Introduction

Crystals with unique ionic arrangements and strong electronic correlations serve as a fertile ground for the emergence of exotic phases, as evidenced by the coexistence of charge density wave (CDW) and superconductivity in vanadium (V) Kagome metals of AV3Sb5 (A for K, Rb, and Cs). Exotic phases involving CDW and superconductivity (SC), arising from intricate electronic structures within geometrically frustrated ionic arrangements, have spurred active investigation into the Kagome metal, AV3Sb5 (Fig. 1a)1,2. Experimental findings suggest that mechanisms driving CDW formation extend beyond Peierls distortion that is facilitated by enhanced electron–phonon interactions through nested Fermi surfaces. This has led to new hypotheses regarding electron–hole pairing mediated by phonons3,4,5,6. The van Hove singularity of V d-electrons near the Fermi level has been proposed as a pivotal factor in CDW instability7,8. However, the role of phonons remains ambiguous, as phonon softening, a characteristic of CDW instability, has not been observed to the best of our knowledge5,9. Additionally, the CDW and SC phases exhibit sensitivity to different choices of alkali metal ions in the Kagome system10,11,12,13,14, despite the limited presence of electron population from the cations near the Fermi level7,8. These findings suggest that the electronic potential energy surface may undergo dramatic changes due to cation movement, giving rise to such diverse phases. While there have been several ultrafast optical and ARPES studies on CDW phases15,16,17, further research into the microscopic CDW orderings in excited states remains necessary.

Fig. 1: Time-resolved X-ray scattering investigation of CDW superstructures of CsV3Sb5.
Fig. 1: Time-resolved X-ray scattering investigation of CDW superstructures of CsV3Sb5.The alternative text for this image may have been generated using AI.
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a Crystal structure of CsV3Sb5 with the vanadium-networked Kagome lattice. b CDW order parameters derived from the integrated intensities of the (0.5 0 2) and (0.5 0 1.5) reflections representing the 2 × 2 × 1 and 2 × 2 × 2 superstructures, respectively. Solid lines depict results from BCS gap equations. c Schematic representation of time-resolved X-ray scattering experiments. d Temporal evolution of the 2 × 2 × 1 and 2 × 2 × 2 CDW reflections showing photoinduced melting and recovery. Ultrafast melting within 100 fs is commonly observed for both 2 × 2 × 1 and 2 × 2 × 2, with the peak intensity not fully recovering immediately. Solids lines are from simulations (text). Error bars indicate the standard error of the peak intensity. Notably, intensity oscillation is observed for the 2 × 2 × 2 CDW. It results from a coherent phonon oscillation (red line) but with a phase delay of ωt ~ 400 fs, distinguished from normal displacement excited coherent phonon (DECP, grey line).

In this work, we conducted femtosecond (fs) time-resolved X-ray scattering experiments on CsV3Sb5 to investigate CDW instabilities within a finely balanced potential energy landscape, induced by photoexciting electrons near the Fermi level of the range of ~ 1.5 eV matching with the photon energy of fs-infrared (IR) laser pulses. Mostly electrons in V and Sb ions’ orbitals are involved in this photoexcitation process5,18. Notably, we find that the phonon mode involving Cs ions’ out-of-plane motion becomes energetically frustrated in the CDW phase, impeding its immediate participation in CDW formation. Furthermore, our study reveals that femtosecond laser excitation alleviates this frustration, triggering an asymmetric phonon response and enabling the emergence of a metastable CDW state. X-ray scattering experiments were conducted utilising the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL) and the Pohang Light Source (PLS).

Results

The emergence of superstructures below the CDW transition temperature of 96 K was confirmed, revealing the coexistent 2 × 2 × 1 and 2 × 2 × 2 CDWs (notated as a × b × c in multiples of the unit cell) (Fig. 1a, b)19. Doubling of the unit cell in the ab-plane resulted in a 2 × 2 superstructure due to in-plane displacements of V ions, forming a star-of-David (SoD) or its inverse triangle-and-hexagon (TrH) pattern (Fig. 1a)10,20,21. Additionally, unit cell doubling along the c-axis was observed, establishing the 2 × 2 × 2 superstructure. Another lattice instability is required to induce this superstructure with the phonon mode (\({L}_{2}^{-}\)) involving ions’ c-directional motion attributed to driving this instability9,15. The 2 × 2 × 1 and 2 × 2 × 2 CDWs, corresponding to in-plane distortion with in-phase and phase shifted stacking along the c-direction20, respectively, were identified with different peak widths and temperature dependence of intensities at \({Q}_{{CDW}}^{2\times 2\times 1}=(0.50{{\rm{Int}}}{{\rm{eger}}})\) and \({Q}_{{CDW}}^{2\times 2\times 2}=(0.50{{\rm{Integer}}}+0.5)\). They present in the same physical domain as same CDWs but with a variation in a c-directional stacking. The order parameters are derived from the integrated intensities of the CDW satellites (Fig. 1b and Supplementary Note 1)5,6,22.

