Coherent control of a surface structural phase transition


Active optical control over matter is desirable in many scientific disciplines, with prominent examples in all-optical magnetic switching1,2, light-induced metastable or exotic phases of solids3,4,5,6,7,8 and the coherent control of chemical reactions9,10. Typically, these approaches dynamically steer a system towards states or reaction products far from equilibrium. In solids, metal-to-insulator transitions are an important target for optical manipulation, offering ultrafast changes of the electronic4 and lattice11,12,13,14,15,16 properties. The impact of coherences on the efficiencies and thresholds of such transitions, however, remains a largely open subject. Here, we demonstrate coherent control over a metal–insulator structural phase transition in a quasi-one-dimensional solid-state surface system. A femtosecond double-pulse excitation scheme17,18,19,20 is used to switch the system from the insulating to a metastable metallic state, and the corresponding structural changes are monitored by ultrafast low-energy electron diffraction21,22. To govern the transition, we harness vibrational coherence in key structural modes connecting both phases, and observe delay-dependent oscillations in the double-pulse switching efficiency. Mode-selective coherent control of solids and surfaces could open new routes to switching chemical and physical functionalities, enabled by metastable and non-equilibrium states.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Ultrafast LEED set-up and structural phase transition in atomic indium wires on silicon.
Fig. 2: Coherent control of the (8 × 2) to (4 × 1) phase transition efficiency.
Fig. 3: Control mechanisms and comparison between ULEED and optical pump–probe spectroscopy.
Fig. 4: Two-dimensional picture of the phase transition dynamics.

Data availability

The data that support the findings of this study are available on request from the corresponding author.


  1. 1.

    Kimel, A. V. et al. Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses. Nature 435, 655–657 (2005).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  2. 2.

    Schlauderer, S. et al. Temporal and spectral fingerprints of ultrafast all-coherent spin switching. Nature 569, 383–387 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  3. 3.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  4. 4.

    Rini, M. et al. Control of the electronic phase of a manganite by mode-selective vibrational excitation. Nature 449, 72–74 (2007).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Mitrano, M. et al. Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461–464 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. 6.

    Nova, T. F., Disa, A. S., Fechner, M. & Cavalleri, A. Metastable ferroelectricity in optically strained SrTiO3. Science 364, 1075–1079 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. 7.

    Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet–Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  9. 9.

    Zewail, A. H. Femtochemistry: atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel lecture). Angew. Chem. Int. Ed. 39, 2586–2631 (2000).

    CAS  Google Scholar 

  10. 10.

    Nuernberger, P., Vogt, G., Brixner, T. & Gerber, G. Femtosecond quantum control of molecular dynamics in the condensed phase. Phys. Chem. Chem. Phys. 9, 2470–2497 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Morrison, V. R. et al. A photoinduced metal-like phase of monoclinic VO2 revealed by ultrafast electron diffraction. Science 346, 445–448 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  12. 12.

    Liu, M. et al. Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial. Nature 487, 345–348 (2012).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  13. 13.

    Wall, S. et al. Atomistic picture of charge density wave formation at surfaces. Phys. Rev. Lett. 109, 186101 (2012).

    ADS  PubMed  PubMed Central  Google Scholar 

  14. 14.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  15. 15.

    Nicholson, C. W. et al. Beyond the molecular movie: dynamics of bands and bonds during a photoinduced phase transition. Science 362, 821–825 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Chávez-Cervantes, M., Krause, R., Aeschlimann, S. & Gierz, I. Band structure dynamics in indium wires. Phys. Rev. B 97, 201401 (2018).

    ADS  Google Scholar 

  17. 17.

    Hase, M., Fons, P., Mitrofanov, K., Kolobov, A. V. & Tominaga, J. Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons. Nat. Commun. 6, 8367 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  18. 18.

