pulses. Appl. Phys. Lett. 101, 081901 (2012).

    ADS  Google Scholar 

  36. Maxson, J. et al. Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance. Phys. Rev. Lett. 118, 154802 (2017).

    ADS  Google Scholar 

  37. Gerbig, C., Senftleben, A., Morgenstern, S., Sarpe, C. & Baumert, T. Spatio-temporal resolution studies on a highly compact ultrafast electron diffractometer. New J. Phys. 17, 043050 (2015).

    ADS  Google Scholar 

  38. Storeck, G., Vogelgesang, S., Sivis, M., Schäfer, S. & Ropers, C. Nanotip-based photoelectron microgun for ultrafast LEED. Struct. Dyn. 4, 044024 (2017).

    Google Scholar 

  39. Raman, R. K., Tao, Z., Han, T.-R. & Ruan, C.-Y. Ultrafast imaging of photoelectron packets generated from graphite surface. Appl. Phys. Lett. 95, 181108 (2009).

    ADS  Google Scholar 

  40. Park, H. & Zuo, J. M. Direct measurement of transient electric fields induced by ultrafast pulsed laser irradiation of silicon. Appl. Phys. Lett. 94, 251103 (2009).

    ADS  Google Scholar 

  41. Mancini, G. F. et al. Design and implementation of a flexible beamline for fs electron diffraction experiments. Nucl. Instrum. Methods Phys. Res. Sect. 691, 113–122 (2012).

    ADS  Google Scholar 

  42. Hommelhoff, P., Sortais, Y., Aghajani-Talesh, A. & Kasevich, M. A. Field emission tip as a nanometer source of free electron femtosecond pulses. Phys. Rev. Lett. 96, 077401 (2006).

    ADS  Google Scholar 

  43. Ropers, C., Solli, D. R., Schulz, C. P., Lienau, C. & Elsaesser, T. Localized multiphoton emission of femtosecond electron pulses from metal nanotips. Phys. Rev. Lett. 98, 043907 (2007).

    ADS  Google Scholar 

  44. Ehberger, D. et al. Highly coherent electron beam from a laser-triggered tungsten needle tip. Phys. Rev. Lett. 114, 227601 (2015).

    ADS  Google Scholar 

  45. Wilson, J. A., Salvo, F. J. D. & Mahajan, S. Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides. Adv. Phys. 24, 117–201 (1975).

    ADS  Google Scholar 

  46. Rossnagel, K. On the origin of charge-density waves in select layered transition-metal dichalcogenides. J. Phys. Condens. Matter 23, 213001 (2011).

    ADS  Google Scholar 

  47. Stojchevska, L. et al. Ultrafast switching to a stable hidden quantum state in an electronic crystal. Science 344, 177–180 (2014).

    ADS  Google Scholar 

  48. Fazekas, P. & Tosatti, E. Electrical, structural and magnetic properties of pure and doped 1T-TaS2 . Philos. Mag. B 39, 229–244 (1979).

    ADS  Google Scholar 

  49. Ritschel, T. et al. Orbital textures and charge density waves in transition metal dichalcogenides. Nat. Phys. 11, 328–331 (2015).

    Google Scholar 

  50. Spijkerman, A., de Boer, J. L., Meetsma, A., Wiegers, G. A. & van Smaalen, S. X-ray crystal-structure refinement of the nearly commensurate phase of 1T-TaS2 in (3 + 2)-dimensional superspace. Phys. Rev. B 56, 13757–13767 (1997).

    ADS  Google Scholar 

  51. Nakanishi, K. & Shiba, H. Domain-like incommensurate charge-density-wave states and the first-order incommensurate–commensurate transitions in layered tantalum dichalcogenides. I. 1T-Polytype. J. Phys. Soc. Jpn 43, 1839–1847 (1977).

    ADS  Google Scholar 

  52. Han, T.-R. T. et al. Exploration of metastability and hidden phases in correlated electron crystals visualized by femtosecond optical doping and electron crystallography. Sci. Adv. 1, e1400173 (2015).

    ADS  Google Scholar 

  53. Nakanishi, K., Takatera, H., Yamada, Y. & Shiba, H. The nearly commensurate phase and effect of harmonics on the successive phase transition in 1T-TaS2 . J. Phys. Soc. Jpn 43, 1509–1517 (1977).

    ADS  Google Scholar 

  54. Hellmann, S. et al. Time-resolved X-ray photoelectron spectroscopy at FLASH. New J. Phys. 14, 013062 (2012).

    ADS  Google Scholar 

  55. Bray, A. J. Theory of phase-ordering kinetics. Adv. Phys. 51, 481–587 (2002).

    ADS  MathSciNet  Google Scholar 

  56. Toussaint, D. & Wilczek, F. Particle–antiparticle annihilation in diffusive motion. J. Chem. Phys. 78, 2642–2647 (1983).

    ADS  Google Scholar 

  57. Toyoki, H. Pair annihilation of pointlike topological defects in the ordering process of quenched systems. Phys. Rev. A 42, 911–917 (1990).

    ADS  Google Scholar 

  58. Laulhé, C. et al. Ultrafast formation of a charge density wave state in 1T-TaS2: observation at nanometer scales using time-resolved X-ray diffraction. Phys. Rev. Lett. 118, 247401 (2017).

    ADS  Google Scholar 

  59. McMillan, W. L. Landau theory of charge-density waves in transition-metal dichalcogenides. Phys. Rev. B 12, 1187–1196 (1975).

    ADS  Google Scholar 

  60. McMillan, W. L. Theory of discommensurations and the commensurate–incommensurate charge-density-wave phase transition. Phys. Rev. B 14, 1496–1502 (1976).

    ADS  Google Scholar 

  61. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 2000).

    Google Scholar 

  62. Overhauser, A. W. Observability of charge-density waves by neutron diffraction. Phys. Rev. B 3, 3173–3182 (1971).

    ADS  Google Scholar 

  63. Lee, W. S. et al. Phase fluctuations and the absence of topological defects in a photo-excited charge-ordered nickelate. Nat. Commun. 3, 838 (2012).

    ADS  Google Scholar 

  64. McMillan, W. L. Time-dependent Laudau theory of charge-density waves in transition-metal dichalcogenides. Phys. Rev. B 12, 1197–1199 (1975).

    ADS  Google Scholar 

Download references

Acknowledgements

This work was funded by the European Research Council (ERC Starting Grant ‘ULEED’, ID: 639119) and the Deutsche Forschungsgemeinschaft (SFB-1073, project A05). We gratefully acknowledge insightful discussions with S. V. Yalunin and A. Zippelius. Furthermore we thank K. Hanff for help with sample preparation.

Author information

Authors and Affiliations

Authors

Contributions

The project was planned by S.V., G.S., S.Schramm, S.Schäfer and C.R. Experiments and data analysis were conducted by S.V. and G.S., with contributions from J.G.H., T.D. and M.S. The investigated samples were provided by K.R. Numerical simulations and writing of the paper were carried out by S.V. and C.R. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to C. Ropers.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Movie

Supplementary Movie 1 (MP4 2880 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vogelgesang, S., Storeck, G., Horstmann, J. et al. Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction. Nat. Phys. 14, 184–190 (2018). https://doi.org/10.1038/nphys4309

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys4309

This article is cited by

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