Upon excitation with an intense laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways different from those in thermal equilibrium. The mechanism underlying these photoinduced phase transitions has long been researched in the study of condensed matter systems1, but many details in this ultrafast, non-adiabatic regime still remain to be clarified. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) in LaTe3. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a fast (approximately 1 picosecond) recovery of the CDW amplitude is followed by a slower re-establishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other photoinduced phase transitions by identifying the generation of defects as a governing mechanism.


The understanding of equilibrium phase transitions caused by spontaneous symmetry breaking is a hallmark achievement of twentieth-century physics. When these transitions are induced by adiabatically cooling from a disordered to an ordered phase, they are marked by a diverging correlation length and correlation time of equilibrium fluctuations at the transition temperature2, Tc. Much less is understood about non-adiabatic transitions, or quenches, where fluctuations are not expected to exhibit a diverging correlation length and time, preventing the onset of long-range order. This absence of critical behaviour is often linked to the creation of topological defects in the ordered phase. The conventional framework for treating non-adiabatic transitions, Kibble–Zurek theory3,4, suggests that as the system is quenched through a phase transition from a disordered state, topological defects are generated as a result of the simultaneous emergence of the ordered phase in disconnected regions of space. Although such a picture is supported by experiments, for example, in liquid crystals5,6 and 3He7,8, it has so far seen only limited experimental support in a broad new class of non-adiabatic transitions induced in ordered systems by photoexcitation9,10.

Photo-induced phase transitions present a unique platform to study non-adiabatic transitions. They have emerged as an intense research field in recent decades1,11 as a consequence of the technological advances offered by ultrafast lasers. During these transitions, the initial state appearing immediately after photoexcitation, from which order recovers, is far from equilibrium. Moreover, topological defects in this case are not necessarily generated through a complete melting of the broken symmetry phase, but may also arise within the ordered state as a result of spatially localized absorption of high-energy photons.

Materials that exhibit a unidirectional incommensurate CDW are well suited for investigating photoinduced phase transitions. Topological defects in these systems, such as dislocations, have been classified theoretically12,13 and are thought to play a negligible role in an equilibrium metal-to-CDW transition14. Indeed, if a sample is adiabatically cooled below Tc, a resolution-limited diffraction peak appears15,16,17. This observation indicates that the phase coherence extends macroscopically without impedance from topological defects, which, when present, reduce the correlation length and disrupt long-range order. In contrast, previous studies on photoinduced phase transitions in unidirectional CDW systems have hinted at the existence of topological defects9,10, but more direct probes are needed to elucidate how their presence affects the order parameter dynamics.

In this work, we use three different time-resolved probes to gain insight into the light-driven phase transition kinetics in LaTe3. In each probe, an incident pump pulse perturbs or melts the CDW, and a delayed probe pulse is utilized to measure the ensuing dynamics of the relevant observable (see Methods). We employ ultrafast electron diffraction to probe the long-range density correlations18, while using transient reflectivity and time- and angle-resolved photoemission spectroscopy (tr-ARPES) to track the CDW gap amplitude9,19,20,21,22,23. Transient reflectivity has the advantage that it possesses the highest temporal resolution and signal-to-noise ratio among the probes used, enabling us to additionally investigate the coherent response from collective excitations. The main benefit of tr-ARPES lies in its energy and momentum resolution; hence, it can directly probe the relevant gap dynamics. As tr-ARPES is a surface sensitive probe, the transient reflectivity measurements are essential in providing a bulk-sensitive view of the CDW amplitude dynamics (see Supplementary Note 10). Each of the three techniques provides a different perspective, allowing us to gain a comprehensive view of the photo-induced phase transition.

The material we choose to study, LaTe3, is a unidirectional CDW compound. It has a simple phase diagram17, making the effects of photoexcitation easier to understand. Its layered structure, whose b-axis lies out-of-plane24, makes it susceptible to CDW order that forms below an estimated transition temperature of approximately 670 K, with an associated gap of 2Δ ≈ 750 meV25. Because of a small in-plane anisotropy in the material, the CDW forms solely along the crystallographic c-axis, with an incommensurate wavevector \({\bf{q}}_0 \approx {\textstyle{2 \over 7}}{\bf{c}}^ \ast\), where c* is the reciprocal unit vector26. The high value of Tc ensures that, in the course of the photoinduced phase transition, the transient lattice temperature is maintained below Tc despite laser heating (Supplementary Fig. 2 and Supplementary Note 2).

