Ultrafast dynamics of vibronically dressed core excitons in graphite: a femtosecond RIXS perspective

Domain: physics
Published: 2025-12-29
Editorial outcome: major_revision

Abstract
Time-resolved resonant inelastic X-ray scattering (tr-RIXS) is a powerful technique for probing quasiparticle interactions in quantum materials under nonequilibrium conditions. Here, we implement tr-RIXS at the carbon K-edge to investigate the ultrafast dynamics of core excitons coupled to vibrational modes in graphite. Using femtosecond X-ray pulses from a free-electron laser, we monitor the temporal evolution of vibronically dressed excitons and their interaction with symmetry-selective optical phonons. By tuning the incident photon energy across the 1s → σ* resonance and analyzing the integrated inelastic sideband intensity, we reveal a detuning-controlled crossover between two complementary dynamical regimes. Phenomenological modeling and first-principles calculations reproduce both the magnitude and detuning dependence of the spectral-weight changes. In this work, enabled by the unique capabilities of X-ray free-electron lasers, we demonstrate how tr-RIXS can access coupled electronic and lattice dynamics with elemental and symmetry specificity, opening new routes to control vibronic interactions in light-element and low-dimensional quantum materials.

Introduction
Excitons, defined as Coulomb-bound electron-hole pairs, play a fundamental role in understanding various phenomena in condensed matter physics. These states emerge across a wide range of materials, including semiconductors, molecules, semimetals, low-dimensional systems, and metals with weak electronic screening1. Among excitonic subclasses, core excitons (CE) remain relatively unexplored. These excitons form when a photon excites an electron from a core atomic level into the conduction band, resulting in a strongly localized Frenkel excitonic state2. Despite their typically short lifetimes (≤10 fs, depending on the core level and atomic species), CEs significantly impact the scattering processes in material where exciton screening is ineffective.

A key manifestation of CE effects is the renormalization of X-ray absorption spectra (XAS). At the carbon K-edge, XAS provides critical insights into the electronic properties of molecules and graphitic systems2–11. However, the spectra are shaped by intermediate excitonic states, necessitating advanced theoretical modeling for accurate interpretation. Furthermore, CEs significantly influence the structure of resonant inelastic X-ray scattering (RIXS) spectra. Recent research demonstrates that CEs can activate optical phonons8,12–16, emphasizing the dynamic coupling between excitons and phonons. This coupling is particularly critical in time-resolved RIXS, where photoinduced screening of CEs and the excitation of strongly coupled hot optical phonons alter the spectroscopic fingerprints of exciton-phonon interactions.

The electronic screening of core holes, a complex and pivotal aspect of light-matter interactions, determines the spectral features in both XAS and RIXS. Although metals efficiently screen core holes because of their high density of conduction electrons, leading to negligible excitonic effects, materials with reduced screening capabilities can sustain bound excitonic states. CEs may distort the local crystal lattice in such systems, resulting in vibronically dressed excitons that enhance phonon activation.

Graphite, a two-dimensional material with pronounced electronic anisotropy, provides an exemplary case for studying CE-phonon interactions2,5,8,17. Experimental and theoretical investigations have shown that carbon 1s core holes in graphite, which are inadequately screened in this van der Waals system, trigger multiple scatterings of CEs with optical phonons. These phonons are activated by local Jahn-Teller (JT) distortions caused by the unscreened core hole.

In this study, our objective was to modulate the screening efficiency of core holes in graphite, induced by femtosecond extreme ultraviolet (XUV) pulses, and to monitor the temporal evolution of the vibronic dressing of CEs. By optically exciting the system to generate hot electrons in the conduction band, we increased the available charge density in this semimetal, enhancing the screening capability. The extent of screening was indirectly probed through the dynamics of the phonon sidebands in the RIXS loss spectrum, serving as a qualitative indicator of exciton-phonon coupling strength (ExPC). Throughout this work, the coupling between lattice vibrations and the core-excited state is referred to as exciton-phonon coupling, rather than the more general term electron-phonon coupling. This distinction is important, as the resonant inelastic signal in RIXS originates from interactions between phonons and the localized charge distribution associated with the core-exciton intermediate state. While early RIXS studies often described such coupling in terms of electron-phonon interactions, recent literature (e.g., 13) has clarified that, under strong resonance conditions, the extracted coupling constants should be more accurately interpreted as exciton-phonon in nature.

Only a handful of tr-RIXS studies have been reported to date, primarily targeting electronic and magnetic excitations in transition-metal compounds such as cuprates, iridates, and vanadates18–24. These pioneering works have demonstrated the potential of Free Electron Laser (FEL)-based tr-RIXS to resolve transient phenomena such as ultrafast melting and recovery of magnetic order, the interplay between spin and lattice degrees of freedom, and light-induced changes in orbital and charge correlations. Theoretical and computational advances have further highlighted the sensitivity of RIXS to coupled electron-lattice dynamics25,26. However, direct time-domain access to phonon excitations—particularly in light-element systems—has remained beyond reach due to technical challenges in both energy resolution and spectral interpretation.

To our knowledge, this is the first time-resolved RIXS study to report a pump-induced reduction of ExPC at the carbon 1s → σ* resonance in graphite, approximately 8 eV above the Fermi level, where the intermediate state lies in the σ conduction manifold. Previous ultrafast studies in graphitic systems have primarily focused on near-EF excitations, revealing that the electron-phonon coupling (EPC) strength can either increase or decrease depending on the excitation conditions, such as in coherent-phonon generation or electronic softening mechanisms27,28. More recently, time-resolved experiments and first-principles simulations in transition-metal dichalcogenides have demonstrated that EPC itself can be renormalized in nonequilibrium conditions, with modifications in phonon lifetimes, band dispersions, and mode-specific coupling matrix elements under optical pumping29,30. However, those studies were limited to low-energy Dirac-like bands and did not probe the deeper-lying σ* states relevant for core-level RIXS. These works collectively underscore that EPC is a dynamic quantity, not a fixed material parameter, and its evolution can serve as a sensitive probe of many-body interactions under ultrafast excitation. Our findings extend this perspective, revealing how photoexcited π − π* carriers transiently suppress ExPC via enhanced screening in the σ* manifold.

By studying the dynamics of ExPC at the carbon K-edge in graphite, we capture the femtosecond evolution of vibronically dressed CE following ultrafast photoexcitation and establish a new spectroscopic window into phonon-coupled excitonic states and extend the reach of tr-RIXS into the domain of weakly screened systems.

Results
Pump-probe RIXS scheme and experimental layout
A conceptual scheme of the RIXS process in graphite is depicted in Fig. 1a, b. An incident X-ray photon promotes an electron from the 1s core orbital in the ground state to the 2sp2 σ bands, where it experiences a partially screened potential caused by the core hole. The presence of the core hole in the intermediate state induces a substantial modification in the local atomic configuration around the interaction site5,12,16,31–34. This modification arises from the ionic coupling between the core exciton and lattice phonon systems, leading to dynamical symmetry breaking within the core-excited states. As a result, a significant JT distortion (~0.20 Å)8,35 occurs, displacing the core-excited atom from its equilibrium position in the ground state.

The excited electron subsequently relaxes in a few femtoseconds (the inverse of the natural linewidth Γ associated with the core-hole state) to fill the core hole, emitting a photon in the process. The energy difference between the incident and scattered photons manifests as overtones corresponding to the energy of the phonons ℏωp remaining in the final state as depicted in Fig. 1b.

Representative static RIXS loss spectra measured in this experiment are shown in Fig. 1c. The black and gray curves correspond to on-resonance and off-resonance conditions, respectively, and were acquired with an experimental energy resolution of approximately 350 meV. For comparison, a high-resolution RIXS loss spectrum from Feng et al.12, measured at a similar incident photon energy with a resolution of ~50 meV, is also included. This comparison highlights the presence of a broad loss tail in our on-resonance spectrum, consistent with previously reported vibronic progressions despite the lower resolution.

The high-resolution carbon K-edge RIXS spectrum of graphite exhibits a prominent elastic peak at 0 eV energy loss, accompanied by a sequence of equally spaced inelastic features attributed to vibronic replicas arising from ExPC12,14,36. These overtones correspond primarily to the coupling between CE and the zone-center E2g phonon mode, with an energy of approximately 196 meV, and follow a characteristic Poissonian progression as described by the Ament model31. Each overtone reflects an increasing number of phonon excitations, representing a quantized vibrational ladder coupled to the intermediate core-exciton state37. Recent work by Dashwood et al.14 demonstrated that a complete interpretation of this fine structure requires a full multi-mode analysis, as the phonon sidebands include contributions not only from the E2g mode at Γ but also from finite-momentum phonons such as the A0 mode at K, which produce asymmetric lineshapes and mixed-mode replicas. In particular, the detuning dependence of the multiphonon envelope was shown to be sensitive to both the phonon dispersion and the momentum-dependent EPC matrix elements.

In the present experiment, individual vibronic overtones are not resolved due to the limited energy resolution (see spectra in Fig. 1c). However, a broad inelastic sideband is clearly visible in the resonant on- and off-resonance spectra and represents the loss tail. Reprinted with permission from X. Feng et al., Phys. Rev. Lett. 125, 116401 (2020). Copyright (2020) American Physical Society. d Schematic representation of the RIXS excitation scheme and photoinduced processes. The green solid arrow indicates the optical pump pulse, tuned to the resonant energy corresponding to the π → π* transition at the M saddle point of the Brillouin zone (BZ). This process generates photoexcited hot electrons that are primarily confined between the graphene layers. Due to the peculiar band topology of graphite, the resulting bottleneck in the phonon channel deexcitation prolongs the average lifetime of valence-band quasiparticles27,41,78. The blue dashed arrow represents the X-ray probe absorption process, promoting a 1s core-level electron into the σ* conduction band at the Γ point. The intermediate state persists for an effective scattering duration τs, which depends on both the intrinsic core-hole lifetime and the photon energy detuning36,79.