    Weiner, A. M., Leaird, D. E., Wiederrecht, G. P. & Nelson, K. A. Femtosecond pulse sequences used for optical manipulation of molecular motion. Science 247, 1317–1319 (1990).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Feurer, T., Vaughan, J. C. & Nelson, K. A. Spatiotemporal coherent control of lattice vibrational waves. Science 299, 374–377 (2003).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Potter, E. D., Herek, J. L., Pedersen, S., Liu, Q. & Zewail, A. H. Femtosecond laser control of a chemical reaction. Nature 355, 66 (1992).

    ADS  CAS  Google Scholar 

  21. 21.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Vogelgesang, S. et al. Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction. Nat. Phys. 14, 184–190 (2018).

    CAS  Google Scholar 

  23. 23.

    Polanyi, J. C., Wong, W. H. & Mok, M. H. Location of energy barriers. J. Chem. Phys. 51, 1439–1450 (1969).

    ADS  CAS  Google Scholar 

  24. 24.

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

    ADS  PubMed  PubMed Central  Google Scholar 

  25. 25.

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

    ADS  CAS  Google Scholar 

  26. 26.

    Sciaini, G. et al. Electronic acceleration of atomic motions and disordering in bismuth. Nature 458, 56–59 (2009).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  27. 27.

    Peierls, R. E. Quantum Theory of Solids (Oxford Univ. Press, 2001).

  28. 28.

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Wall, S. et al. Ultrafast changes in lattice symmetry probed by coherent phonons. Nat. Commun. 3, 721 (2012).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Sokolowski-Tinten, K. et al. Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature 422, 287–289 (2003).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Rettig, L., Chu, J.-H., Fisher, I. R., Bovensiepen, U. & Wolf, M. Coherent dynamics of the charge density wave gap in tritellurides. Faraday Discuss. 171, 299–310 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  32. 32.

    Beaud, P. et al. A time-dependent order parameter for ultrafast photoinduced phase transitions. Nat. Mater. 13, 923–927 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. 33.

    Neugebauer, M. J. et al. Optical control of vibrational coherence triggered by an ultrafast phase transition. Phys. Rev. B 99, 220302 (2019).

    ADS  CAS  Google Scholar 

  34. 34.

    Nibbering, E. T. J., Fidder, H. & Pines, E. Ultrafast chemistry: using time-resolved vibrational spectroscopy for interrogation of structural dynamics. Annu. Rev. Phys. Chem. 56, 337–367 (2005).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  35. 35.

    Yeom, H. W. et al. Instability and charge density wave of metallic quantum chains on a silicon surface. Phys. Rev. Lett. 82, 4898–4901 (1999).

    ADS  CAS  Google Scholar 

  36. 36.

    Song, S. K., Samad, A., Wippermann, S. & Yeom, H. W. Dynamical metal to charge-density-wave junctions in an atomic wire array. Nano Lett. 19, 5769–5773 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Speiser, E., Esser, N., Wippermann, S. & Schmidt, W. G. Surface vibrational Raman modes of In:Si(111) (4 × 1) and (8 × 2) nanowires. Phys. Rev. B 94, 075417 (2016).

    ADS  Google Scholar 

  38. 38.

    Nicholson, C. W. et al. Excited-state band mapping and momentum-resolved ultrafast population dynamics in In/Si(111) nanowires investigated with XUV-based time- and angle-resolved photoemission spectroscopy. Phys. Rev. B 99, 155107 (2019).

    ADS  CAS  Google Scholar 

  39. 39.

    Wippermann, S. & Schmidt, W. G. Entropy explains metal–insulator transition of the Si(111)–In nanowire array. Phys. Rev. Lett. 105, 126102 (2010).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  40. 40.

    Jeckelmann, E., Sanna, S., Schmidt, W. G., Speiser, E. & Esser, N. Grand canonical Peierls transition in In/Si(111). Phys. Rev. B 93, 241407 (2016).

    ADS  Google Scholar 

  41. 41.

    Li, Y. & Heinz, T. F. Optical models for thin layers. Preprint at (2018).

  42. 42.

    Wippermann, S. Understanding Substrate-Supported Atomic-Scale Nanowires from Ab Initio Theory. PhD thesis, Univ. Paderborn (2010).

  43. 43.