We first describe the ultrafast electron diffraction experiments, which monitor the structural modulation through the intensity and width of diffraction peaks. These experiments, carried out in a transmission geometry, are sensitive to both the amplitude and phase coherence of the CDW13,27. Figure 1a shows an equilibrium electron diffraction cut along the (3 0 L) line at room temperature, where (H K L) are Miller indices. Superlattice peaks, characteristic of CDW formation, are indicated by arrows, and signify the presence of long-range order.

Fig. 1: Time evolution of electron diffraction after photoexcitation.
Fig. 1

a, Electron diffraction cut along (3 0 L). Superlattice peaks are indicated by arrows. The line cut is obtained by integrating the coloured strip along the H direction. A full diffraction pattern is shown in Supplementary Fig. 1b. b, Time evolution of integrated intensities, I(t), of the (4 0 0) Bragg peak and the (5 0 δ) superlattice peak after photoexcitation with an excitation density of 9.4 × 1019 cm−3. Intensities are normalized to values before the arrival of the light pulse. The inset shows snapshots of the superlattice peak at selected time delays, indicated by the triangles in the main panel. The transient broadening is isotropic along both H and L directions, and normalized line profiles shown are along H, from which full-width at half-maximum (FWHM) is computed by fitting to a Lorentzian function (solid curves). c, The time evolution of the superlattice peak width, normalized to values before photoexcitation, showing substantial broadening through the CDW transition. Error bars represent one standard deviation in the Lorentzian fittings. Solid curves in b and c are fits to a phenomenological relaxation model (Supplementary Notes 3 and 7), while dashed lines in the dark orange curve are extrapolated to regions where the peak vanishes. d, Time evolution of the integrated intensity of the (5 0 δ) superlattice peak (circles) overlaid onto the CDW correlation length (squares), showing good agreement. Excitation densities are the same as in c. Missing orange squares correspond to the time range where the CDW peaks are indistinguishable from the background and the width cannot be reliably extracted. CDW correlation length is measured in terms of crystallographic unit cells.

Following photoexcitation at t = 0, the integrated intensity of the superlattice peak initially decreases within approximately 1 ps (Fig. 1b), a timescale limited by the temporal resolution of our setup28. The intensity then recovers to a quasi-equilibrium value. Meanwhile, the peak width (measured by FWHM) also increases by several times its equilibrium value and subsequently decreases (inset to Fig. 1b and Fig. 1c). The peak broadening observed here is a signature of a loss of long-range order, which, in turn, requires the appearance of topological defects in high concentrations18,29, a non-trivial consequence of the photoinduced phase transition. The peak width does not relax fully within the time window examined, and this partial recovery is attributed to a residual defect density. In principle, the presence of crystallographic disorder can also cause a linewidth broadening during a phase transition30,31. However, this scenario is ruled out by the width of the structural Bragg peaks, which is resolution-limited. In the dataset corresponding to Fig. 1b, the maximum value of the peak width implies a CDW correlation length of less than approximately ten crystallographic unit cells (blue squares in Fig. 1c, d). Using these estimates, we calculate that for every two photons absorbed, approximately one defect–antidefect pair is created (see Supplementary Note 6).

We next study how the time evolution of the superlattice peak changes with excitation density, F, where F is quoted in terms of absorbed photons per unit volume (see Supplementary Note 4). Beyond a critical value, Fc ≈ 2.0 × 1020 cm−3, the CDW melts, as the peak becomes indistinguishable from noise after photoexcitation (Fig. 2a and Supplementary Fig. 4a). We estimate that the critical excitation density, Fc, corresponds to approximately one defect every six crystallographic unit cells, a length-scale below which it is no longer appropriate to define the CDW with the wavevector \({\bf{q}}_0 \approx {\textstyle{2 \over 7}}{\bf{c}}^ \ast\).