Static and pumped RIXS across the CK σ-edge in graphite
The X-ray absorption spectrum of graphite is shown in Fig. 2a at both the π and σ thresholds. The peak at the lower photon energy (~284 eV) corresponds to the transition of the 1s photoelectron into the unoccupied out-of-plane 2pπ* orbitals (1s → π*). Conversely, the peak at a higher energy (~291.8 eV) is assigned to contributions from the hybridized 2sp2 σ in-plane σ* (C-C) orbitals. This higher energy edge does not directly reflect the electronic dynamics induced by the photoexcitation of the π → π* transition. Instead, it primarily responds to structural changes within the material’s configuration50. The graphite XAS is predominantly influenced by Frenkel-type excitonic effects at resonance energies. The Frenkel-like exciton is primarily localized on the core-excited site with appreciable weight on nearest neighbors (spatial extent of a few bonds), rather than a fully delocalized Wannier state2,4,11,53.

The one-electron density of states alone does not explain the absorption spectra because the excited electron occupies a highly localized state pulled off the bottom of the band gap. This mechanism leads to the appearance of white lines and a significant modification of the XAS cross-section54. Similar effects are evident in the resonant emission spectra of graphite at the carbon K edge7,8,55–58.

In Fig. 2b, c, the experimental data illustrate the impact of core-exciton vibronic interactions on the loss spectra in both the ground and the optically excited states. Figure 2b shows the unpumped loss spectra of graphite (black curves), recorded at FEL photon energies (indicated by coloured markers in panel a) tuned across the K σ resonance. These spectra are plotted as a function of energy loss and displayed in order of increasing photon energies. The on-resonance spectra are compared with an off-resonance unpumped spectrum (blue curve), recorded at a photon energy beyond the absorption edge (blue open circle in Fig. 2a). As aforementioned, when the photon energy hν is tuned close to the absorption resonance (hνres ~291.8 eV), thereby reducing the energy detuning value Ω = h(ν − νres), an asymmetric incoherent loss shoulder emerges, as indicated by the coloured areas between the blue and black curves in Fig. 2b. Figure 2c displays the corresponding pumped loss spectra (red solid lines), acquired at a fixed pump-probe delay of 150 fs. These are compared against two references: (i) the unpumped spectra recorded at the same photon energies (black dashed lines), and (ii) the off-resonance spectrum (blue curve), whose intensity is rescaled as discussed below.

The lineshape of the off-resonance spectrum lacks the asymmetric loss tail and exhibits a symmetric profile. This symmetry arises because, in the emission process, the final state of the RIXS process mirrors the initial state and does not involve ExPC scattering (see Supplementary Note 7 in SI for further discussion). This portion of the spectrum is commonly referred to as the coherent component. We note that the apparent increase in spectral intensity at energy losses below −2.5 eV in the off-resonant spectrum shown in SI is not due to an asymmetry of the elastic or inelastic phonon features, but rather reflects the onset of valence band emission, as shown in the full-range spectrum provided in the SI Supplementary Note 2, Fig. 2.

Particular attention should be given to the pair of pumped and unpumped spectra measured off-resonance (top spectra in panel c of Fig. 2, blue open dot), specifically at a photon energy of 294.5 eV with a detuning of approximately Ω = 2.7 eV. In this case, the overtone tails are absent due to the large detuning value, and the spectra are symmetric. Furthermore, the effect of the pump on the excited spectrum is negligible, as indicated by the complete overlap of the pumped and unpumped spectra. This lack of pump-induced changes in the off-resonance spectra is a key observation, highlighting that the influence of the photoinduced electron-hole pairs predominantly impacts the excitonic state and its dynamics. Properties such as exciton energy, screening, and vibronic coupling are affected, while the density of states remains largely unchanged in the out-of-equilibrium state.

In this work, the limited energy resolution (~350 meV) of the RIXS spectra prevents a clean spectral separation between the elastic peak and low-energy phonon sidebands. As a result, direct access to the absolute inelastic intensity is not feasible. To overcome this limitation, we introduce a relative metric R(Ω) that tracks the integrated excess weight in the loss region as a function of photon energy detuning Ω. Importantly, R(Ω) is not a direct measurement of the absolute phonon spectral weight, but rather a baseline-independent proxy that captures its detuning- and pump-dependent modulation. To ensure that this proxy is robust and not sensitive to arbitrary assumptions about the elastic baseline or absorption cross-section, we implemented three independent normalization schemes: (i) a zero-loss alignment of the off-resonance spectrum as elastic reference, (ii) a normalization of the resonant spectra to the XAS absorption threshold at the corresponding photon energy, and (iii) an XAS-weighted scaling of the reference spectrum before subtraction. These approaches are described in detail in Supplementary Note 5 in SI, Fig. 6). All three methods yield a consistent trend for R(Ω), demonstrating that our conclusions do not rely on a specific treatment of the elastic baseline or absorption cross section. Because no method allows for a complete deconvolution of elastic and inelastic components at this resolution, we do not attempt to extract absolute ExPC constants from R(Ω). Instead, we focus on relative changes in R(Ω) between the pumped and unpumped conditions. These changes are interpreted as qualitative signatures of ExPC modulation in the non-equilibrium regime.

For the pump-probe data, we applied the same zero-loss rescaling procedure using the off-resonant reference spectrum, ensuring full consistency with the unpumped analysis. This choice allows direct comparison between equilibrium and photoexcited conditions within the same normalization framework, without introducing additional assumptions about absorption or elastic-inelastic separation.

Detuning Ω controls inelastic weight and scattering time
The experimental inelastic proxy R(Ω), shown for both pumped Rp(Ω) (red colored stars) and unpumped Rup(Ω) (black colored stars) data in Fig. 3a, displays a clear resonant enhancement near the 1s → σ* absorption threshold and a monotonic decay at larger detuning. The detuning dependence of R(Ω) is qualitatively reproduced by integrated inelastic intensities computed from static Ament models incorporating one and two phonon modes. The resulting theoretical curves are shown in Fig. 3a as dashed blue (one-phonon) and red (two-phonon) lines, and compared to the experimental unpumped R(Ω). These two model variants yield nearly identical detuning trends after convolution with the experimental resolution, highlighting the robustness of R(Ω) as a resolution-limited indicator of total vibronic strength, and its insensitivity to the specific phonon composition assumed. The underlying RIXS spectra generated from these models are shown in Supplementary Fig. 3 and Fig. 5, while the phonon coupling strengths M, Huang-Rhys factors g, and mode energies ω are listed in Supplementary Table 2. These parameters are extracted from high-resolution CK-edge studies by Feng12 and Dashwood14. Specifically, the two phonon modes used, ω1 = 0.196 eV and ω2 = 0.165 eV, correspond to the dominant E2g mode and a secondary lower energy mode, respectively. The associated couplings (M1 = 0.42 eV, M2 = 0.30 eV) and Huang-Rhys parameters (g1 = 4.59, g2 = 3.31) were chosen to reflect the strength and spacing of vibronic sidebands reported in those works. Additional details on the modeling assumptions, numerical implementation, and convolution procedure are provided in SI Supplementary Note 3, Figs. 3 and 4. This modeling is motivated by two considerations. First, under the moderate experimental energy resolution (~350 meV), individual phonon overtones are not resolved, and only the integrated inelastic weight in the [−2.5, 0] eV range can be reliably tracked.

Second, first-principles calculations of the electron-phonon coupling (see Fig. 3 panel c, and SI Supplementary Note 6, Fig. 7) show that the dominant coupling at the accessed energies involves zone-center optical phonons near the Γ point in the σ* conduction manifold. This result reflects the strong renormalization of the unoccupied σ* states by lattice vibrations, most prominently visible at k ≃ Γ, where the parabolic conduction band exhibits the largest spectral deformation compared to the equilibrium DFT band (white dashed line). This deformation arises from electron-phonon interactions and points to a dominant coupling to Γ-point optical phonons, in particular the E2g mode. Physically, when resonantly probing the C 1s → σ* transition, the excited electron occupies high-lying states in the σ* manifold several eV above EF, forming a bound core exciton with the localized 1s hole. At these excitation energies (~8 eV above EF), the electron resides near k=Γ, where the available phase space for scattering strongly favors small-q phonon modes. The electron-phonon phase space is constrained by momentum conservation, so the large density of states and the small-q nature of the transition point to the prevalence of Γ-point optical phonons as the dominant scattering channel. While the σ* band extends toward the M point - where van Hove singularities and finite-q phonons (e.g., at K or M) might contribute - our ab initio results show that the electron-phonon matrix elements and corresponding spectral renormalization are significantly weaker at those k-points. Therefore, Γ-point E2g phonons are expected to dominate the vibronic structure in the accessible intermediate-state manifold. This picture is further reinforced by prior theoretical work on the energy-dependent evolution of electron-phonon coupling channels in graphite and graphene. In particular, calculations by Margine and Giustino59 and Mazzola et al.60 demonstrate that the dominant phonon coupling mode depends strongly on the excitation energy. Near the Dirac point, coupling to the A0 phonon mode at the K point dominates, whereas at higher excitation energies associated with σ-like bands, the coupling shifts toward Γ-point optical phonons (E2g) and out-of-plane ZO modes. Extrapolating this trend to the higher-energy σ* resonance above EF indicates that small-q phonons are the most efficient scattering channels, consistent with the strong Γ-localized renormalization seen in our spectral-function calculations. Taken together, these results provide a solid microscopic foundation for employing an effective Einstein-mode description to capture the detuning dependence of the integrated inelastic spectral weight. They also justify the use of a single dominant mode in the phenomenological Ament-model envelope and reinforce the interpretation that the observed inelastic response arises primarily from coupling to zone-center optical phonons, without invoking phonon-mode resolution or fine-structure reproduction.

