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


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.

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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.


  1. 1

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

  2. 2

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

  3. 3

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

  4. 4

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

  5. 5

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

  6. 6

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

  7. 7

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

  8. 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).

  9. 9

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

  10. 10

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

  11. 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).

  12. 12

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

  13. 13

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

  14. 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).

  15. 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).

  16. 16

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

  17. 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).

  18. 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).

  19. 19

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

  20. 20

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

  21. 21

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

  22. 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).

  23. 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).

  24. 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).

  25. 25

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

  26. 26

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

  27. 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).

  28. 28

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

  29. 29

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

  30. 30

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

  31. 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).

  32. 32

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

  33. 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).

  34. 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).

  35. 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).

  36. 36

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

  37. 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).

  38. 38

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

  39. 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).

  40. 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).

  41. 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).

  42. 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).

  43. 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).

  44. 44

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

  45. 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).

  46. 46

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

  47. 47

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

  48. 48

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

  49. 49

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

  50. 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).

  51. 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).

  52. 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).

  53. 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).

  54. 54

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

  55. 55

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

  56. 56

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

  57. 57

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

  58. 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).

  59. 59

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

  60. 60

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

  61. 61

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

  62. 62

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

  63. 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).

  64. 64

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

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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

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.

Correspondence to C. Ropers.

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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) doi:10.1038/nphys4309

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