Ultrafast dynamics evidence of strong coupling superconductivity in LaH10±δ | Nature Communications

Nature Communications volume 15, Article number: 9683 (2024) Cite this article

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Recently, tremendous research interest has been aroused in clathrate superhydrides. However, their microscopic properties, especially the superconducting (SC) gap and electron-phonon coupling (EPC) strength, are largely unexplored experimentally. Here, we investigate the time-resolved ultrafast spectroscopy of a superconductor LaH10±δ under an ultrahigh pressure of 165 GPa. By analyzing the ultrafast dynamics of the quasiparticles, we experimentally obtain the SC gap Δ(0) = 53 ± 5 meV, revealing a gap ratio 2Δ(0)/kBTc = 5.6 and a gap parameter ϑ = 1.95. Significantly, we experimentally estimate \(\lambda \langle {\Omega }^{2}\rangle\) = (2.4 ± 0.1) × 104 (meV)2, which corresponds to an EPC strength λ = 2.58 ± 0.11. These results together provide direct experimental evidence that strong EPC is responsible for the near-room-temperature superconductivity in clathrate superhydrides. Our investigation significantly advances the experimental exploration of superhydrides, and contributes to the ultrafast dynamics investigations of quantum materials under high pressures.

The recent advances in hydrogen-rich superconductors1,2,3,4,5,6,7,8 with near-room-temperature superconductivity has aroused tremendous research interest9,10,11,12,13,14,15,16,17. After the exciting experimental discovery of superconductivity in sulfur hydride with a superconducting (SC) transition temperature Tc = 203 K18, a large family of theoretically predicted clathrate-type metal superhydrides1,2,3,4,7,9 were subsequently synthesized and confirmed to superconduct with near-room-temperature Tc values5,6,8,9,10,11,12,13,19,20,21. Among the known clathrate superhydrides, LaH10±δ exhibits the highest Tc of 250–260 K under pressures of 165–190 GPa5,6,20.

To date, the experimental investigations on the SC properties and mechanisms of these clathrate superhydrides are mainly via electrical transport measurements, owing to the limited small sample size (typically of 5–10 μm) when using diamond anvil cell (DAC) to endow an ultrahigh pressure (>150 GPa) condition. Other experimental explorations, such as Meissner effect22,23,24, X-ray diffraction5,12,22, Raman scattering25, etc., only emerge recently.

There have rarely been reports on spectroscopy investigations on the clathrate superhydrides, leaving the microscopic SC pairing mechanism of their superconductivity almost unexplored experimentally. Particularly, direct experimental evidence of strong electron-phonon coupling (EPC) responsible for the high-Tc superconductivity in these clathrate superhydrides is still lacking to date. Furthermore, experimental observation of the SC gap in clathrate superhydrides has rarely been reported. These leave the theoretical predictions of a strong EPC based on the BCS mechanism not directly verified experimentally.

Spectroscopy experiments (e.g., infrared spectroscopy, ultrafast spectroscopy, scanning tunneling spectroscopy, angle-resolved photoelectron spectroscopy, neutron spectroscopy, Raman spectroscopy, etc.) under megabar pressures will be challenging26,27 owing to the limited sample space and size, sample quality, pressure uniformity, two-beam alignment, laser heating15,23, etc. Hence, more effective spectroscopy experimental means are urgently needed to investigate such quantum materials under ultrahigh pressure conditions.

Ultrafast pump-probe spectroscopy has ultrahigh time resolution and unique capability of exploring non-equilibrium states far above the Fermi surface28,29,30,31, especially in high temperature superconductors31,32,33. Recently, on-site in situ high-pressure ultrafast spectroscopy has been developed to investigate high pressure ultrafast dynamics26,27, which achieved the capability of precisely measuring both the amplitude and lifetime of the quasiparticles (QPs), enabling it to probe the SC phase transitions. However, to date there has been no reports on ultrafast dynamics investigations of quantum materials under an ultrahigh pressure.