Fig. 2: Dependence of CDW diffraction peak and optical reflectivity on excitation density.
Fig. 2

a, Time evolution of integrated intensity of the (5 0 δ) superlattice peak upon photoexcitation at different excitation densities. The colour scale is the same as used in b. Error bars are obtained from the standard deviation of noise prior to photoexcitation. Solid curves are fits to a phenomenological relaxation model (Supplementary Note 3). The arrow indicates the time delay at which the intensity is plotted against the excitation density in Supplementary Fig. 4a. b, Transient reflectivity as a function of delay time at different excitation densities. The inset shows the Fourier transform of the oscillatory component measured at an excitation density of 4.1 × 1019 cm−3 (see Supplementary Note 5).

To understand how the CDW is re-established after photoexcitation, we focus on the recovery timescale of the integrated intensity and linewidth shown in Fig. 1c,d. Most importantly, the characteristic time it takes for the peak to recover to quasi-equilibrium increases with excitation density. It should be noted that the recovery timescales are similar for the integrated intensity and the correlation length (Fig. 1d and Supplementary Note 6). This connection can be understood if we consider the ways by which the superlattice peak intensity can be reduced: (i) a suppression of the CDW amplitude; (ii) the excitation of phase modes (phasons)27,32; (iii) a decrease of out-of-plane CDW correlation length13, which we were not able to access in the transmission geometry of our experiment; and (iv) scattering from defect cores, which redistributes intensity across the entire Brillouin zone18. The latter two factors are controlled by the concentration of topological defects. The increased population of phasons originate partially from the temperature rise due to the laser pulse, but can also stem from defect motion9. These factors suggest that the dynamics of topological defects are intimately tied to the recovery of the superlattice peaks. Therefore, we infer that it is the re-establishment of CDW phase coherence that dominates the recovery timescale of the superlattice peak.

The CDW amplitude—the first factor in the above list—recovers on a quicker timescale than the phase coherence, as we demonstrate in the following. For this purpose, we examine the structural Bragg peaks. In theory, their dynamics reflect the response of the CDW amplitude, whereas superlattice peaks additionally retain information about the phase coherence27. In Fig. 1b, we show that when the CDW is suppressed, the Bragg peak first intensifies; subsequently, it weakens as the CDW amplitude recovers and the Debye–Waller factor dominates. This initial intensification signifies a reduction of the CDW amplitude, as distorted atoms return to their high-symmetry positions. We note that the Bragg peak enhancement disappears on a quicker timescale than it takes for the superlattice peak to regain its intensity (Supplementary Fig. 5 and Supplementary Note 7), suggesting that the CDW amplitude and phase coherence recover at different rates.

To confirm this picture, we turn to transient reflectivity and tr-ARPES measurements, which can probe the fast evolution of CDW amplitude9,19,20,21,22,23 with a finer temporal resolution (see Methods). In Fig. 2b, we present the transient reflectivity results where two components in each trace are visible: an incoherent response arising from the excitation and relaxation of quasiparticles, and an oscillatory coherent response predominantly from the 2.2 THz CDW amplitude mode21. The negative tail at long delay times results from laser-induced heating. From the coherent amplitude mode response, we determined that the CDW melts at the critical excitation density, Fc, consistent with the ultrafast electron diffraction measurements (Supplementary Fig. 4 and Supplementary Note 5). However, the CDW recovery timescale, extracted from the incoherent response, is much quicker (up to approximately 1 ps) when compared to that of the superlattice peak, which reaches 5.5 ps for the largest value of excitation density (Figs. 2a,b and 4a). As the incoherent response is known to be a sensitive probe of the CDW gap size9,19,20,21, we again infer that the amplitude recovers on a faster timescale than the phase coherence.