To contextualize this detuning behavior, Fig. 3b schematically illustrates the detuning dependence of the effective scattering time τs(Ω)-the characteristic duration during which the intermediate core-excited state remains active and can exchange energy with other degrees of freedom (see Supplementary Note 7 in SI, Fig. 8). This duration determines the temporal window over which phonon interactions can imprint signatures onto the RIXS final state. Near resonance (|Ω| ≪ Γ), τs is long and approximates 1/Γ, allowing sufficient time for vibronic dressing of the core exciton and strong coupling to optical phonons. In contrast, far off-resonance (|Ω| ≫ Γ), τs ~ 1/|Ω| becomes too short for coherent phonon processes to develop, and the inelastic intensity is suppressed. The crossover between these regimes follows τs(Ω) = 1/sqrt(Ω2 + Γ2), as introduced by Gel’mukhanov and co-workers36,61 and further discussed in15,31. This framework highlights how tr-RIXS acts as a temporal filter, selectively probing excitations based on their intrinsic timescales.

Upon optical excitation (pump-probe delay ~150 fs), the integrated inelastic weight Rp(Ω) is significantly reduced compared to the unpumped case Rup(Ω), consistent with transient screening of the core exciton and a weakening of ExPC. The contrast between pumped and unpumped spectra decreases progressively with detuning and vanishes far from resonance. This behavior reflects the detuning-dependent sensitivity of the RIXS cross section: near resonance, the intermediate core-excited state is strongly formed, allowing efficient coupling to lattice vibrations, whereas off-resonance the intermediate state becomes rapidly virtual and the interaction time (τs) too short for vibronic processes to develop. Consequently, the diminishing difference between R and Rp originates from reduced exciton-phonon interaction sensitivity at large |Ω|, rather than from changes in pump efficiency or overall screening strength. Since R integrates all unresolved phonon contributions, its suppression upon photoexcitation provides a clear qualitative signature of reduced ExPC in the σ* manifold under nonequilibrium conditions.

The effects of the optical pump on the parameters R (representing the inelastic component of the spectra) and r (the rescaling factor representing the coherent component, see caption of Fig. 2) suggest the following scenario. At a fixed delay of 150 fs between the pump and probe pulses, the coherent component r decreases compared to the unpumped case. Since r reflects changes in the absorption cross-section, its reduction indicates a decrease in the white line intensity characteristic of the resonant K-edge XAS spectrum. As the white line directly results from Frenkel core-exciton formation, this reduction provides initial evidence of core-exciton screening.

Interestingly, the similar detuning dependence of both R and r suggests that core-hole screening by the hot electrons and energy transfer from the electrons to the phononic system occur simultaneously. Johannsen et al.45 have shown that ultrafast electron dynamics in graphene, and similarly in graphite, involve rapid electron-electron scattering and thermalization of the electronic subsystem. This aligns with studies reporting sub-picosecond energy transfer to strongly coupled optical phonons, followed by energy dissipation through optical phonon emission46,62. These timescales agree well with the evolution of the phonon sideband spectral weight observed in the present study.

Detuning-dependent ultrafast dynamics
The temporal evolutions of the relative change ΔR(Ω, t)/R0(Ω) are plotted in the main panel of Fig. 4. Here, R(Ω, t) is the integrated inelastic RIXS weight (phonon-sideband proxy), and we plot ΔR/R ≡ [R(Ω, t) − R0(Ω)]/R0(Ω), where R0(Ω) is taken from the unpumped (negative-delay) spectrum. These dynamics were recorded at four different FEL photon energies across the resonance threshold, as indicated by the arrows in the inset of Fig. 4a. The analysis of the dynamic traces was carried out using a model double exponential decay-recovery function, as outlined in Supplementary Note 8 in SI, with a rapid decay time followed by a slower recovery process. The values corresponding to these ultrafast dynamic processes are plotted (black open circles) in the inset of Fig. 4a. The time traces reveal two distinct regimes as a function of the energy detuning Ω governed by different physical mechanisms. Rather than a sharp boundary, the time traces display a smooth crossover, whereby the relative weights of two mechanisms evolve continuously as Ω approaches the resonance threshold or moves away from it. As a result, the two regimes coexist, with their relative contributions to the ΔR/R dynamics varying continuously with Ω.

For small detuning (near threshold), the effective intermediate-state time is τs ≈ 10 fs (see also Supplementary Note 7 in SI, Fig. 8), and the inelastic sideband weight decays rapidly with a ~65 fs time constant, close to our resolution (Fig. 4a). This fast component reflects ultrafast screening of the core exciton by photoexcited carriers, which reduces exciton-phonon interactions and suppresses the local Jahn-Teller distortion; the corresponding microscopic picture is schematized in Fig. 4b by a transient displacement of a single carbon atom from equilibrium. The selectivity of this near-edge response, dominated by symmetry/orbital-resolved core-exciton intermediates at the Kσ edge, is consistent with attosecond K-edge measurements that resolve near-edge carrier dynamics on tens of femtoseconds and with theoretical descriptions of excitonic/vibronic near-edge behavior50.

As the detuning increases from the absorption threshold, τs drops below a few femtoseconds, suppressing the efficacy of coherent local lattice distortions. In this off-resonant window, the dynamics slow to a robust relaxation time of τ ~330 fs (Fig. 4a), which we assign to a nonthermal screening regime governed by two concurrent processes: energy-dependent quenching of the Jahn-Teller ExPC and the buildup of hot phonons via impulsive electron-phonon scattering. The evolution of this behavior with detuning is naturally explained by a growing scattering phase space: as the excitation energy moves toward the high-DOS σ* manifold, both electron-electron and electron-phonon scattering rates increase, enhancing quasiparticle decay and energy transfer to lattice vibrations. This picture is supported by GW-based lifetime calculations in graphite41, which show markedly reduced carrier lifetimes near van Hove singularities (e.g., π* saddle at M), and by attosecond K-edge XANES50, which identifies distinct relaxation pathways for π*- and σ*-derived states and links the σ* response to strong coupling with optical phonons on few-hundred-fs scales. The schematic in Fig. 4c depicts this off-resonant regime as the buildup and relaxation of collective hot phonon oscillations (SCOPs). While fundamentally different from near-Fermi-level dynamics, our observations are consistent with the broader hierarchy of relaxation timescales in graphitic systems. Specifically, (a) electron-electron thermalization near the Fermi level occurs within 10–100 fs, as measured by trARPES and THz spectroscopy63–65; (b) the sub-ps evolution of SCOP populations via strong mode-projected electron-phonon coupling is well documented in pump-probe and ultrafast optical studies62,65; and (c) full lattice thermalization and macroscopic strain effects develop only at multi-ps delays66–68. The off-resonant ~330 fs response observed here occupies a distinct window between ultrafast screening and long-timescale lattice expansion, governed by energy-resolved phonon dynamics. Finally, we stress that unlike low-energy probes such as trARPES and UED, which primarily access Dirac-like carriers near EF, tr-RIXS selectively addresses symmetry- and orbital-resolved excitonic states at the C K-edge, accessing a unique sector of the scattering phase space that governs nonthermal coupling pathways and hot-phonon behavior in the σ* regime.

To summarize, detuning acts as a selective control knob for complementary dynamical channels in graphite. Near the absorption threshold, tr-RIXS accesses symmetry- and orbital-resolved core-exciton intermediates at the Kσ edge, revealing a tens-of-femtoseconds suppression of the Jahn-Teller distortion driven by ultrafast exciton screening. As the detuning moves away from threshold, the evolving scattering phase space shortens electronic lifetimes and shifts the response into a nonthermal hot-phonon regime, where SCOPs are impulsively populated and relax on a few-hundred-femtosecond timescale41,50,62,65,69. This off-resonant regime corresponds to excitation energies approaching the σ* density of states, approximately 8 eV above the Fermi level, where the enhanced electronic screening originating from π → π* transitions (and the concomitant rise in carrier and phonon temperatures) leads to a marked reduction of the effective ExPC. The experiment therefore provides, for the first time, a direct observation, albeit qualitative, of the ultrafast modification of the ExPC constant g2 at high excitation energies, a parameter that is commonly assumed to remain fixed in time-resolved studies. These findings demonstrate that photoexcitation can dynamically tune the coupling strength between electronic and lattice degrees of freedom, providing a new handle on nonequilibrium screening phenomena in light-element materials. Subsequent anharmonic redistribution of the hot-phonon energy to acoustic modes46,52 and, at later times, full lattice thermalization and strain on multi-ps scales66–68 complete the energy-flow pathway. Overall, tr-RIXS reveals a previously unexplored regime in which the ExPC itself becomes transiently modified by the evolving screening environment, opening new possibilities for manipulating vibronic interactions at the core level.

Methods
Sample preparation
Time-resolved RIXS experiments were performed on a highly oriented pyrolytic graphite (HOPG) sample. Immediately before insertion into the UHV chamber of the MagneDyn endstation, the sample surface was freshly peeled in air to remove the topmost contaminated layers and expose a clean basal plane. The sample was then mounted with the graphite ab planes approximately perpendicular to the surface normal, such that the scattering geometry maximized sensitivity to in-plane σ states at the CK σ threshold.