The rapid redistribution of electrons near the Fermi level due to fs-IR photoexcitation disturbed these CDW orderings. Subsequently, the ultrafast reaction dynamics of the CDWs were investigated using femtosecond X-ray pulses from the PAL-XFEL (Fig. 1c and Method). The temporal evolution of peak intensity from the 2 × 2 × 2 CDW reflection exhibited an oscillation without full recovery until approximately 2 ns, whereas no oscillation was observed for the 2 × 2 × 1 CDW (Fig. 1d). These features were explicitly resolved by simulating exponential decay and recovery reactions (drawn with a solid line) (Supplementary Note 2). Both CDWs underwent rapid melting at approximately 100 fs, followed by a quick yet partial recovery of intensity in 300 fs. These timescales match with previously reported in CDW systems with electron–phonon interactions17,23,24. After the photoinduced melting, rapid reconstruction of the CDW within hundreds of femtoseconds was observed, but into a metastable state with reduced intensity involving an asymmetric vibration of Cs ions changed from the intact CDW’s native \({L}_{2}^{-}\) mode. This metastable state, persisting for nanoseconds, is induced by photoinduced electronic perturbation rather than thermal disorder as noted by slow recovery of Bragg reflection in several hundred picoseconds (Supplementary Note 3)25.

The oscillating intensity of the 2 × 2 × 2 CDW reflected a coherent phonon with a frequency of approximately 1.3 THz. This resembles aforementioned \({L}_{2}^{-}\) phonon but with a critical difference9,15. One should note that native \({L}_{2}^{-}\) phonon involves symmetric motions of two Cs ions moving upward while the other two move downward, exhibiting a specific symmetry. From the 3Q degenerate CDW structure of this system, this phonon mode can affect the 2 × 2 × 2 superstructure intensity but only for the one case out of three CDWs, as a minor contribution. (Supplementary Note 4)15,20. Hence, the observed oscillatory intensity suggests a fundamental modification of the native \({L}_{2}^{-}\) phonon, which induces intensity variations across all triply degenerate CDW states, caused by the fs-IR photoexcitation of conduction electrons. Consistent with this, the coherent phonons detected through CDW reflection exhibited an unusual phase delay of approximately π (Supplementary Note 2)26,27. This phase delay indicates the presence of competing interactions that delay the prompt excitation of coherent phonons and distort the native phonon mode28,29,30.

The emergence of strong diffuse signals along the c-direction around the 2 × 2 × 2 CDW reflection strongly supports the interpretation of competing interactions between the 2 × 2 × 2 CDW and the \({L}_{2}^{-}\) phonon mode (Fig. 2a). The first diffuse streak, which developed at 200 fs, was of the ordinary type resulting from CDW melting, with a reduced domain size of approximately 60% of the intact value (Fig. 2b). As the peak sharpened with CDW reconstruction, another strong diffuse streak appeared at around 400 fs, coinciding with the delayed onset of the coherent phonon (Fig. 2b). This transiently formed diffuse signal, observed at approximately 400 fs, exhibited a two-wing structure relative to the main CDW reflection. These diffuse scattering peaks developed at positions with symmetric offsets (± δq ~ 5 × 10−3 2π/c) relative to the 2 × 2 × 2 CDW superstructure at 1.5 (2π/c), arising from disordered phase slip while relieving the frustrated phonon (Fig. 2b)31,32,33. The two-wing structure represents random period in the phase slip (Supplementary Note 5).