In this work, we successfully combine co-linear microscopic ultrafast pump-probe spectroscopy with ultrahigh pressure and with low temperature technology (see Methods), with which reliable ultrahigh pressure ultrafast dynamics data (in both amplitudes and lifetimes) are achieved. The SC gap and EPC strength are both experimentally obtained. Consequently, we have discovered experimental evidence for the strong-coupling nature of SC mechanism in clathrate superhydrides.

We measure the photo-induced relative differential reflectivity ΔR/R of our LaH10±δ sample (see Methods). The experimental setup is similar to the on-site in situ high pressure ultrafast system we recently innovated26,27, except that here the DAC is cooled to low temperatures, with the high pressure remaining constant. The sample is anchored in a DAC (inset of Fig. 1), whose photograph is shown in Supplementary Fig. 1. Figure 1 illustrates a typical time-resolved scanning trace of such an ultrafast relaxation process at 190 K and 165 GPa, ranging from −3 to 140 ps. It is well known that |ΔR/R| is proportional to the density of photo-excited QPs (see Methods).

The relaxation results are fitted by a three-exponential function (red solid curve), which is decomposed into the fast (yellow curve), slow (blue curve), and slowest (purple curve) components. These three processes are more distinctly seen by a log-scale presentation in Supplementary Fig. 2. Left panel inset: schematic details of the ultrahigh pressure ultrafast light-matter interaction encapsulated in the DAC. The crystal structure of LaH10±δ is schematically shown, sandwiched in between a pair of diamonds. The two-color pump and probe light pulses are also depicted, between which the time interval Δt is scanned. Right panel inset: temporal zoom-in view of the ultrafast dynamics signal, revealing the initial fast relaxation process.

Following the convention32,33, the data are quantitatively analyzed by employing a fitting equation f(t) = ΔR/R(t) = Afastexp(-t/τfast) + Aslowexp(−t/τslow) + A0, where Afast, Aslow and A0 denote the amplitudes of the QP relaxation, and τfast and τslow are the QP lifetimes. Deconvolution of the data is conducted to account for the finite temporal duration of the light pulse, with \([f\otimes g](t)\equiv {\int }_{-\infty }^{+\infty }f(\xi )g(t-\xi )d\xi\), where \(g(t)=\frac{1}{\sigma \sqrt{\pi }}{e}^{-{t}^{2}/{\sigma }^{2}}\) is a Gaussian function with a width \(FWHM=2\sqrt{{\mathrm{ln}}\,2}\sigma\)34. The fitting result is plotted in Fig. 1 as a red solid curve, which is fully consistent with the experimental data. A more distinctive identification of the three components is presented in Supplementary Fig. 2 by using a logarithmic plotting. The three components are plotted as dashed curves in Fig. 1: the fast component (yellow curve) is attributed to EPC, the slow component (blue curve) is ascribed to phonon-phonon scattering (e.g., anharmonic decay of optical phonons into acoustic phonons), and the constant term (purple line) is assigned to heat diffusion involving acoustic phonons31,35 with a much longer lifetime at the order of 1 ns.

The temperature dependence data of the ultrahigh-pressure ultrafast dynamics are shown in Fig. 2. Both the amplitudes and lifetimes of the QP relaxation vary significantly with temperature (Fig. 2a). Figure 2b illustrates the normalized data, which better reveals the gradually varying lifetimes with temperature. To qualitatively identify whether there is a SC phase transition, we plot a color map of the ΔR/R signals (Fig. 2a) in Fig. 2c. Two distinct color regions can be identified, reflecting the dynamic variations in the density and lifetime of the photo-excited carriers. The color change at 220 K qualitatively indicates a possible SC transition. We also re-measure the resistance of our LaH10±δ sample upon increasing temperature (the same as for our ultrafast dynamics measurement) without external field right before our ultrafast spectroscopy experiment, which is plotted as the blue curve in Fig. 2c. The likely SC transition temperature we observe in the ultrafast spectroscopy is consistent with the re-measured transport result, manifesting that the sample still well-preserves its SC properties, and the slight lowering of the Tc as compared with ref. 20 can be attributed to the long-time-caused slight relaxation.