Tr-RIXS measurements
The experiment was carried out at the time-resolved RIXS endstation of the MagneDyn beamline at the FERMI FEL (Elettra Sincrotrone Trieste, Italy)38. A standard pump–probe configuration, as described in ref. 38 was employed to probe the ultrafast dynamics of CE in graphite. For the probe, an extreme-ultraviolet/free-electron laser (FEL) pulse was tuned across the carbon K edge, resonant with the 1s!2sp2 σ transition (the Kσ threshold). The FEL polarization was maintained in the horizontal scattering plane, providing a substantial in-plane electric-field component and thereby enhancing the cross-section for excitations into the σ-bonding orbitals in the ab plane. The FEL beam impinged on the sample at an incidence angle of 30∘ with respect to the surface normal, quasi-collinear to the optical pump beam. Under these conditions, the scattering geometry (30∘ incidence and ~90∘ detection) corresponded to a small momentum transfer |q| ≈ 0.26 Å−1, close to the Brillouin-zone center, where zone-center optical phonons are preferentially probed. The incident FEL bandwidth, and hence the source energy resolution, was approximately 60 meV (see Supplementary Note 1 in the Supplementary Information). Inelastic RIXS spectra were recorded with a Scienta XES355 soft X-ray spectrometer70. Representative static loss spectra, acquired with this configuration, exhibited an overall experimental energy resolution of ~350 meV, obtained from the width of the elastic peak and dominated by the spectrometer response. The resonantly emitted photons were detected on a two-dimensional detector on a stroboscopic, pulse-to-pulse basis, enabling single-shot acquisition of spectra at each pump–probe delay. Details of the absolute energy calibration and determination of the instrumental energy resolution are provided in Supplementary Note 1 in the Supplementary Information. The sample was photoexcited by the third harmonic of the FERMI User laser, generated from the fundamental at 795 nm. The resulting ultraviolet pump pulses had a wavelength of 265 nm (photon energy 4.71 eV), p polarization, and operated at a repetition rate of 50 Hz38,71,72. Each pump pulse carried an energy of approximately 10 μJ at the sample. Taking into account the measured pump spot size and an incidence angle of 32.5∘ with respect to the surface normal, the optical fluence at the sample surface was about 32 mJ/cm2, corresponding to an estimated excitation of ~14% of the carbon atoms, as detailed in Supplementary Note 10 in the Supplementary Information. The pump photon energy was chosen to resonantly drive the π → π* transition at the M saddle point in the graphite Brillouin zone, thereby exciting valence quasiparticles in the 2p orbitals while keeping them decoupled from the σz states directly probed by the 1s!2sp2 σ core transition. This configuration mitigates saturation of the absorption channel and avoids pump-induced distortions of the x-ray absorption lineshape. The temporal overlap between pump and probe was established using a standard optical cross-correlation procedure at the beamline38, yielding an overall time resolution of approximately 50 fs (FWHM), limited by the convolution of the FEL and optical pulse durations and the timing-jitter compensation scheme. In this regime, the lifetime of the optically excited quasiparticles at the M point exceeds the experimental time resolution and significantly surpasses the typical C 1s core-exciton lifetime (~10 fs), ensuring that the tr-RIXS response is governed by the evolution of a long-lived valence-carrier population rather than by the core-hole decay alone. For additional background on the graphite C 1s absorption edges and excitonic response, we refer to Ahuja et al.2.