To further investigate the amplitude restoration in a momentum- and energy-resolved fashion, we use tr-ARPES to probe the gap dynamics. Figure 3a shows a segment of the Fermi surface excited with a density above Fc. Following photoexcitation, spectral weight fills in the gapped portions of the Fermi surface. In particular, Fig. 3b shows the time evolution of the momentum-integrated intensity of a representative gapped region (orange box in Fig. 3a), where the Fermi level, EF, lies approximately at the centre of the CDW gap33. The gap size decreases and is subsequently restored to its quasi-equilibrium value within a couple of picoseconds (Supplementary Fig. 6 and Supplementary Note 8). To characterize the gap recovery more quantitatively, we plot in Fig. 3c the time evolution of in-gap spectral weight obtained by integrating the intensity over an energy window of ±0.1 eV around EF (orange box in Fig. 3b). After fitting the recovery with an exponential decay, the time constant obtained is less than 1.1 ps for all excitation densities measured, consistent with the transient reflectivity results (Fig. 4a). We thus identify the characteristic timescale for the restoration of the CDW amplitude as approximately 1 ps, whereas the phase coherence takes up to 5.5 ps to recover at the highest excitation density measured (Fig. 4a).

Fig. 3: tr-ARPES spectra showing CDW gap dynamics.
Fig. 3

a, The top panel shows the tight-binding plot of the normal-state Fermi surface formed by the Te p-bands in the first Brillouin zone. The circle shows the probed part of the Fermi surface and the arrow marks the CDW wavevector q0. The bottom panel shows a section of the Fermi surface through the photoexcitation process with an excitation density of 3.31 × 1020 cm−3. Intensities are integrated over ±10 meV around EF. Cuts along the k|| line (yellow arrow) are shown in Supplementary Fig. 6a–e. b, The time evolution of the gapped region highlighted with the orange box drawn in the t = −1,300 fs slice of a. c, The time evolution of the in-gap spectral weight obtained by integrating the intensity over ±0.1 eV, as outlined by the orange box in b. The three traces correspond to different excitation densities, all normalized between 0 and 1. Curves are fits to a single-exponential relaxation model (Supplementary Note 3).

Fig. 4: Summary of CDW recovery timescales and dynamics.
Fig. 4

a, Characteristic recovery times of the amplitude and phase coherence as a function of excitation density. Transient reflectivity and tr-ARPES track the amplitude dynamics. The recovery timescale of the phase coherence is quantified by the diffraction intensity instead of the peak width owing to the better signal-to-noise ratio (Fig. 1d). Error bars, when larger than the symbol size, denote one standard deviation of fits in Supplementary equation (2). Lines are fits to the data; the dashed segment is extrapolated. be, Schematic illustration of the CDW evolution after photoexcitation. In each image, the unidirectional charge density modulation is depicted as stripes in real space. Stripe brightness indicates the strength of the CDW amplitude and smearing represents phase excitations. A cartoon of the CDW diffraction peak is presented in the lower left corner. Δ and ξ denote CDW amplitude and correlation length, respectively; Δ0 and ξ0 are values at equilibrium. b, Before photoexcitation, the CDW amplitude is large and the CDW is long-range ordered. The corresponding superlattice diffraction is represented by a narrow-width peak. c, Following photoexcitation, the CDW amplitude is suppressed and topological defects are formed. These effects lead to a reduction in the integrated intensity and a broadening of the peak width. d, After approximately 1 ps, the CDW amplitude is largely restored, while defects persist. The diffraction peak remains broad owing to the presence of these topological defects. e, Many defects annihilate at a further time delay though a non-zero defect concentration remains. The superlattice peak narrows substantially as the phase coherence sets in.

Taken together, our investigations of LaTe3 are consistent with the interpretation sketched in Fig. 4b–e. In this picture, the laser pulse excites energetic quasiparticles that create topological defects as they relax and dissipate energy. In the illustration, these defects are depicted as CDW dislocations12,29,32. In the meantime, the CDW gap and hence the amplitude of the CDW order parameter decreases, while the long-range phase coherence is suppressed or destroyed (Fig. 4c). Within approximately 1 ps, the CDW amplitude recovers to quasi-equilibrium. Meanwhile, the long-range phase coherence is not fully restored (Fig. 4d). It takes several more picoseconds or longer, depending on the excitation density, for the defects to annihilate and for the CDW phase coherence to set in (Fig. 4e).