Fig. 2: Metastable CDW states with localised phonon mode.
Fig. 2: Metastable CDW states with localised phonon mode.The alternative text for this image may have been generated using AI.
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a Photoinduced melting of the 2 × 2 × 2 CDW with strong diffuse signals developed along the c-direction at ~ 200 fs and 400 fs (blue arrows). The color scale represents the normalized intensity. b The L-scan at 400 fs displays diffusive two-wing structure, centered on 2 × 2 × 2 CDW reflection, caused by a phase slip in the CDW domain (lower panel), distinguishable from the signal at 200 fs with diffuse tails resulting from reduced domain size (upper panel). c Phase-slip in the 2×2 × 2 CDW. The red-coloured sinusoidal wave indicates the domain with three-one Cs displacements newly formed from the native two-two vibration (blue colour). The orange area and dotted red line denote a CDW phase-slipped region. Right panel displays the diffuse scattering pattern corresponding to this phase-slip structure. d Comparison between the symmetric but energetically frustrated two-two vibration in the native CDW and the modified, frustration-relieved Cs vibration initiated at ~ 400 fs, which persists as a metastable CDW ordering. In panels (c, d), the red and blue shaded circles represent Cs ions, the red line with red circles illustrates the vanadium kagome net, and the grey lines indicate the 2 × 2 × 2 unit cell. e Potential energy surface calculation with an eye-guide solid line demonstrates that Cs ions, located at the centre of the 2 × 2 dimerised V structure, become more stable by moving toward (or out of) the TrH (SoD) mesh.

Other possibilities on the origin of the diffuse peaks have been attempted to include thermal diffuse scattering34, order-disorder transitions35, or critical scattering. Observed broad diffuse tail extending to inelastic excitation up to ~3 eV, and with symmetric contribution, is beyond ordinary quasiparticle excitations. The order-disorder transitions often involving in single broad diffuse scattering is not the current case. A possibility of critical scattering with two lengths scale, ordered region with long correlation along with disordered domains short correlation length, can be considered, which usually happen near the phase transition point36. We do not explicitly rule out this possibility but want to mention that such two length scale peaks were not observed in static temperature dependent measurement, not to support such interpretation. Yet, our phase-slip domain interpretation generally accounts for the observed intensity pattern.

Here, we present a schematic model describing the phase slip resulted from the asymmetric alterations: three-up (down) and one-down (up) deviated from the symmetric two-up and two-down displacements (Fig. 2c). The proposed structural model was consistent with the diffuse scattering pattern developed along the c-direction (Supplementary Note 5). One notes that increased disorder in phase slip domain size results in broadened width of the satellite diffuse peaks to bury the two-peak structure to a single diffusive peak alongside a sharp CDW reflection (Supplementary Note 5). However, this also reflects on a phase slip consistent with the present interpretation.

Further to confirm the modification of the native \({L}_{2}^{-}\) phonon mode after the photoexcitation, we have carried out time-dependent density functional theory (TD-DFT) calculations (Methods). The TD-DFT revealed that photoexcited electrons predominantly originate from V and Sb orbitals, as shown in density of occupied states (Supplementary Fig. 6b). This photoexcitation disturbs the local electrostatic potential experienced by Cs atoms to promote site-dependent displacements (Supplementary Movie 1). Accordingly, this photoinduced CDW breathing motion reshapes the potential energy to cause inverted displacement of one Cs ion, resulting in a three-to-one vibration (Supplementary Fig. 6c). This inversion of the Cs-ion displacement was also corroborated by potential energy surface calculations, indicating that the system reaches a lower energy state with the Cs ions at the centre of TrH (or SoD) moving toward (out of) the V superstructure (Fig. 2e). The calculation confirmed an energy gain of 6 meV by displacing the Cs ions toward the TrH centre by 0.1 Å compared to the original position (Fig. 2e). In the native \({L}_{2}^{-}\) phonon mode, for the paired Cs ions, one ion was situated at the centre of the SoD (or TrH), whereas the other was not (Fig. 2d). Therefore, the native \({L}_{2}^{-}\) phonon mode with two-up and two-down vibrations was incompatible with the lower energy configuration, thus being frustrated in the CDW phase. With a significant perturbation of the potential energy landscape by redistributing electronic states in the V and Sb orbitals through fs-IR laser excitation, the CDW was transiently restructured. The phonon frustration became alleviated by inverting the movement of one Cs ion to align with the lower total energy configuration of the CDW phase. This resulted in asymmetric three-up (down) and one-down (up) vibrations, consistent with the observation of the oscillatory intensity of the 2 × 2 × 2 CDW reflection (Fig. 2d).