a Relative differential reflectivity scanning traces at different temperatures. Both the amplitudes and lifetimes vary with temperature. b Normalized ΔR/R of the data in a clearly manifesting the variation in lifetimes. For clarity, the initial dynamics (from −2 to 18 ps) and the longer-range dynamics (from 18 to 140 ps) are separated by a dashed line. Solid curves: fittings using three-component functions. c Color map of the ΔR/R data in a as a function of both delay time and temperature. Blue curve: temperature-dependent resistance of the LaH10±δ sample during a warming up process. The SC Tc qualitatively exhibited and that from the transport measurement are in line with each other.

Quantitatively, the temperature dependence data of the dynamics are analyzed, which yields the fitting parameters Afast, τfast, Aslow, and τslow, as summarized in Fig. 3. While the fast component varies in a regular way with temperature, the slow component exhibits salient features. The Afast exhibits a regular decrease that can be seen in many quantum materials, and the τfast is nearly a constant, reflecting a constant EPC strength. We will discuss how we quantitatively obtain the EPC strength λ from τfast in a later paragraph, together with the varying fluence experimental results. The Aslow experiences a sharp decrease with temperature at 150−220 K. Simultaneously, for the same temperature region, τslow first decreases then exhibits a dramatic enhancement with temperature near 220 K. The two characteristic temperatures coincide with each other, exhibiting an identical Tc = 220 K, which manifests the well-known phonon bottleneck effect27,32,33,36,37,38,39. Such simultaneous critical behaviors in both amplitude and lifetime of the slow component correspond to a gap closing at the critical temperature.

a, b Amplitude Afast and lifetime τfast of the fast component. The Afast decreases with increasing temperature, which is regular for quantum materials. The τfast is nearly a constant, reflecting a constant electron-phonon coupling strength. The slight decrease at above 250 K may be due to some lattice structure relaxation. c, d Amplitude Aslow and lifetime τslow of the slow component. Both Aslow and τslow exhibit a feature near an identical critical temperature Tc: Aslow experiences a decrease with increasing temperature, reaching a minimum value near Tc = 219 K; τslow first decreases, then increases dramatically when approaching the same Tc. Solid curves in c, d: fitting curves using the RT model. I and II mark the SC and normal phases, respectively. Color background: a guide to the eyes for the SC phase transition. Temperature dependence of the A0 term is discussed in Supplementary Fig. 6. The error bars represent the fitting errors.