An important implication of Fig. 4a is that the phase coherence takes longer to recover with a higher concentration of topological defects (orange line). While pinpointing the exact reason behind this relationship requires a detailed theoretical treatment, here we limit ourselves to mentioning two possible mechanisms. If the recovery is determined by the annihilation of pairs of two-dimensional topological defects, then the presence of a large number of defects disturbs the coupling between CDWs in adjacent planes. Hence, this renormalized out-of-plane coupling reduces the restoring force that brings together defect–antidefect pairs. A related possibility is that larger concentrations of photoinduced defects renormalize the effective Tc downward2 to a value close to that of the laser-heated sample in ultrafast electron diffraction (see Supplementary Note 2), and as a result, the restoration of the CDW order exhibits critical slowing down associated with proximity to the renormalized Tc2.

The combination of the three time-resolved probes used in this work has provided a comprehensive view of the photoinduced phase transition in a symmetry-broken state. From these techniques, a consistent picture is obtained in which a quick recovery of the CDW amplitude is followed by a slower restoration of phase coherence. Topological defects, in particular, inhibit the re-establishment of long-range order in the non-equilibrium setting. A transition driven by photoexcitation, where topological defects are generated in the ordered phase, therefore represents a distinct framework in which non-adiabatic transitions may be instigated. Rapid improvements in the temporal resolution of ultrafast electron diffraction may further allow the destruction of the ordered state to be investigated in detail in subsequent work34. The results presented in this Letter pave the way to future studies on non-equilibrium defect-mediated transitions and the optical manipulation of topological defects in other ordered states of matter.


Sample preparation

Single crystals of LaTe3 were grown by slow cooling of a binary melt24. For ultrafast electron diffraction measurements, LaTe3 was mechanically exfoliated to a thickness between 10 nm and 30 nm and then transferred to a 10-nm-thick silicon nitride TEM window in an inert gas environment (see Supplementary Fig. 1a and Supplementary Note 1). For tr-ARPES and transient reflectivity measurements, bulk single crystals were cleaved in ultrahigh vacuum (< 1 × 10−10  torr) and in inert gas, respectively, to expose a pristine surface.

Ultrafast electron diffraction

The 1,038 nm (1.19 eV) output of a commercial Yb:KGW regenerative amplifier laser system (PHAROS SP-10-600-PP, Light Conversion) operating at 250 kHz was split into pump and probe branches. The pump branch was focused onto the sample at room temperature, while the probe branch was frequency-quadrupled to 260 nm (4.78 eV) and focused onto a gold-coated sapphire in high vacuum (< 4 × 10−9 torr) to generate photoelectrons. These electrons were accelerated to 26 kV in a direct-current field and focused with a solenoid before diffracting from LaTe3 in a transmission geometry, making the K = 0 diffraction plane visible. Diffracted electrons were incident on an aluminium-coated phosphor screen (P-46), whose luminescence was recorded by a commercial intensified charge-coupled device (iCCD PI-MAX II, Princeton Instruments) operating in shutter mode. A pulse picker was used to tune the laser repetition rate from 0.5 to 250 kHz adopted in the measurement. The operating temporal resolution was 1 ps with 1,000 to 4,000 electrons per pulse.

Transient reflectivity

The 780 nm (1.59 eV) output of a commercial Ti:sapphire regenerative amplifier laser (Wyvern 500, KMLabs) operating at 30 kHz was split into pump and probe branches. The probe branch was focused onto a sapphire crystal to generate a white light continuum (500 nm to 700 nm). Both pump and probe pulses were focused onto the sample, which was held at room temperature, at near-normal incidence with parallel polarization. The pump wavelength was 780 nm (1.59 eV), while the probe wavelength was 690 nm (1.80 eV). The reflected probe beam was directed to a monochromator and photodiode for lock-in detection. The overall temporal resolution, as determined from the pump–probe cross-correlation, was 70 fs.


The same laser system employed in ultrafast electron diffraction measurements was used for tr-ARPES. The pump branch was passed to a commercial optical parametric amplifier (ORPHEUS, Light Conversion) to generate a 720 nm (1.72 eV) output used to photoexcite the sample. The probe branch was first frequency-tripled to 346 nm (3.58 eV) and then focused into a hollow fibre filled with xenon gas (XUUS, KMLabs) to generate the 9th harmonic at 115 nm (10.75 eV). The resulting extreme-ultraviolet pulse was passed through a custom-built grating monochromator (McPherson OP-XCT) to minimize pulse width broadening and to enhance throughput efficiency35, before it was focused onto the sample, which was held at 15 K for optimal resolution (see Supplementary Note 9). Photoelectrons were collected by a time-of-flight detector (Scienta ARTOF 10k), which made simultaneous measurements of the energy and in-plane momenta possible. The operating temporal resolution was 230 fs at a laser repetition rate of 250 kHz. The energy resolution for the measurements was 50 meV.

Data availability

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

Additional information

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We acknowledge discussions with S. Brazovskii, Z. Ding, T. Xie, P. A. Lee, J. Ruhman, B. Skinner, A. Krikun, W. H. Zurek, S.-Y. Xu and D. Chowdhury. We thank M. Bajaj for assistance on instrumentation. We acknowledge support from the US Department of Energy, BES DMSE (experimental setup and data acquisition), from the Gordon and Betty Moore Foundation’s EPiQS Initiative grant GBMF4540 (data analysis and manuscript writing), the Army Research Office (equipment support for the tr-ARPES), and the Skoltech NGP Program (Skoltech-MIT joint project) (theory). Y.-Q.B. and P.J.-H. acknowledge support from the Center for Excitonics, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number DESC0001088, as well as the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 (sample preparation and characterization). Work at Stanford was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract number DE-AC02-76SF00515 (sample growth and characterization). P.W. was supported in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4414. E.B. acknowledges support by the Swiss National Science Foundation under fellowship P2ELP2-172290.

Author information

Author notes

    • Timm Rohwer

    Present address: Center for Free-Electron Laser Science, DESY, Hamburg, Germany

    • Byron Freelon

    Present address: Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA

    • Edbert J. Sie

    Present address: Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA

    • Hengyun Zhou

    Present address: Department of Physics, Harvard University, Cambridge, MA, USA

  1. These authors contributed equally: Alfred Zong, Anshul Kogar.


  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    • Alfred Zong
    • , Anshul Kogar
    • , Ya-Qing Bie
    • , Timm Rohwer
    • , Changmin Lee
    • , Edoardo Baldini
    • , Emre Ergeçen
    • , Mehmet B. Yilmaz
    • , Byron Freelon
    • , Edbert J. Sie
    • , Hengyun Zhou
    • , Pablo Jarillo-Herrero
    •  & Nuh Gedik
  2. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA

    • Joshua Straquadine
    • , Philip Walmsley
    •  & Ian R. Fisher
  3. Department of Applied Physics, Stanford University, Stanford, CA, USA

    • Joshua Straquadine
    • , Philip Walmsley
    •  & Ian R. Fisher
  4. SIMES, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    • Joshua Straquadine
    • , Philip Walmsley
    •  & Ian R. Fisher
  5. Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Moscow, Russia

    • Pavel E. Dolgirev
    • , Alexander V. Rozhkov
    •  & Boris V. Fine
  6. Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow, Russia

    • Alexander V. Rozhkov
  7. Institute for Theoretical Physics, University of Heidelberg, Heidelberg, Germany

    • Boris V. Fine


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A.Z., A.K., T.R., C.L., E.B., E.E., and M.B.Y. performed the time-resolved measurements. J.S. and P.W. synthesized single crystals of LaTe3, supervised by I.R.F. Y.-Q.B. prepared and characterized the samples, supervised by P.J.H. B.F., H.Z., T.R., A.Z. and A.K. built the ultrafast electron diffraction setup. T.R., C.L., E.J.S., E.B. and A.Z. built the 10.75 eV beamline for the tr-ARPES setup. E.E. and M.B.Y. built the optical spectroscopy setup. A.Z. and A.K. performed the data analysis with theoretical input from P.E.D., A.V.R. and B.V.F. A.K. wrote the manuscript with crucial input from A.Z., I.R.F., A.V.R., B.V.F., N.G. and all other authors. This project was supervised by N.G.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Nuh Gedik.

Supplementary information

  1. Supplementary Information

    Supplementary Figure 1–7; References 36–42

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