Theory
Ground state electronic band structure was calculated with Quantum Espresso (QE) plane-wave code with the use of semi-local PBE exchange-correlation functional73. Phonon dynamics and electron-phonon coupling calculations were performed with density functional perturbation theory74, where we combined QE-PHonon and EPW codes75. The latter code uses Wannier interpolation76 to provide phonon energies and electron-phonon matrix elements on a denser momentum grid, which are then needed to simulate Fan-Migdal electron self-energy and electron spectral function77. More details can be found in Supplementary Note 6 in the Supplementary Information.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, Malvesuto et. al., look at the effect of pumping graphite on the (low resolution) RIXS specrtum following\npumping. The work is particularly timely, as LCLS-II is just turning on now which should increase the importance of time\nresolved RIXS significantly. The RIXS spectrum as a function of detuning energy and being pumped is measured. The\nspectrum is then broken down (to over simplify) by what part is due to electron phonon coupling and what part isn't. They use\nthis to determine information about graphite and its excited states.\nWhile the results are well supported, and the methods appear to be sound, there are several issues I would like to see\nresolved. In particular, the presentation does not make it easy for the reader to follow. Figure 2 is challenging to follow along.\nThe presentation of this figure is not optimal, and the authors should strongly consider splitting this figure into two figures. In\nparticular, figure d is challenging to understand, as the caption isn't particularly adequate, and one has to dig through the text\nand the caption to really understand what is going on here. Relatedly, while I'm not sure figure 2S should be in the main text,\nand in a sense the authors commitment to brevity is laudable, it makes it harder to follow as one has to read the SI and return\nto really understand what is being presented. Incorporating some of that figure 3 might (or might not) help with clarity.\nBasically, while I quite like the manuscript, I spent a noticable portion of time trying to figure out what was being presented.\nIn terms of science, a large portion of the results is pinned on the fitting of equation 1, which has 3 free parameters (although,\nthe justification for using this equation is well supported and justified). The changes between the ground and excited state\nare quite large, but it is completely opaque to the reader how sensitive these fitting values are. Given that a large portion of\nthe interpretation hinge on this, it would be nice to understand the sensitivity here. (Ultimately I think this will not totally the\nconclusions, as changes are readily visible anyways so I think that is still on safe ground no matter what).\nTriviality - Your third harmonic has a typo and should be 265 nm not 263 nm assuming 795 nm fundamental.", "reviewer_2": "Malvestuto and collaborators present a carbon 𝐾-edge RIXS pump-probe study of graphite. We\nbelieve the authors are the first to have considered ultrafast RIXS measurements of phonons. We\nconsequently hold the methodological innovation and ambition of the work in very high regard.\nThat said, we have some scientific concerns.\n1. The data in Figs. 2b and 2c appear to be cut off. The full shape of the elastic line on the right is\nnot visible, and the complete extent of the key inelastic component is also not shown. It is\ndifficult to determine which values correspond to zero intensity due to the same issue of cut-offs.\nThe full extent of the spectra should be plotted, if available. If these data were not collected, a\ncomment should be added to the text.\n2. The energy resolution of the experiment (350 meV) is substantially larger than the energy scale\nof the phonons (200 meV). As a result, the phonon series appears as a blob rather than a sequence\nof peaks. Individual phonons cannot be identified in the data, and the first order phonon cannot be\nunambiguously separated from the elastic line. We highlight this because it unfortunately limits\nthe information content and the degree of certainty with which conclusions can be drawn.\n3. In equilibrium, it has been previously shown that the low-energy window is dominated by\nphonons. In the transient state, however, carriers are excited and may be scattered within a low-\nenergy electronic continuum. How can the authors exclude a contribution from this effect?\n4. The off-resonant spectra in Fig. 2b show significant structure, dropping to lower values around\n–1.2 eV and then rising again. Given the plotting window, we cannot be sure whether this line\nshape is indeed symmetric, as claimed in line 267.\n5. We ask the authors to justify the procedure of scaling the off-resonant spectrum to match the\nintensity at zero energy and then subtracting it. This does not necessarily seem like a robust\nmethod for isolating the phonons, given (a) the intensity away from the inelastic region,\nas mentioned above, and (b) the fact that some phonon intensity will appear at 0 eV due to the\nenergy resolution being larger than the phonon energy.\n6. The Ament model has not been shown to effectively explain the overtone modes in graphite.\nPrevious studies have demonstrated that the data cannot be explained solely in terms of\novertones of the Γ-point phonon but instead involve combinations of phonons from different\nparts of the Brillouin zone for higher-order overtones (see Refs. [1,2]). In light of this, it is unclear\nwhether Equation 1 is appropriate for the data. Furthermore, Equation 1 clearly yields a\nprediction for the full shape of the spectrum as a function of energy and not just a prediction for\nthe total intensity. It is concerning not to see a comparison between the predicted energy\ndependent intensity for the model and data in the draft. This must be added.\n7. The value of 𝑀 from [1] has been contested in [2]. This controversy needs to be acknowledged\nand discussed.\n8. It would be valuable to include some discussion situating the present work in the context of\nother XFEL RIXS experiments. Only a handful of ultrafast XFEL RIXS studies probing\nquasiparticles have been published since the first experiments about a decade ago, so it should\nbe straightforward to provide a comprehensive overview.\nOverall, this work is quite novel in many respects, and we are glad to see it carried out. However,\nwe have concerns regarding both the experiment and the data analysis. Conducting the\nexperiment with an energy resolution that cannot resolve the phonons in question poses a\nserious limitation to the information obtained.\nFor instance, it raises concerns about whether the intensity of the first\nphonon can be uniquely distinguished from the elastic line, and whether other inelastic signals,\nsuch as charge scattering, might exist out of equilibrium and might be mixed up with the phonon\nspectrum. The analysis appears to rely on an equation that has not been shown to accurately model\nthe material under investigation. The omission of a basic test to verify whether the equation\nreproduces the energy-dependent shape of the equilibrium and transient spectra is a significant\nshortcoming of the current draft.\nWe believe these issues are, in principle, fixable to make the work publishable. However, we\nremain skeptical about whether these problems can be resolved convincingly enough to merit\npublication in Nature Communications.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_4": "In this manuscript, the authors present a time-resolved RIXS study on graphite, using a UV (4 eV) pump pulse to generate\nphotoexcited carriers and investigate the effect of photo-induced screening on the coupling between phonons and the core-\nhole exciton created by the XUV probe photon.\nBy tuning the incident photon energy across the carbon K-edge resonance, the authors probe how photo-induced screening\nmodifies both the elastic (coherent) and inelastic (incoherent) parts of the RIXS spectrum associated with the Jahn-Teller\n(JT) distortion from exciton-phonon coupling. While individual phonon peaks are not fully resolved, the spectral changes are\nconsistent with prior literature.\nStrengths:\n• The experimental dataset is valuable and adds time-domain insight into exciton-phonon coupling and screening effects in\ngraphite.\n• The use of time-resolved RIXS to study suppression of incoherent phonon-related spectral features is a promising\napproach.\nMajor concerns:\n1. Clarity of interpretation:\nThe manuscript’s discussion switches between “exciton-phonon coupling” and “electron-phonon coupling” when describing\nthe fits of parameter R and its time evolution. This inconsistency creates ambiguity about the physical mechanism driving the\nobserved spectral changes. It is crucial for the authors to clarify whether the spectral dynamics arise predominantly from\nchanges in the JT distortion due to exciton-phonon coupling, or from broader electron-phonon interactions affected by\nscreening.\n2. Ambiguity in spectral origin:\nThe manuscript sometimes leaves unclear whether the changes in spectra with detuning or pump delay arise from\nmodifications to the JT distortion or from screening effects, making interpretation difficult for readers.\n3. Novelty claims:\nThe authors state that this is among the first demonstrations of time-resolved RIXS. However, to my knowledge, multiple\nrecent reviews and studies have demonstrated tr-RIXS probing dynamical processes and phase transitions in various\nmaterials. Additionally, electron-phonon coupling in graphite has been extensively studied previously. The present work’s\nnovelty lies primarily in demonstrating the time-domain suppression of incoherent exciton-phonon related features via\nphotoinduced screening, which is sometimes obscured in the manuscript’s framing. The authors should revise their novelty\nclaims accordingly.\n4. Suitability for Nature Communications:\nWhile the data are valuable, I am not currently convinced the manuscript meets the threshold for publication in Nature\nCommunications without addressing the above issues, especially clarity and novelty. Improvement in the discussion of\nexciton vs electron phonon coupling and stronger justification of the unique insight provided by their experimental approach\nwould significantly enhance the manuscript.\n________________________________________\nGeneral comments:\n• Citation clarity could be improved. For example, line 136 cites six references on JT distortion, but the exact source of the\nquoted JT magnitude (line 139) is not explicitly referenced, forcing readers to track through earlier citations.\n________________________________________\nSpecific comments:\nIntroduction:\n1. Line 72: The authors use the term “radiation-matter interactions.” This phrasing is unusual in the community, which\ntypically uses “light-matter interactions.” Do the authors intend to include non-photon radiation (e.g., alpha, beta particles)? If\nnot, “light” might be a clearer choice.\n2. Line 88: Referring to photoexcited carriers as an “electron-hole plasma” is not accurate here, as plasma usually implies a\nstate of free charges at high density. Consider revising this wording.\n________________________________________\nFigure 1:\n• Fig. 1c:\na. The authors claim an energy resolution of 350 meV. How was this determined? The off-resonance peak appears broader\nthan 350 meV, which raises questions about the actual resolution.\nb. Line 167 states a source bandwidth of ~60 meV, which seems contradictory to the 350 meV resolution claim. Please\nclarify this discrepancy.\nc. The “on-resonance” asymmetric peak shows small oscillations that do not match phonon peaks in the high-resolution\nreference [12]. Could the authors comment on their origin?\n• Fig. 1d: The colored pulses/arrows lack explanation in the caption and seem randomly assigned. Adding clear labels and\ndescriptions would improve reader understanding.\n• Line 197: The statement about “anomalous valence quasiparticle lifetimes” attributed to a phonon bottleneck and band\nstructure deserves further elaboration. What specifically is anomalous, and how does graphite’s band structure produce this\nbehavior?\n________________________________________\nFigure 2:\n• The static and pumped RIXS spectra (on and off resonance) are well presented. The authors attribute the asymmetric on-\nresonance lineshape to exciton-phonon coupling, which diminishes off resonance and upon pumping due to screening.\n• Line 313: The phrase “diminishing impact of the photoexcitation as photon energy deviates from resonance” is ambiguous.\nDoes this mean the screening effect weakens, the sensitivity to exciton-phonon coupling reduces off resonance, or the\nexciton is less effectively excited? Clarification is needed.\n• The pump-probe delay time shown in Fig. 2d is not specified and should be clearly stated.