We use the Rothwarf-Taylor model40 and its extended derivation33,36 to fit the temperature dependence of Aslow and τslow, which is a multi-process model based on SC gap and Cooper pairs. The amplitude and lifetime of the slow component are depicted by \({A}_{\rm{slow}}(T)=\Upsilon {[\sqrt{\Delta (T)T}\exp (-\Delta (T)/{k}_{\rm{B}}T)+C]}^{-1}\) and \({\tau }_{\rm{slow}}(T)={\{\varGamma [\delta +2{n}_{T}(T)][\Delta (T)+\alpha T\Delta {(T)}^{4}]\}}^{-1}\), where \({n}_{T}\propto \sqrt{\Delta (T)T}\exp (-\Delta (T)/{k}_{\rm{B}}T)\) is the density of the equilibrium thermal QPs, \(\Delta (T)=\Delta (0) \tanh (\vartheta \sqrt{{T}_{c}/T-1})\) is the empirical trial SC gap function41, kB is the Boltzmann constant, ϑ is a parameter reflecting the correlation strength. Here, the ϒ, Г, ϑ, C, Δ(0), α, and δ are all independent fitting parameters (for their physical essence and the detailed data fitting procedure, see Supplementary Information). In Fig. 3c, d the experimental data are fitted well (red curves) and the SC transition is clearly discernable. Explicitly, we obtain the SC Tc = 219 ± 4 K and SC gap Δ(0) = 53 ± 5 meV. This experimentally observed SC gap value is reasonably consistent with the theoretically predicted value (e.g., 62 meV at 170 GPa in ref. 42). Considering the long-time relaxation of the ultrahigh pressure sample after months, the SC Tc value is also reasonably consistent with the original 250 K Tc value20. Importantly, no pre-specified coefficient is set between Δ(0) and Tc; thus, the values are obtained independently in our spectroscopic experiment. With the observed values, we obtain a gap ratio of 2Δ(0)/kBTc = 5.6, which is clearly above the BCS weak-coupling ratio 3.5, and is consistent with the theoretical value of 5.54 at 170 GPa42. By fitting the slow component (Fig. 3c, d), we obtain ϑ = 1.95, where by convention ϑ > 1.74 corresponds to a strong-coupling BCS gap41. Therefore, both the gap ratio and gap parameter ϑ lead us to conclude that we have evidenced a strong-coupling BCS gap in LaH10±δ. In addition, we also obtain an empirical expression for the temperature-dependent SC gap, \(\varDelta (T)=\Delta (0)\tanh (1.95\sqrt{{T}_{c}/T-1})\), which has not been previously reported for near-room temperature superconductors.

The variation feature at 120–150 K (Fig. 3c, d) has rarely been observed in superconductors under ambient pressure. Both the quality and fitting of the time-domain data are good, as explicitly shown in Supplementary Figs. 3 and 4. The temperature dependence of the static reflectivity R exhibits no feature at 120–150 K (see Supplementary Fig. 5). Our transport measurement shows no feature at 120–150 K either20. We do not know the exact origin of this feature. Several possible explanations can be thought of. The feature could be due to some extrinsic change of the DAC; It could also be that the sample is a mixed multi-phase crystal—the sample may not be so uniform; Even a second SC phase could also be possible to potentially account for the feature at 120–150 K. Note that this feature occurs far away from the SC Tc; thus, the discussion does not affect our understanding of the superconductivity.

a Time-resolved transient signal ΔR/R under different pump fluences at 78 K (offset for clarity), which exhibits a prominent enhancement upon increasing fluence. b Normalized ΔR/R at fluences of 2.6, 4.5, and 6.2 mJ/cm2, respectively, displaying the temporal zoom-in view of the initial dynamics. The y-axis is in log-scale, clearly revealing the fast and slow components, each marked by a line segment. c Pump fluence dependence of |ΔR/R|max near the so-called time-zero, where the solid line is a linear fit to the data. The linear fluence dependence without saturation clearly shows that there is no thermal effect. d Lifetime τfast and amplitude Afast of the fast component. τfast slightly increases with fluence at below 4.5 mJ/cm2, corresponding to a constant EPC strength λ35,46. For fluences larger than 4.5 mJ/cm2, τfast slightly decreases due to saturation. In the inset, Afast steadily increases with fluence, reflecting the increase in excited state carrier density. e Lifetime τslow and amplitude Aslow of the slow component. τslow overall slightly increases with fluence, and Aslow increases steadily with fluence. The combined trends in Afast and Aslow are consistent with the result in c. The A0 component is also investigated, which remains a constant with increasing fluence (see Supplementary Fig. 6b). The error bars in c represent the measurement fluctuation. The error bars in d, e denote the fitting errors.

Furthermore, we measure the fluence dependence of the ultrafast relaxation signals at 78 K (see Methods), for which the results are shown in Fig. 4. As expected, the transient dynamics strongly depend on the laser fluence (Fig. 4a), qualitatively exhibiting a proportional relation. For the normalized scanning traces (Fig. 4b), the log-scale figure clearly reveals the different relaxation channels, where the fast and slow components are clearly identified. In Fig. 4c, the experimental data |ΔR/R|max are very well fitted by a linear relation, manifesting the transient differential reflectivity is proportional to the photo-excited carrier density. It spans from 0 to 6.2 mJ/cm2, fully covering the 5.0 mJ/cm2 working fluence for harvesting the data in Fig. 3, which demonstrates that the thermal effects are negligible33,43,44,45 although the sample is small. For each experiment, linear dependence on fluence (or power) needs to be tested to ensure there is no laser heating (see Methods and Supplementary Information). Such linear dependence reflects there is no Coulomb blockade or renormalization in the electronic bands, allowing the Fermi golden rule and RT model to apply.

Significantly, we quantitatively investigate the EPC strength λ based on the direct experimental observation of the ultrafast dynamics of LaH10±δ, particularly by measuring τfast. Usually, one needs to know the specific heat coefficient (i.e., Sommerfeld parameter) and the light penetration depth at the excitation wavelength of the material32,33. For LaH10±δ under ultrahigh pressure, these two physical properties are not reported so far, owing to the lack of experimental investigations. Nevertheless, it has been demonstrated that these obstacles can be circumvented by temperature-dependence or fluence-dependence experimental results35,46, by regarding the specific heat coefficient and penetration depth as constant fitting parameters. Extending the phenomenological Allen relation \(1/{\tau }_{{{\rm{fast}}}}=3\hslash \lambda \langle {\Omega }^{2}\rangle /\pi {k}_{\rm{B}}{T}_{e}\)47 to its temperature dependence version, we have35 \({\tau }_{{{\rm{fast}}}}=\frac{\pi {k}_{\rm{B}}\sqrt{\Theta F}}{3\hslash \lambda \langle {\Omega }^{2}\rangle }(1+\frac{{T}_{L}^{2}}{2\Theta F})\), where \(\lambda \langle {\Omega }^{2}\rangle\) is the second moment of the Eliashberg function, Θ is a parameter determined by the reflectivity, optical penetration depth, and specific heat coefficient (see Supplementary Information), F is the pump fluence, TL is the lattice temperature (i.e., environmental temperature), λ is the EPC strength, and Ω is the phonon frequency. Fitting the temperature-dependent τfast data in Fig. 3b using this relation, we obtain a red solid curve (Fig. 3b), yielding an EPC strength of \(\lambda \langle {\Omega }^{2}\rangle \approx 2.45\times {10}^{4}\,\)(meV)2. Note that the slight decrease in τfast at T > 250 K may be due to some lattice structural relaxation. In parallel, the fluence-dependence experimental data are carefully analyzed by employing the three-exponential decaying function aforementioned, of which the fitting parameters Afast, τfast, Aslow, and τslow are summarized in Fig. 4d, e. Extending the Allen’s relation to the fluence dependence version46, and later on the fluence dependence version at a given temperature35, we have \({\tau }_{\rm{fast}}=\scriptstyle\frac{\pi {k}_{\rm{B}}^{2}\sqrt{{T}_{L}^{2}+\Theta F}\left(\sqrt{{T}_{L}^{2}+\Theta F}-{T}_{L}\right)}{3\lambda {\hslash }^{2}\langle {\Omega }^{3}\rangle \scriptstyle\left[\frac{1}{{e}^{\hslash \langle \Omega \rangle /{k}_{\rm{B}}\sqrt{{T}_{L}^{2}+\Theta F}}-1}-\frac{1}{{e}^{\hslash \langle \Omega \rangle /{k}_{\rm{B}}{T}_{L}}-1}\right]}\). By fitting the experimentally measured lifetime data τfast in Fig. 4d (red curve), we obtain \(\lambda \langle {\Omega }^{2}\rangle \approx 2.3\times {10}^{4}\) (meV)2, which is fairly consistent with the value we obtained above. The consistency between the two methods corroborates the reliability of the EPC value we obtain. Here, we adapt an averaged value \(\lambda \langle {\Omega }^{2}\rangle=(2.4\pm 0.1)\times {10}^{4}\) (meV)2 in our further discussion (for details, see Supplementary Information). This value is in line with all the reported theoretical predictions with explicitly calculated values nearby 165 GPa7,9,48 (see Supplementary Table 1). Following the convention49, we substitute Ω by the logarithmic frequency average Ωlog in \(\lambda \langle {\Omega }^{2}\rangle\). Taking Ωlog = 96.4 meV at 163 GPa7, we estimate λ = 2.58 ± 0.11 for LaH10±δ under 165 GPa, which is in good agreement with the theoretical value of λ = 2.67 in ref. 7. Therefore, our ultrahigh-pressure ultrafast dynamics investigation provides a unique crucial experimental evidence of strong coupling superconductivity in clathrate superhydride superconductors. We have also performed a separate control experiment to repeat the whole set of experiments, including fabricating a new LaH10±δ sample and re-perform the high-pressure ultrafast spectroscopy experiments, as well as data analysis. Overall, the results are in line with the data we presented above (for details, see Supplementary Information).

In conclusion, we have developed a low-temperature ultrahigh-pressure ultrafast pump-probe spectroscopy technique to investigate the excited state QP ultrafast dynamics of LaH10±δ at 165 GPa. We directly measure that the SC gap is Δ(0) = 53 ± 5 meV and the EPC strength is λ = 2.58 ± 0.11, which provide a unique experimental evidence for the long-sought strong coupling superconductivity in clathrate superhydrides. Moreover, a gap ratio of 2Δ(0)/kBTc = 5.6 and a gap parameter of ϑ = 1.95 are also experimentally obtained, both corroborating the strong-coupling characteristic of LaH10±δ. Our results greatly advance the experimental understanding about the SC mechanism of the near-room temperature superconductivity. Our investigation greatly boosts the field of high-pressure ultrafast science, which can be extended to other near-room temperature superconductors and other quantum materials. Thus, we foresee the dawn of a promising unexplored frontier area, which canvasses extensive investigations of non-equilibrium quantum states under high pressures.

The experimental setup is similar to the on-site in situ high pressure ultrafast system we recently innovated (see refs. 26,27), except that here the DAC is cooled down to liquid nitrogen temperature in an open cycle continuous flow cryostat. During the whole experiment, the high pressure in the DAC is kept constant. Two-color ultrahigh pressure femtosecond pump-probe spectroscopy experiment has been carried out, with a pulse duration of 70 fs, using a 250 kHz optical parametric amplifier system to reduce the thermal effect. Our temperature-dependence experiment is carried out from liquid nitrogen to room temperature. The wavelengths of the pump and probe beams are 620 and 800 nm, the powers are 200 and 60 μW, the 1/e2 beam diameters are 4.5 and 4.3 μm, and the fluences are 5.0 and 1.6 mJ/cm2, respectively. Note that, during the experiment, the chopper blocks a half of the pump power (i.e., the 200 μW power is reduced to 100 μW), which actually reduces the potential thermal effect (the same is true for the fluence dependence experiment). For the fluence dependence experiment, the pump and probe wavelengths are 650 and 800 nm, respectively; the pump power varies from 100 to 240 μW, and the probe power is kept at 40 μW; the 1/e2 pump and probe beam diameters are 4.4 and 2.5 μm, respectively; the pump fluence varies from 2.6 to 6.2 mJ/cm2 and the probe fluence is fixed at 3.2 mJ/cm2.

For both the temperature-dependence and fluence-dependence ultrafast experiments, cross-polarization detection geometry is implemented to reduce interference. An optical cage system is constructed in the light path to reduce the fluctuations of the laser spot position on the sample surface. In our experiment, the influence of the static reflectivity R (Supplementary Fig. 5) is excluded by measuring the relative differential reflectivity ΔR/R.

It is well known that |ΔR/R| is proportional to the density of photo-excited QPs and the process is described by the Fermi Goden Rule. The pump pulse incidents on the sample surface, which promotes the ground-state electrons to the excited state far above the Fermi surface. As the pump pulse propagates away, the photo-excited nonequilibrium state carriers relax back to the ground state due to the EPC and phonon-phonon interactions, which is detected by the probe pulse with controlled scanning delay time.

Several major challenges have been overcome in our experiment. First, low temperature and varying temperature experiments are needed for our investigation, which is prominently more challenging than our recently achieved room temperature high-pressure ultrafast spectroscopy instrumentation and experiment26,27. The cooling down and warming up of the whole DAC take much longer time (e.g., t > 1.5 h) for each of the temperature point, especially because for such an ultrahigh pressure experiment the frame of the DAC is made of steel. Second, the DAC cell needs to be compatible with the low temperature cryostat. Particularly, thermal sensor needs to be anchored as close as possible to the sample and highly transparent optical window is needed. Third, the sample size is as small as 10 × 20 μm2 due to the ultrahigh-pressure synthesis and experiment. Consequently, microscopic ultrafast spectroscopy experiment has to be implemented. Thus, relatively strong laser beam has to be avoided due to the tight focusing and weak signal detection is needed. Forth, because an objective lens has to be used, co-linear geometry has to be implemented, making it more challenging to remove the unfavorable interference between the pump and probe beams. Fifth, two-color experiment thus has to be implemented. Diamonds have strong absorptions in the ultraviolet wavelength range50. As a result, we avoid the much easier 400–800 nm laser wavelength setup and choose to implement the tunable visible light. Overall, based on the above five aspects of technical breakthroughs, our method is challenging in implementing a two-beam low temperature high-pressure ultrafast pump-probe experiment26 and has the advantage of employing much smaller laser spot sizes, ensuring probing the sample itself without any interference from the electrodes, substrates, and other parts (Supplementary Fig. 1).

Ultrafast pump-probe spectroscopy usually employs lock-in amplifiers, which contain an internal reference signal when detecting the real signal. There is a reference phase shift between the reference signal and input signal, which can be adjusted by pressing the auto-phase button on the front panel of the lock-in amplifier. This will introduce an overall positive or negative sign upon the scanning trace. By moving the motorized linear stage to a location with negative value, pressing the auto-phase button, then doing the scan again, the whole new scanning curve will be flipped, like being multiplied by a negative sign. In such a way, whether the peak is upward or downward can be easily controlled by the electronics. This electronic phase is additional to the input signal from the sample. This sign is different from the sign change (at different wavelength) due to real absorption. Such an overall sign needs to be decided at the beginning of the whole set of experiment, and should not be changed during the latter-on measurements. In our experiments, we do the “auto-phase” only at the beginning and do not do it again throughout the entire experiment.

In general, the pump beam might enhance or reduce the reflectivity of a sample. Hence, the sign of the pump-probe data can be calibrated, such as by using a reference sample under intense pump and probe beams, without involving the chopper and lock-in electronic phase. Here, due to the lack of a reference sample, we did not carry out this calibration, which will not affect the conclusions in this work.

Although an objective lens is used in the pump-probe light paths and the laser spots are as small as a few microns on the sample surface, the repetition rate is low (250 kHz), and the total power (~0.1 mW) in this experiment is much lower than those in a regular pump-probe experiment. Hence the thermal effect is effectively avoided. It has been well known that laser heating is more prominent at lower temperatures and higher repetition rate excitations. Here, the temperature is relatively high (around 220 K), and the repetition rate is low (250 kHz, much lower than 80 MHz), which further confirms that there are no thermal effects (i.e., no laser heating) in our experiment. Indeed, for thermal effect, the total power in pump and probe beams is more crucial than the fluences, because thermal effects are due to accumulated heat, which is mainly related to the laser power input and heat dissipation by cooling. The most reliable and widely accepted criteria that there is no thermal effect is that the |ΔR/R|max signal is linearly proportional to the pump laser fluence33.

Our LaH10±δ sample was synthesized at 165 GPa ultrahigh pressure and 1700 K high temperature, with a lateral size of 10 × 20 μm2, for which the details are described in ref. 20. The characteristic onset transition temperature Tc of our LaH10±δ sample was initially determined to be 240–250 K by the transport measurement20. The re-measured transition temperature is depicted in the main text. The symmetry of the lattice structure of LaH10±δ has been previously identified to be \({Fm}\bar{3}m\), using XRD measurements, where the \({Fm}\bar{3}m\) phase were found to be a stable phase under an ultrahigh pressure of 138–170 GPa5,6,22,51.

The data that support the findings of this study are available from the corresponding author upon request. The source data underlying Figs. 2 and 4 are provided as a Source Data file. Source data are provided with this paper.

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This work was supported by the National Key R&D Program of China (Grants No. 2021YFA1400201 J.Z., 2017YFA0303603 J.Z., 2022YFA140390 J.P.H., 2023YFA1608900 X.H.Y., 2021YFA1400300 F.H.), CAS Project for Young Scientists in Basic Research (Grant No. YSBR-059 J.Z.), Strategic Priority Research Program of CAS (Grants No. XDB30000000 J.Z., XDB33000000 X.H.Y.), National Natural Science Foundation of China (Grants No. 12025408 J.G.C., 11574383 J.Z., 12204400 Y.L.W.), International Partnership Program of Chinese Academy of Sciences (Grant No. GJHZ1826 J.Z., GJTD−2020-01 J.G.C.), Beijing Natural Science Foundation (4191003 J.Z.), CAS Interdisciplinary Innovation Team (J.Z.), and New cornerstone investigator program (J.P.H.).

These authors contributed equally: Y. L. Wu, X. H. Yu, J. Z. L. Hasaien.

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China

Y. L. Wu, X. H. Yu, J. Z. L. Hasaien, Fang Hong, P. F. Shan, Z. Y. Tian, Y. N. Zhai, J. P. Hu, J. G. Cheng & Jimin Zhao

Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao, China

Y. L. Wu

School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

X. H. Yu, J. Z. L. Hasaien, Fang Hong, P. F. Shan, Y. N. Zhai, J. P. Hu, J. G. Cheng & Jimin Zhao

Songshan Lake Materials Laboratory, Dongguan, Guangdong, China

X. H. Yu & Jimin Zhao

New Cornerstone Science Laboratory, Beijing, China

J. P. Hu

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J.Z. conceived the idea and supervised the project. Y.L.W., J.Z.L.H., and J.Z. conducted the low-temperature ultrahigh pressure ultrafast pump-probe spectroscopy experiment with assistance from Z.Y.T. and Y.N.Z.; X.H.Y., F.H., P.F.S., and J.G.C. prepared the samples and characterized resistance. Y.L.W. and J.Z. analyzed the data. J.Z., J.G.C., and J.P.H. discussed the results. J.Z. wrote the paper with inputs from J.G.C. and all authors.

Correspondence to Fang Hong, J. G. Cheng or Jimin Zhao.

The authors declare no competing interests.

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

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Wu, Y.L., Yu, X.H., Hasaien, J.Z.L. et al. Ultrafast dynamics evidence of strong coupling superconductivity in LaH10±δ. Nat Commun 15, 9683 (2024). https://doi.org/10.1038/s41467-024-53103-w

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Received: 04 February 2024

Accepted: 30 September 2024

Published: 08 November 2024

DOI: https://doi.org/10.1038/s41467-024-53103-w

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