    Stekolnikov, A. A. et al. Hexagon versus trimer formation in In nanowires on Si(111): energetics and quantum conductance. Phys. Rev. Lett. 98, 026105 (2007).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Kumpf, C. et al. Low-temperature structure of indium quantum chains on silicon. Phys. Rev. Lett. 85, 4916–4919 (2000).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  45. 45.

    González, C., Ortega, J. & Flores, F. Metal–insulator transition in one-dimensional In-chains on Si(111): combination of a soft shear distortion and a double-band Peierls instability. New J. Phys. 7, 100 (2005).

    ADS  Google Scholar 

  46. 46.

    Nelson, K. A. in Mode Selective Chemistry (eds Jortner, J. et al.) 527–533 (Springer, 1991).

  47. 47.

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

    PubMed  PubMed Central  Google Scholar 

  48. 48.

    Van Hove, M. A., Weinberg, W. H. & Chan, C.-M. Low-Energy Electron Diffraction: Experiment, Theory and Surface Structure Determination (Springer, 1986).

  49. 49.

    Terada, Y. et al. Optical doping: active control of metal−insulator transition in nanowire. Nano Lett. 8, 3577–3581 (2008).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Snijders, P. C. & Weitering, H. H. Colloquium: Electronic instabilities in self-assembled atom wires. Rev. Mod. Phys. 82, 307–329 (2010).

    ADS  CAS  Google Scholar 

  51. 51.

    Klasing, F. et al. Hysteresis proves that the In/Si(111) (8×2) to (4×1) phase transition is first-order. Phys. Rev. B Condens. Matter Mater. Phys. 89, 121107 (2014).

    ADS  Google Scholar 

Download references


This work was funded by the European Research Council (ERC Starting Grant ‘ULEED’, ID: 639119) and the Deutsche Forschungsgemeinschaft (SFB-1073, project A05). We acknowledge discussions with N. S. Kozák, H. Schwoerer, R. Ernstorfer, M. Wolf, A. M. Wodtke and M. Horn-von Hoegen.

Author information




The project was conceived by C.R., with contributions from J.G.H. Experiments and data analysis were conducted by J.G.H., with contributions from H.B., B.W., G.S. and F.K. The manuscript was written by J.G.H., H.B. and C.R. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Claus Ropers.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Stefan Wippermann and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data figures and tables

Extended Data Fig. 1 ULEED set-up.

a, Ultrashort laser pulses (P1: λc = 1,030 nm, Δτ = 212 fs) from an Yb:YAG amplifier (left) pump a non-collinear OPA (output: λc = 400 nm, Δτ = 40 fs) and an OPA (output: P2, λc = 800 nm, Δτ = 232 fs). The 1,030-nm and 800-nm beams are independently attenuated and collinearly focused onto the sample by a single lens (400 mm focal length). The relative on-axis position of the two foci is controlled by adjusting the divergence of the 1,030-nm beam. The ultraviolet pulses are focused onto the tungsten needle emitter inside the electron gun (e-gun) to generate ultrashort electron pulses. The relative timing between the electron probe and each of the two optical pump pulses is controlled independently by two separate optical delay stages. The pump-induced changes in the LEED pattern are recorded using a microchannel plate assembly. b, Cross-correlation of the two pump pulses recorded with a nonlinear photodiode to determine the temporal resolution of the double-pump experiment.

Extended Data Fig. 2 Diffraction images.

ac, Diffraction images and lineouts of the clean (7 × 7)-reconstructed Si(111) surface (a), the (4 × 1) phase (b) and the (8 × 2) phase (c) recorded in our ultrafast LEED set-up (Ekin = 130 eV). Coloured areas correspond to the unit cells in reciprocal space, arrows indicate the location of the lineouts shown below. In the transformation from the (4 × 1) to the (8 × 2) phase, the unit cell is doubled in both dimensions. The twofold streaks in the diffraction pattern of the (8 × 2) phase originate from a weak coupling between the atomic chains. The diffraction patterns of the indium-reconstructed phases feature contributions from three domains rotated by 120° with respect to each other, as the hexagonal structure of the underlying substrate allows for three different orientations of the atomic indium chains.