\n• The discussion inconsistently refers to changes in the incoherent spectral weight (R) as due to exciton-phonon coupling in\nsome places, but attributes it to electron-phonon coupling in the Eq. 1 discussion (line 343). This contradiction is confusing\nand should be resolved. Additionally, while screening should reduce exciton binding energy and lifetime, the authors\nassume an unchanged exciton lifetime in the nonequilibrium state (line 337), which appears inconsistent.\n________________________________________\nFigure 3:\n• Line 432: The off-resonance dynamics are attributed to thermal modification of interplanar distances, supported only by the\ntimescale (330 fs). This explanation is insufficiently developed. Could other mechanisms (e.g., optical phonons) contribute?\nThe authors should expand or qualify this interpretation.\n________________________________________\nIf the authors address the above points and clarify their interpretation and novelty claims, this manuscript would be\nsignificantly improved."}, "author_response": "Response to Reviewer #1:\nWe appreciate this constructive suggestion. In the revised version, we have split Figure\n2 into two separate figures:\n• Figure 2a–b now contains the XAS and unpumped/pumped RIXS spectra.\n• Figure 2c–d has been moved to a new Figure 3, dedicated to the analysis of\nintegrated inelastic spectral weights (R) and scaling factors (r), along with the\ncomparison to theoretical fits. We have expanded the figure captions to provide a\nclearer explanation and ensure that the panels can be understood independently from\nthe main text. We have also summarized key elements of Fig. S2 (now included in\nthe main text as part of revised Figure 3) for clarity.\n• In addition, we include in Figure 3b a conceptual illustration of the scattering process\nduration τ(Ω) as a function of detuning, which clarifies the physical origin of the\nobserved spectral changes.\nThese changes follow the Reviewer’s suggestion and aim to improve clarity by separating\nexperimental observations from interpretative elements. The figure captions have also\nbeen revised to ensure that each panel is self-contained and easily understood without\ncross-referencing the main text or supplementary material.\nIn terms of science, a large portion of the results is pinned on the fitting of equation 1, which has\n3 free parameters (although, the justification for using this equation is well supported and\njustified).\nThe changes between the ground and excited state are quite large, but it is completely opaque to\nthe reader how sensitive these fitting values are. Given that a large portion of the interpretation\nhinge on this, it would be nice to understand the sensitivity here. (Ultimately I think this will not\ntotally the conclusions, as changes are readily visible anyways so I think that is still on safe\nground no matter what).\nResponse: We thank the Reviewer for this thoughtful comment and for highlighting the\nimportance of clarifying the fitting procedure used in our analysis.\nAlthough Equation 1 involves multiple parameters, we emphasize that only one\nparameter—the exciton-phonon coupling strength M (or equivalently, the dimensionless\ncoupling constant g)—is treated as a free parameter in the fitting. The phonon energy ω₀\n= 0.196 eV and the core-hole lifetime broadening Γ = 0.304 eV are kept fixed throughout,\nbased on established values from the literature. Specifically, ω₀ corresponds to the energy\nof the dominant E₂g phonon mode in graphite, and Γ reflects the intrinsic linewidth of the\ncarbon K-edge (Sette et al., 1990), using the relation Γ = γ/ω₀ with γ/ω₀ = 1.55. The\ndetuning energy W is an independently controlled experimental variable and not a fitting\nparameter.\nTo address the Reviewer’s concern regarding the sensitivity and robustness of the\nextracted coupling values, we have now included a detailed error and sensitivity analysis\nin the revised Supplementary Information (Section A.6). This includes:\n• A quantitative assessment of uncertainties in the fitted parameter g, incorporating\nexperimental noise and model fitting tolerance;\n• A systematic test showing how moderate variations in the fixed input parameters\n(Γ, Ω, and ω₀) influence the extracted values of g and the integrated spectral weight\nR;\n• A demonstration that, despite limited energy resolution, the observed reduction in\ncoupling strength g between unpumped and pumped conditions is robust and\nstatistically significant.\nThese results confirm that our main conclusions regarding photoinduced suppression of\nexciton-phonon coupling remain valid within experimental uncertainties\nTriviality - Your third harmonic has a typo and should be 265 nm not 263 nm assuming 795 nm\nfundamental.\nResponse: thank you for pointing this out. We have corrected the typo — the correct\nwavelength for the third harmonic of a 795 nm fundamental is indeed 265 nm, not 263\nnm.\nReviewer #2 (Remarks to the Author):\nMalvestuto and collaborators present a carbon 𝐾-edge RIXS pump-probe study of graphite. We\nbelieve the authors are the first to have considered ultrafast RIXS measurements of phonons. We\nconsequently hold the methodological innovation and ambition of the work in very high regard.\nThat said, we have some scientific concerns.\n1. The data in Figs. 2b and 2c appear to be cut off. The full shape of the elastic line on the right is\nnot visible, and the complete extent of the key inelastic component is also not shown. It is\ndifficult to determine which values correspond to zero intensity due to the same issue of cut-offs.\nThe full extent of the spectra should be plotted, if available. If these data were not collected, a\ncomment should be added to the text.\nResponse:\nWe thank the Reviewer for this important observation. We agree that the truncation limited\ninterpretability. We have now replotted the spectra to include the full energy range,\ndisplaying the elastic peak and its tail where available (see revised Figs. 2b, 2c). For\ndatasets where the acquisition window was limited, we explicitly indicate this in the revised\ncaptions. The apparent truncation of the energy loss axis in Figs. 2b and 2c of the\nmanuscript was an intentional choice made purely for clarity purposes. Our goal was to\nhighlight the relative changes in the spectral weight within the low-energy inelastic region,\nwhere the phonon-related dynamics occur, and to avoid visual compression of the data\nnear the elastic line due to the large intensity contrast between elastic and inelastic\ncomponents.\nTo fully address the Reviewer’s concern, we now provide in this rebuttal letter a new figure\n(Figure 2S, SI Section A.2 ) showing the full extent of the measured spectra, including both\nthe elastic peak and the high-energy loss region extending into the valence band. This full-\nrange plot allows direct and quantitative evaluation of the entire spectral shape, including\nthe zero-intensity baseline and the complete profile of the elastic peak.\nWe emphasize that the data were collected over the entire energy loss range, and no\ntruncation was applied during measurement. The zero level is well defined and preserved\nboth in the full-range data and in the cropped version presented in the manuscript.\nWe also clarify that in all plots, the dotted lines represent the raw experimental data, while\nthe continuous curves are smoothed versions shown for improved visual readability. As\ndiscussed in response to Reviewer #4, this smoothing slightly reduces the effective energy\nresolution but does not affect the integrity of the spectral features within the phonon region.\nFurthermore, we note that the off-resonance spectra exhibit a cut-off above approximately\n1.5 eV energy loss, which corresponds to the physical limit of the detector active area at\nthe time of the measurement. Since the spectrometer and detector positions were kept\nfixed throughout the photon energy scan to maintain consistent alignment and response\nfunction, the maximum detectable energy loss varies slightly across different incident\nphoton energies. This experimental constraint is now explicitly mentioned in the revised\nfigure captions for improved clarity.\nFinally, we have updated the captions of Figs. 2b and 2c in the manuscript to explicitly\nstate that the displayed energy window was limited for clarity purposes and that the full\nspectral range is available and shown in the Supplementary Information (now updated with\nthe full-range plot).\nWe hope these clarifications fully resolve the concern\nFull and Zoomed Pump-Probe RIXS Spectra: On-resonance and Off-resonance\n12\n10\n8\n6\n4\n2\n-30 -25 -20 -15 -10 -5 0\nEnergy loss (eV)\nFigure R1 Panel A shows the full energy loss range of the measured RIXS spectra, including the elastic line and the\nvalence band region, for both on-resonance (red: pumped, black: unpumped) and off-resonance (red: pumped,\nblack: unpumped) conditions. The shaded regions indicate the pump-induced difference between pumped and\nunpumped spectra. Dotted lines represent the raw experimental data, while continuous curves correspond to\nsmoothed spectra shown for visual clarity. As discussed in our response to Reviewer #4, the smoothing slightly\nreduces the effective energy resolution but preserves the key spectral features of interest. Panel B shows the same\nspectra, zoomed in on the low-energy-loss region where phonon excitations dominate. The apparent rise in intensity\nat higher energy losses in the off-resonance spectrum reflects the onset of valence band emission and not an\nasymmetry of the elastic line. Additionally, the cut-off above approximately 1.5 eV observed in the off-resonance\ndata is due to the detector’s active area limit, since the spectrometer and detector positions were kept\nfixed during the photon energy scan to ensure geometric consistency. This figure demonstrates that the data cover the entire\nmeasured energy loss range and clarifies both the baseline and zero-intensity level, addressing the Reviewer’s\nrequest for full spectral visibility..\n2. The energy resolution of the experiment (350 meV) is substantially larger than the energy scale\nof the phonons (200 meV). As a result, the phonon series appears as a blob rather than a sequence\nof peaks. Individual phonons cannot be identified in the data, and the first order phonon cannot be\nunambiguously separated from the elastic line. We highlight this because it unfortunately limits\nthe information content and the degree of certainty with which conclusions can be drawn.\nResponse (see also response to point 6 below): we thank the Reviewer for raising this\nimportant point regarding the energy resolution of the experiment and its implications for\nthe interpretation of the phonon sideband structure.\nWe acknowledge the energy resolution (350 meV) is larger than the phonon energy (~200\nmeV), which precludes resolution of individual vibrational sidebands. However, previous\nstudies (e.g., Ref. 12 and Harada et al. [16]) demonstrate that in this resolution regime,\nvibronic features manifest as asymmetric tails in the loss spectrum. Our interpretation is\nbased on the observed trends in the inelastic tail intensity across detuning and time delays.\nThese changes are consistent with modulation of vibronic coupling, rather than continuum\nelectronic states.\nHowever, our analytical approach explicitly accounts for this resolution limitation by\nfocusing on the integrated inelastic spectral weight rather than the intensity of individual\nphonon peaks. This methodology follows the strategy adopted in earlier RIXS studies at\nthe carbon K-edge with comparable or lower energy resolution with respect to our case,\nincluding the work by Carlisle et al. and others, who interpreted the inelastic spectral\ncontinuum as a cumulative effect of multiple phonon excitations.\n).\nu\n.bra(\nytisnetnI\n-3Panel A: Full spectral range P-a3nel B: Zoom on phonon region\n10 10\n3.5\noff resonance spectra\n3\n2.5\n2\non resonance spectra\n1.5\n1\n-5 -4 -3 -2 -1 0 1 2\nEnergy loss (eV)\nThe fitting model employed in our study, based on the single-site coupling framework\ndeveloped by Ament et al. (Phys. Rev. B 83, 115123 (2011)), intrinsically captures this\ncumulative nature. In this formalism, the total inelastic weight, as described by the\nsummation over all overtone orders in Equation 1 of the manuscript, does not require\nexplicit spectral separation between the elastic line and the first phonon order. The\ndetuning dependence of the total inelastic spectral weight, even when unresolved into\nindividual phonon peaks, contains all the relevant information on the exciton-phonon\ncoupling strength.\nIndeed, Rossi et al. (Phys. Rev. Lett. 123, 027001 (2019)) and others used the intensity of\nthe first resolved phonon overtone to extract the “electron-phonon coupling” constant at\nhigher energy resolution, but the same underlying formalism (the Einstein oscillator model\nand the Ament formulation) governs the dependence of either the first overtone intensity\nor the cumulative inelastic weight on the detuning. As can be seen from direct\ncomparison of the Ament formula for single-order versus total intensity, both I (Δ) and\ntotal\nI (Δ) share the same characteristic dependence on detuning, shaped by the\n1st\ndenominator term (Δ+iγ+...) of equation 1, which reflects the combined effects of the core-\nhole lifetime and energy mismatch from resonance.\nTo address the Reviewer's concern, the figure below shows a direct comparison between\nthe first-order phonon intensity (dashed line) and the total inelastic spectral weight\n(solid line), both as functions of photon energy detuning Ω. The calculation follows the\nAment model as implemented in our fitting procedure.\nAs evident from the plot, both\nquantities exhibit the same\nfunctional dependence on detuning,\ndiffering only in absolute scale. This\ndemonstrates that, for the purposes of\ntracking the evolution of exciton-\nphonon coupling strength with\ndetuning, integrating the total\ninelastic weight (R) over the energy\nloss range provides equivalent\nphysical information to analyzing single\novertone intensities.\nAdditionally, it is important to emphasize that the main goal of our study is not to extract\nan absolute, high-precision value for the exciton-phonon coupling constant in\ngraphite, which is already well established in the literature. Instead, the focus is on\ntracking the relative change in exciton-phonon coupling under non-equilibrium,\nphotoexcited conditions induced by the resonant π−π∗ optical pump. This relative change\nis clearly observable, even with the available energy resolution.\nFinally, this experiment demonstrates, using graphite as a model system, how the\nextension of RIXS into the time domain can reveal dynamical changes in exciton-phonon\ncoupling, an aspect that remains inaccessible to static measurements, even those\nperformed at higher spectral resolution.\nWe have clarified this reasoning in the revised manuscript and have included an explicit\ndiscussion in the Supplementary Information (Section A.8) to emphasize both the validity\nand the limitations of our resolution-constrained approach.\n3. In equilibrium, it has been previously shown that the low-energy window is dominated by\nphonons. In the transient state, however, carriers are excited and may be scattered within a low-\nenergy electronic continuum. How can the authors exclude a contribution from this effect?\nWe thank the Reviewer for raising this important and nuanced point. In equilibrium, the\nlow-energy inelastic window of the carbon K-edge RIXS spectrum in graphite is indeed well\nknown to be dominated by phonon excitations.\nIn the transient state following photoexcitation, carriers are excited into the conduction\nband, and in principle, they may scatter within an electronic continuum, potentially\ncontributing to a broad, featureless background at low energy loss. However, multiple\nfactors strongly argue against a significant contribution from this effect in our data:\nOrbital symmetry selectivity of the RIXS process\nThe resonance condition used in this experiment corresponds to the excitation of a carbon\n1s core electron into the unoccupied 2pσ* antibonding state. This sets the symmetry of the\nintermediate state in the RIXS process. On the other hand, the optical pump excites\ncarriers predominantly from the π to π* bands at the M saddle point of the Brillouin zone,\nwhich are states of 2pπ character. As noted by the Reviewer, after excitation, hot electrons\nrapidly relax to lower-energy conduction states around the Dirac cone at the K point (panel\nb of the attached figure). These relaxed states remain of 2pπ character and thus do not\noverlap with the intermediate 2pσ* state probed in the RIXS process.\nConsequently, the mismatch in orbital character and momentum between the conduction\nband states populated by the pump and the intermediate state of the RIXS probe renders\nthe probability of electronic continuum scattering negligible. This is schematically illustrated\nin the figure:\n• Panel a: the optical pump excites electrons from the π valence band to π*\nconduction band at the M point.\n• Panel b: these hot electrons relax toward the Dirac cone at the K point via\nelectronic intraband processes, all within the π* manifold.\n• Panel c: the probe photon promotes a core 1s electron to the 2pσ* state, forming\nan intermediate exciton. The RIXS emission probes the relaxation of this state,\nprimarily through phonon-coupled de-excitation back to the ground state or low-\nenergy excitonic states.\nBecause the intermediate state of the RIXS process is defined by a transition into the 2pσ*\norbital and the pump-populated states lie within the 2pπ* manifold, there is no direct overlap\nbetween the hot carrier population and the intermediate state. As a result, excess charge\nin the conduction band does not contribute to the observed low-energy RIXS features.\nAbsence of broad spectral background in the experimental data:\nIn the pumped condition, the inelastic RIXS response retains a well-defined spectral\nstructure consistent with phonon excitations, despite the limited energy resolution (~350\nmeV). We do not observe the emergence of any broad or featureless background at low\nenergy loss that would indicate scattering from a low-energy electronic continuum. The\ntransient modifications are instead confined to the inelastic sideband region and remain\nspectroscopically compatible with phonon-coupled RIXS emission. This is further\nsupported by our time- and energy-resolved analysis, which quantitatively reproduces the\nobserved spectral evolution using a phonon-based model..\nCore-hole lifetime and selection rules suppress non-resonant channels:\nThe relatively short core-hole lifetime (Γ ~ 0.4 eV) and the strict resonance condition favor\ninelastic channels involving well-defined excitonic intermediate states and symmetry-\nallowed phonon couplings. Incoherent or off-resonant scattering channels—such as those\nthat might involve an electronic continuum—are strongly suppressed due to poor matrix\nelement overlap with the intermediate state.\n4. The off-resonant spectra in Fig. 2b show significant structure, dropping to lower values around\n–1.2 eV and then rising again. Given the plotting window, we cannot be sure whether this line\nshape is indeed symmetric, as claimed in line 267.\nResponse: (see also response to comment 1) The energy range shown in Fig. 2b was\nintentionally limited to the low-energy-loss region near zero energy loss, to focus on the\nphonon-related inelastic response that is the central topic of this manuscript. This cropped\nplotting window was chosen to avoid compressing the relevant low-energy features and to\nimprove the visibility of the phonon dynamics relative to the much more intense elastic line.\nTo clarify the full spectral context, we now provide in the Supplementary Information\n(Supplementary Figure 2S, Section A.2) the complete measured off-resonance spectrum,\nextending up to higher energy losses well into the valence band region (see also figure in\nResponse for issue number 1). As visible in this full-range plot, the observed drop in\nintensity around –1.2 eV and the subsequent slight rise at higher energy loss do not\noriginate from any asymmetry of the elastic peak or from features related to the phonon\nresponse. Instead, the intensity remains essentially constant (background counts) from 0\nto approximately –5 eV and then begins to increase due to the onset of valence band\nemission at larger energy losses (approximately –7 to –15 eV), where the core holes\ncreated during the core absorption process are filled by electrons from the p-symmetry\nprojected valence band states of graphite.\nThis experimental observation confirms that the spectral rise at larger energy loss is\nunrelated to the symmetry of the elastic or phonon features discussed in the manuscript.\nFor further clarity, we have added a note in the revised manuscript (see line 314), explicitly\nstating that the energy window shown in Fig. 2b was cropped for clarity and that the\napparent spectral rise at larger energy loss is associated with the onset of valence band\nemission.\nA detailed study of the valence band emission and its pump-probe dynamics, which we\nalso measured at the carbon 2p resonance, will be the subject of a separate publication,\np\nas it extends beyond the phonon-focused scope of the present work.\n5. We ask the authors to justify the procedure of scaling the off-resonant spectrum to match the\nintensity at zero energy and then subtracting it. This does not necessarily seem like a robust\nmethod for isolating the phonons, given (a) the intensity away from the inelastic region,\nas mentioned above, and (b) the fact that some phonon intensity will appear at 0 eV due to the\nenergy resolution being larger than the phonon energy.\nResponse:\nWe thank the Reviewer for raising this important methodological point. This comment\nhelped us to further clarify the rationale behind the off-resonance normalization and\nsubtraction procedure in the revised manuscript (see lines 319 ).\nOur working assumption is that the elastic component of the RIXS spectrum serves as a\ndirect, proportional measure of the resonant X-ray absorption cross-section at each\nincident photon energy. The elastic scattering intensity follows the absorption profile\nbecause it results from direct scattering without energy loss, scaling with the number of\navailable core holes and the resonant enhancement. This assumption is supported by the\nobserved near-symmetric lineshape of the elastic peak, as shown by our off-resonance\nspectrum.\nSimilarly, the inelastic scattering intensity from phonon overtones is also expected to scale\nwith the absorption cross-section, since the creation of multiple phonons is a second-order\nresonant process driven by the same intermediate-state core hole population. Therefore,\nby normalizing the off-resonant spectrum to match the elastic peak height at zero energy\nloss, we ensure that both elastic and inelastic spectral weight are proportionally scaled\naccording to the cross-section at each excitation energy.\nThe goal of this normalization-subtraction procedure is to isolate the resonantly enhanced\ninelastic spectral weight, removing the underlying energy-dependent absorption profile that\nequally affects both elastic and inelastic contributions. This allows us to track the resonant\nenhancement of the phonon-coupled RIXS signal as a function of detuning.\nWe are fully aware that the finite energy resolution causes some phonon-related intensity\nto appear at 0 eV, leading to partial spectral overlap between elastic and phonon\ncomponents. However, the off-resonant reference spectrum already contains this\nconvolution of elastic and non-resonant contributions under the same instrumental\nresolution. By using this reference and applying the same scaling to both elastic and\ninelastic parts, we minimize potential systematic errors introduced by the resolution\nbroadening.\nImportantly, the robustness of this approach is validated by the consistency between the\ndetuning-dependent inelastic intensity trends and the expected theoretical scaling from the\nAment model, as shown in Figure 3a.\n6. The Ament model has not been shown to effectively explain the overtone modes in graphite.\nPrevious studies have demonstrated that the data cannot be explained solely in terms of overtones\nof the Γ-point phonon but instead involve combinations of phonons from different parts of the\nBrillouin zone for higher-order overtones (see Refs. [1,2]). In light of this, it is unclear whether\nEquation 1 is appropriate for the data. Furthermore, Equation 1 clearly yields a prediction for the\nfull shape of the spectrum as a function of energy and not just a prediction for the total intensity. It\nis concerning not to see a comparison between the predicted energy dependent intensity for the\nmodel and data in the draft. This must be added.\nResponse:\nWe acknowledge that the Ament model simplifies the multi-phonon structure and does not\naccount for all phonon branches. However, within our resolution-limited regime, the loss\nfeature cannot resolve different contributions from phonon combinations. Equation 1\nprovides a tractable and physically motivated approximation for analyzing vibronic coupling\nvia a single mode. We have added a new panel (Figure R2) comparing the predicted\nenergy-dependent spectral shape from the model to our data. This comparison supports\nthe model’s relevance in our experiment.\nWe fully agree that the complete vibrational spectrum in graphite includes contributions\nfrom phonons across different points of the Brillouin zone. In particular, prior high-\nresolution studies (e.g., Feng et al., PRL 125, 116401 (2020); Dashwood et al., PRX 11,\n041052 (2021)) have demonstrated that multiple phonon modes—including the zone-\ncenter E₂g (G mode) and the zone-edge A₁′ (2D mode)—can contribute to the overtone\nstructure in static RIXS spectra.\nHowever, those results were obtained under optimized conditions for energy resolution\nand symmetry detection, with resolutions better than 100 meV. In contrast, our experiment\nwas performed in a pump-probe configuration at moderate energy resolution (~350 meV),\nwhere the individual overtone peaks are spectrally unresolved. In this regime, the RIXS\nspectral response is dominated by the zone-center E₂g phonon, which couples strongly at\nthe Γ point due to dipole selection rules associated with the C 1s → σ* resonance. This\nresonance and momentum selectivity has been extensively discussed in the literature and\njustifies the use of a single-mode, Γ-centered optical phonon model for interpreting our\nspectra.