To comprehend the impact of photoexcited electrons on frustrated phonons and CDW instability systematically, we explored the fluence dependence of fs-IR pump laser (Fig. 3). A more pronounced reduction in peak intensities was consistently observed owing to increased CDW melting with higher laser fluence (Fig. 3a). The response times for melting and subsequent short recovery appeared relatively unaffected by variations in laser fluence ranging from 0.05 to 2.5 mJ cm−2 (Fig. 3c, d). The melting time remained approximately 100 fs, displaying minimal dependence on laser fluence (Fig. 3c). This timescale is similarly noted for previously reported dynamics of nesting-mediated CDW systems17,23,24. Following this melting, there was a prompt intensity recovery, yet it failed to fully return to the intact state with the reopening of the CDW gap. This rapid recovery occurred at ~300 fs, consistent with both the 2 × 2 × 1 and 2 × 2 × 2 CDWs (Fig. 3d).

Fig. 3: Laser fluence dependence of CDW melting and recovery.
Fig. 3: Laser fluence dependence of CDW melting and recovery.The alternative text for this image may have been generated using AI.
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a Laser fluence dependence of the 2 × 2 × 2 (left) and 2 × 2 × 1 CDW (right) peak intensities, showing a larger reduction in peak intensities with higher laser fluence. Underdamped intensity at ~ 400 fs develops more strongly in the 2 × 2 × 2 CDW with increasing laser fluence, but the oscillation period is insensitive to the laser fluence. The horizontal dashed lines indicate a peak intensity value of 1, representing the idealized baseline intensity before time zero. Error bars indicate the standard error of the peak intensity. b Intensities of partially recovered CDWs obtained for different laser fluences, showing a similar behaviour of gradual decrease until ~ 1.4 mJ cm−2 before saturation. Intensity of the underdamped oscillation at 400 fs is also compared, displaying a similar pattern of monotonic increase until 1.4 mJ cm−2 followed by saturation (right). c, d Comparison of melting and short recovery time of the two CDWs, displaying a similar timescale for melting in 100 fs and short recovery in ~ 300 fs without notable dependence on laser fluence. Solid lines, in (b–d, are guide to eyes. Error bars in b to d represent the fitting error obtained from simulation functions (Supplementary Note 2).

The fluence-dependent intensity of the 2 × 2 × 2 CDW exhibited intriguing characteristics warranting further investigation. Following the initial reduction upon melting, the intensity rebounded to its maximum value, showing a discernible dependence on laser fluence (Fig. 3a and b). For laser fluences exceeding approximately 0.5 mJ cm−2, the intensity surpassed the intact state, denoted as ‘underdamped CDW’. This transient CDW underdamping was similarly observed in other layered transition metal compounds exhibiting SoD CDW37,38. Subsequent to underdamping at around 400 fs, the intensity oscillated around a mean value lower than the intact state, without full recovery, persisting in a metastable state for several nanoseconds15,16,39. The intensity reduction in this metastable state increased with IR laser fluence until reaching approximately 1.4 mJ cm−2, with a fluence dependence akin to that of the underdamped CDW intensity (Fig. 3b). Overall, the oscillation frequency of the modified coherent phonon remained largely unaffected by laser fluence, exhibiting only weak softening (1.5%) (Supplementary Note 8)5,9,17.

We present a visual representation summarizing the overall photoinduced melting and metastable configuration of the 2 × 2 × 2 CDW (Fig. 4). The harmonic potential of the ions is schematically depicted for the CDW amplitude or mean ionic displacement (A). The potential energy of the intact 2 × 2 × 2 CDW exhibited a ground state with an initial CDW amplitude of A0 (Fig. 4a)40. Fs-IR laser pumping shifted the potential energy surface (PES) to the ground state without a CDW (A = 0), indicating photoinduced gap closing (t ~ 0). With this transiently formed PES, the CDW melted to reach the ground state (ωt ~ π/2)41. While adapting to this new PES, CDW underdamping occurred at ωt ~ π with the displacement, AUD, further shifting the PES to a metastable ground state at AMS. The new CDW then oscillated around the metastable ground state with an amplitude AMS smaller than A0, as observed experimentally15,16,39. Corresponding atomic configurations are depicted (Fig. 4b). The intact CDW, characterised by two-up and two-down displacements of Cs ions relative to the V-dimerised CDW, demonstrated frustration. Upon femtosecond modification of the electron distribution by fs-IR photoexcitation, the symmetric (two-up and two-down) phonon mode, previously frustrated, was relieved, inducing three-up (down) and one-down (up) vibrations compatible with the potential energy surface.