Extended Data Fig. 3 Temperature calibration.

a, Temperature-dependent integrated intensities of (4 × 1) (top) and (8 × 2) (bottom) diffraction spots across the phase transition (Tc ≈ 125 K). b, Integrated diffraction spot intensities for ∆tp–el < 0 in Fig. 1c as a function of incident fluence. c, Temperature calibration: a Debye–Waller model is fitted to the diffraction spot intensities in a for temperatures in the range 60 K < T < 100 K. Comparing the suppressions in b and c, we find a maximum temperature increase ∆Tb ≈ 22 K for the highest fluence value (Fmax ≈ 1.35 mJ cm2) within our measurement range. Note that the resulting base temperature Tb = 82 K is well below the Tc.

Extended Data Fig. 4 Definition of basis vectors and diffraction spot indexing.

a, Schematic LEED pattern of the (8 × 2) phase and basis vectors (red) of the reciprocal lattice used to index the diffraction spots. b, Complete list of diffraction spots used in analysis.

Extended Data Fig. 5 Optical pump–probe set-up.

a, Ultrashort laser pulses (P1: λc = 1,030 nm, Δτ = 212 fs, ‘Pump’) from an Yb:YAG amplifier (left) pump an OPA (output: P2, λc = 800 nm, Δτ = 232 fs, ‘Probe’). The intensity of the pump beam is modulated at a frequency of 25 kHz by an acousto-optic modulator (AOM). Pump and probe beams are independently attenuated and collinearly focused onto the sample by a single lens (200-mm focal length). The relative on-axis position of the two foci can be adjusted using a telescope assembly. The reflected beams pass two short-pass filters (SP) blocking the pump pulses and are focused on a silicon photodiode (PD). The relative timing between pump and probe pulses is controlled by an optical delay stage. The pump-induced reflectivity changes of the sample are measured by processing the PD and reference signals in a lock-in amplifier. RF, radio-frequency; ND, neutral density.

Extended Data Fig. 6 Ultrafast absorption modulation.

a, Reflectivity change ∆R/R of the In/Si(111) surface as a function of the time-delay ∆tp–pr between pump (1,030 nm) and probe pulses (800 nm; F = 0.14 mJ cm−2). Offsets are added to the datasets for clarity. b, Fourier spectra of ∆R/R(∆tp–pr) for F = 0.04–1.22 mJ cm−2, revealing two main coherent contributions (f1 = 0.65 THz, f2 = 0.84 THz for F = 0.04 mJ cm−2) to the signals in a, attributed to the symmetric shear and rotation modes. An additional but minor lower-frequency contribution to the reflectivity cannot be excluded at this point, given the frequency resolution of the experiment. c, Transient (∆tp–pr ≈ 0.25 ps) and long-lived (∆tp–pr ≈ 9 ps) contributions to ∆R/R as a function of pump fluence. The data are normalized to ∆R/R(∆tp–pr < 0) and the respective values for F = 2.30 mJ cm−2. d, Fluence-dependent frequency shifts of the two modes. The rotation mode softens significantly for higher fluences (error bars, 95% CI of the fit). e, Normalized Fourier amplitudes of shear and rotation modes as a function of fluence.

Extended Data Fig. 7 Short-time Fourier transforms.

a, Relative switching efficiency as a function of the double-pulse delay ∆tp–p (top) and short-time Fourier transform (bottom) for equal pump pulses (F1,030 = 0.32 mJ cm−2; F800 = 0.21 mJ cm−2), revealing a pronounced softening/hardening of the shear/rotation component close to ∆tp–p = 0 (see also Fig. 2b). b, Relative switching efficiency and short-time Fourier transform for unequal pump pulses (F1,030 = 0.48 mJ cm−2; F800 = 0.15 mJ cm−2, see also Fig. 3d).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Horstmann, J.G., Böckmann, H., Wit, B. et al. Coherent control of a surface structural phase transition. Nature 583, 232–236 (2020).

Download citation


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing