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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.

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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.


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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 acknowledge discussions with N. S. Kozák, H. Schwoerer, R. Ernstorfer, M. Wolf, A. M. Wodtke and M. Horn-von Hoegen.

Author information

Authors and Affiliations



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.

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Competing interests

The authors declare no competing interests.

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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).

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

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