Fig. 4: Photoinduced underdamping and metastable state of 2 × 2 × 2 CDW.
Fig. 4: Photoinduced underdamping and metastable state of 2 × 2 × 2 CDW.The alternative text for this image may have been generated using AI.
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a Ultrafast reaction in the 2 × 2 × 2 CDW depicted by a pictorial view of photoinduced potential energy changes with the CDW amplitude (A). Fs-IR pumping shifts the potential energy to the ground state without CDW (A = 0) caused by photoinduced gap closing (t ~ 0). Following this transiently formed potential energy, the CDW melts to reach the energy ground state (ωt ~ π /2). While adapting to this new potential, underdamped displacement of the CDW occurs (ωt ~ π) with further displacement of the potential energy surface having the ground state at AMS. The CDW amplitude now oscillates around the new ground state amplitude, AMS, of the metastable state. b Fs-IR pumping alters Cs ions’ c-directional vibration (\({L}_{2}^{-}\) phonon) in a manner to relieve energetically frustrated two-two displacements. Blue circles represent Cs ions, while red circles outlined with grey lines form the vanadium kagome network. The red shaded region indicates the vanadium CDW formation. Upon abrupt disturbance of the electron distribution by fs-IR pumping, the frustrated symmetric (two-up and two-down) phonon mode changes to three-one, compatible with the total energy. The right panel shows the path of the symmetric phonon mode (blue sinusoidal line) changing into the path of the asymmetric phonon mode (red sinusoidal line).

Discussion

In summary, we investigated the ultrafast dynamics of CDWs in the excited PES of CsV3Sb5 by transiently redistributing electrons near the Fermi levels using an fs-IR laser pulse. Through fs-IR photoexcitation, we induced a metastable CDW phase with a localised phonon mode, relieving the energetically frustrated two-up and two-down vibrations of Cs ions in the CDW state. This phonon mode, characterised by symmetric out-of-plane displacements of alkali ions, leads to energy loss directly coupled with the dimerization of V ions within the Kagome net, resulting in phonon frustration in the CDW phase. Restructuring the CDW using fs-IR laser photoexcitation relieves it by inducing a frustration-relieved localised phonon mode in a metastable CDW state. Our study unveiled the intricate coupling of phonons in this strongly correlated electronic system with exotic CDW phases by directly observing the modified asymmetric coherent phonons formed in a transiently disturbed potential energy configuration. It provides a concrete understanding on the mysterious roles of phonons in Kagome metals, emphasizing the crucial role of alkali ions in controlling CDW ordering10,11,12,13,14. While the phonon mode involving alkali ions’ vertical motion emerges in the CDW state, noted with negative frequency in the phonon energy calculation15, we found that this phonon mode becomes unstable in the CDW superstructure. The fs-IR photoexcitation mitigates this frustrated phonon to alter the vibration as three-up (down) and one-down (up) type, more compatible with the CDW structures. We also note that this frustration may defer immediate involvement of the \({L}_{2}^{-}\) phonon to induce the CDW, explaining the absence of phonon softening in this system5,9.

We expect this frustrated phonon dynamics is rather widespread in emerging materials. Whilst no explicit relation of the observed frustrated phonon dynamics to the superconducting transition is drawn in this study, presence of a phonon mode becoming inactive, in layered high-TC superconductors and other layered materials, is discovered from theoretical investigations, which alludes the impact of phonon frustration in keeping the systems in the superconducting state42. This phonon frustration observed in this Kagome net can be direct evidence. This discovery suggests prompt investigation of similar dynamics in other correlated electronic systems and further shares common ground with understanding the energetics behind exotic charge ordering in layered high-TC superconductors and other two-dimensional dichalcogenide materials43,44,45,46,47.

Methods

Single crystal growth

Single-crystals of CsV3Sb5 were grown using typical self-flux methods11,12. Owing to the highly reactive nature of elemental Cs, the subsequent preparation of CsV3Sb5 was conducted inside an argon-filled glove box. Cs liquid (99.98% Alfa Aesar), acid-etched vanadium granules (99.7% Alfa Aesar), and Sb shots (99.99% Alfa Aesar) were placed in alumina crucibles with frit discs, then sealed in Ar-gas purged evacuated quartz tubes. The ampule was heated to 1000 °C for 24 h, then slowly cooled to 600 °C at a cooling rate of 5–3 °C/h. The ampule was then centrifuged to remove the flux, with any remaining flux removed via mechanical cleavage.

Time-resolved X-ray scattering experiments

Time-resolved X-ray scattering (tr-XRS) experiments were conducted at the resonant soft X-ray scattering end station of the PAL-XFEL48. A single-crystal specimen of CsV3Sb5, with its surface normal parallel to the c-axis, was mounted on the cold finger of a liquid helium cryostat (base temperature ~ 20 K). The diffractometer was aligned to have a horizon scattering plane with the sample ac plane and π-polarised incoming X-rays. X-ray pulses had a full width at half maximum pulse duration of approximately 80 fs and a repetition rate of 60 Hz. Incident X-ray photon energies were chosen to target the CDW superstructure reflections: 1240 eV for the 2 × 2 × 2 CDW at (0.5 0 1.5) reflection and 980 eV for the 2 × 2 × 1 CDW at (0.5 0 1). IR photoexcitation of the specimen was induced using a femtosecond Ti:sapphire laser system (wavelength of 800 nm and pulse duration of 50 fs root-mean-square value). The mechanical delay stage controlled the time delay between the pump and probe pulses. The focused X-ray spot size at the sample position was 100 (H) × 200 (V) μm², safely within the fs-IR laser footprint of 500 (H) × 500 (V) μm². Each single-shot X-ray scattering signal was collected using an avalanche photodiode equipped with a high-speed digitiser. For all data collection processes, data were acquired at 30 Hz by interleaving pulses for data without laser pulses to ensure the full recovery of the specimen.

X-ray scattering measurement with temperature dependence

The CDW order parameters were determined from the integrated intensity of the CDW reflections through X-ray scattering experiments conducted at the synchrotron 6 A beamline of the PLS. Crystals were cryo-cooled using a liquid helium cryostat. The photon energy was fixed at 1580 eV, covering the 2 × 2 × 2 (0.5 0 1.5) and 2 × 2 × 1 (0.5 0 2) reflections.

Time-dependent density functional calculation

To investigate the total energy, optimised lattice parameters, and electronic structure in the ground state of CsV3Sb5 through first-principles calculations, density functional theory calculations were performed using the Quantum Espresso package49. The optimised lattice parameters for the 2 × 2 × 2 trigonal CsV3Sb5 system were a = 10.88 Å and c = 18.66 Å. Kohn-Sham wave functions were illuminated by a plane wave with an energy cut-off of 60 Ry. The Perdew (Burke) Ernzerhof generalised gradient approximation functional was employed to describe electron-electron exchange and correlations50. Core electrons and their effects on valence electrons were addressed using norm-conserving pseudopotentials. The Brillouin zone was sampled using a Monkhorst pack with a 3 × 3 × 2 mesh. Ionic structure relaxation was achieved by optimising positions with the force criteria of 1.0 × 10−5 eV Å−1.

To investigate light-induced dynamics using a first-principles approach, we employed Ehrenfest dynamics with real-time TD-DFT51. For time propagation, we utilised a Crank-Nicolson-type time-evolution operator with a time step of 4.8 attoseconds. The optimised Alternative SoD and TrH superstructures10,21 served as the initial geometries for the TD-DFT calculations. An oscillating electric field of gaussian-packet type (E(t)) was applied to the system through the vector potential term, with \(E\left(t\right)={dA}/{dt}\) with \(A\left(t\right)={A}_{0}{e}^{-0.5{[\left(t-{t}_{0}\right)/\sigma ]}^{2}}\sin \omega t\). The laser parameters in the simulation were set to match experimental conditions: ℏω = 1.54 eV and σ = 80 fs, with a laser power density of 3.6 × 1010 W cm−2 and 25% reduced power of 2.7 × 1010 W cm−2. Both power densities produced the same results qualitatively supporting that the interpretation is generally valid without specific laser fluence dependence. The detailed calculation settings mirrored those of the DFT calculations, except for the Brillouin zone sampling (1×1×1).