\nScope and justification for the Ament model\nOur use of the Ament formalism is guided by a clear and constrained purpose: to model\nthe total inelastic spectral weight (i.e., integrated intensity) as a function of detuning from\nresonance (Δ), rather than to resolve individual phonon contributions. As the Reviewer\ncorrectly notes, the full spectral shape in graphite at high order involves contributions\nfrom phonons at various momenta and polarizations. Capturing these details requires a full\nGreen’s function treatment, as performed by Dashwood et al. (PRX 2021), which is beyond\nthe scope of the current work.\nInstead, our analysis follows the approach of previous works (e.g., Carlisle et al., PRL 74,\n1234 (1995); Feng et al., PRL 125, 116401 (2020); Rossi et al., PRL 123, 027001 (2019)),\nwhere the Ament model is used in its integrated form to track the detuning dependence of\nthe inelastic weight. The model has proven successful in capturing qualitative trends in\nresonant enhancement under moderate or limited resolution.\nClarification of equation and implementation\nAs clarified in the revised manuscript (lines 446-450) Equation 1 in our paper corresponds\nto the full energy-dependent RIXS intensity derived from the single-site Ament model.\nTo directly address the Reviewer's request for a shape comparison, we now include in\nthe Supplementary Information (Supplementary Figure 3S and figure below) a detailed\nfigure with two panels:\n• Panel A shows the measured on-resonance RIXS spectrum (smoothed, black line)\nplotted together with the theoretical intensity envelope predicted by the Ament model\nfor Δ = –0.45 eV. We show both the convolved (red dashed line) and the unbroadened\nstick-like (blue) spectra. The model captures the energy-dependent intensity\ndistribution reasonably well, particularly in terms of width and inelastic shoulder, within\nthe constraints of experimental resolution. A resolution-broadened elastic line (green\ndashed-dot) is also included to show the elastic background shape.\n• Panel B shows a full simulated RIXS intensity map I(ω, Δ), where the energy loss\naxis (ω) is plotted against photon detuning (Δ). The map is calculated using the full Ament\nmodel expression above and demonstrates how the total spectral envelope evolves\nwith detuning. The phonon resonance appears as a dispersive tail extending from the\nelastic peak, showing increased intensity and broadening on resonance, consistent\nwith experimental observations.\nWhile the Ament model does not reproduce the fine peak structure (which is unresolved in\nour data) as demonstrated by Dashwood and others, these simulations demonstrate that\nthe overall envelope of the phonon sideband and its detuning-dependent modulation.\nSummary:\n• The Ament model is applied only to the total inelastic spectral weight and not to the\ndecomposition into individual phonon modes or overtones.\n• The goal is not to reproduce the full overtone structure, but to quantify trends in the\nintegrated spectral weight due to resonant enhancement near the Γ-point E₂g phonon.\n• This approach is experimentally justified by the limited resolution and the momentum\nselectivity of the RIXS process at the C 1s → σ* edge.\n• It is also consistent with prior studies (Feng et al., Rossi et al., Carlisle et al.) that used\nintegrated forms of the Ament model to describe similar systems under similar\nconstraints.\n• Additional comparisons are now provided in Supplementary Figure 3S.\nWe believe these clarifications, together with the additional simulations and comparisons,\nsatisfactorily resolve the Reviewer’s concern.\n1.2\n1\n0.8\n0.6\n0.4\n0.2\n0\n-4 -3 -2 -1 0 1 2\nEnergy loss (eV)\nFigure R2 Comparison between experimental RIXS data and the Ament model.(a) Off-resonance equilibrium RIXS\nspectrum (black solid line) measured in graphite, compared to theoretical predictions from the Ament single-site\nexciton-phonon coupling model at a detuning of W = –0.10 eV. The red dashed line shows the model spectrum\nconvolved with the experimental energy resolution (FWHM = 350 meV), while the blue solid line displays the\nunconvolved model using narrow phonon replicas. A resolution-broadened elastic line is also shown (green dot-\ndashed line). The model includes up to 10 phonon overtones. (b) Calculated RIXS intensity map I(ω, W) as a function\nof energy loss (ω) and detuning (W), based on the Ament model. The simulation includes up to 20 multiphonon\ncontributions, with a phonon energy of 0.196 eV, exciton-phonon coupling strength M = 0.32 eV, and core-hole\nlifetime broadening γ = 0.3 eV. The intensity is normalized to the global maximum. This panel highlights the\ndetuning-dependent dispersion of the multiphonon envelope.\n7. The value of 𝑀 from [1] has been contested in [2]. This controversy needs to be\nup\nacknowledged and discussed.\nytisnetnI\ndezilamroN\nPanel A: RIXS Spectrum at = 0.10 eV Panel B: Ament RIXS Intensity Map I( , )\n0.5\nExperimental (Smoothed)\nAment Unbroadened\nAment Convolved\nElastic Line\n0\n-0.5\n-1\n-1.5\n-1 -0.5 0 0.5 1\nDetuning (eV)\n)Ve(\nssol\nygrenE\n1\n0.9\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\nResponse: we thank the Reviewer for pointing out the controversy regarding the value of\nthe exciton-phonon coupling strength M reported in Ref. [1] (Feng et al., Phys. Rev. Lett.\nup\n125, 116401 (2020)) and contested in Ref. [2] (Dashwood et al., Phys. Rev. X 11, 041052\n(2021)). We now explicitly acknowledge this issue in the revised manuscript (lines 510-\n515).\nIn particular, Ref. [1] employed a phenomenological model assuming a single effective\nphonon mode and extracted the coupling constants M and M based on fits to the RIXS\nG A1’\nintensity detuning curves. However, as highlighted in Ref. [2], this approach does not\naccount for the mixing of multiple phonon modes and their full momentum dependence,\nwhich can significantly renormalize the spectral weight across the multiphonon excitations.\nDashwood et al. demonstrated, using a Green’s-function formalism that includes phonon\ndispersion and intermediate-state mode mixing, that the multiphonon features in graphite’s\nRIXS spectra can be more accurately described without invoking unrealistically large\nvalues of the coupling constant.\nWhile both studies agree on the qualitative observation that different phonon modes couple\ndifferently to π* and σ* excitons, they differ on the quantitative magnitude of this coupling,\nparticularly for the G mode. This discrepancy underscores the importance of the underlying\ntheoretical framework: simplified models may lead to overestimated coupling constants if\nthe complex nature of the intermediate state is not fully captured.\nIn our manuscript, we maintain the use of detuning-dependent RIXS intensity as a means\nto gauge exciton-phonon coupling, while acknowledging its limitations and the more\nsophisticated treatment proposed in Ref. [2]. We now clarify that the reported coupling\nconstants should be interpreted as effective values within the approximations of our model,\nand that further theoretical developments, such as those in Ref. [2], provide valuable\nrefinements for quantitatively accurate extraction of EPC parameters in graphite.\n8. It would be valuable to include some discussion situating the present work in the context of\nother XFEL RIXS experiments. Only a handful of ultrafast XFEL RIXS studies probing\nquasiparticles have been published since the first experiments about a decade ago, so it should\nbe straightforward to provide a comprehensive overview.\nResponse: We thank the reviewer for this important suggestion. In the revised Introduction\nand Discussion, we have now added references to prior tr-RIXS studies (e.g., Dean et al.,\nDantz et al., Mitrano et al.) and clarified that, while tr-RIXS has been demonstrated, our\nwork represents a first demonstration of time-domain suppression of vibronic features in a\nvan der Waals solid.\nIn response, we have added a dedicated paragraph to the end of the Introduction that\nsurveys the key developments in the field over the past decade. This new paragraph\n(highlighted in red in the revised manuscript) reviews recent FEL-based tr-RIXS studies\nthat have probed transient electronic, magnetic, and orbital excitations in strongly\ncorrelated materials such as cuprates, iridates, and vanadates. We then clearly delineate\nthe novelty of our work: to our knowledge, this is the first time-resolved RIXS experiment\nresolving phonon-sideband dynamics at the carbon K-edge, and more specifically, the first observation\nof the ultrafast modulation of exciton-phonon coupling due to photoinduced\nscreening in a light-element, weakly screened material such as graphite.\nThis distinction is now clearly articulated in the revised Introduction and Conclusions\n(highlighted in red in the manuscript), where we situate our study in the context of the\nlimited number of tr-RIXS works that have targeted bosonic excitations. While phonon-\nrelated features in graphite have been previously investigated in equilibrium using various\nspectroscopies, our work goes further by probing how exciton-phonon interactions\nevolve in the transient regime, in response to changes in electronic screening induced\nby femtosecond optical excitation.\nImportantly, the primary objective of our study is not to extract the static exciton-\nphonon coupling constants, but to reveal how this coupling is dynamically modified\nin time, shedding light on the interplay between charge carrier screening and vibronic\nstructure in a regime that is uniquely accessible through ultrafast core-level\nspectroscopies.\nWe thank the Reviewer again for encouraging us to refine the framing of our contribution,\nwhich we believe is now more precise and clearly contextualized within the state of the art.\nOverall, this work is quite novel in many respects, and we are glad to see it carried out. However,\nwe have concerns regarding both the experiment and the data analysis. Conducting the\nexperiment with an energy resolution that cannot resolve the phonons in question poses a\nserious limitation to the information obtained.\nFor instance, it raises concerns about whether the intensity of the first phonon can be uniquely\ndistinguished from the elastic line, and whether other inelastic signals, such as charge scattering,\nmight exist out of equilibrium and might be mixed up with the phonon spectrum. The analysis\nappears to rely on an equation that has not been shown to accurately model the material under\ninvestigation. The omission of a basic test to verify whether the equation reproduces the energy-\ndependent shape of the equilibrium and transient spectra is a significant shortcoming of the\ncurrent draft.\nWe believe these issues are, in principle, fixable to make the work publishable. However, we\nremain skeptical about whether these problems can be resolved convincingly enough to merit\npublication in Nature Communications.\nWe once again are grateful for the constructive comments from Reviewer #2 and for\nacknowledging that our work is quite novel in many respects. Also, we hope that we have\nresolved all the issues raised by the Reviewer #2, and that the paper is now suitable for\nNature Communications\nBibliography\n[1] X. Feng et al., Disparate Exciton-Phonon Couplings for Zone-Center and Boundary Phonons\nin Solid-State Graphite, Phys. Rev. Lett. 125, 116401 (2020).\n[2] C. D. Dashwood et al., Probing Electron-Phonon Interactions Away from the Fermi Level with\nResonant Inelastic X-Ray Scattering, Phys. Rev. X 11, 41052 (2021).\nReviewer #3 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nReviewer #4 (Remarks to the Author):\nIn this manuscript, the authors present a time-resolved RIXS study on graphite, using a UV (4\neV) pump pulse to generate photoexcited carriers and investigate the effect of photo-induced\nscreening on the coupling between phonons and the core-hole exciton created by the XUV probe\nphoton.\nBy tuning the incident photon energy across the carbon K-edge resonance, the authors probe\nhow photo-induced screening modifies both the elastic (coherent) and inelastic (incoherent) parts\nof the RIXS spectrum associated with the Jahn-Teller (JT) distortion from exciton-phonon\ncoupling. While individual phonon peaks are not fully resolved, the spectral changes are\nconsistent with prior literature.\nStrengths:\n• The experimental dataset is valuable and adds time-domain insight into exciton-phonon\ncoupling and screening effects in graphite.\n• The use of time-resolved RIXS to study suppression of incoherent phonon-related spectral\nfeatures is a promising approach.\nMajor concerns:\n1. Clarity of interpretation:\nThe manuscript’s discussion switches between “exciton-phonon coupling” and “electron-phonon\ncoupling” when describing the fits of parameter R and its time evolution. This inconsistency\ncreates ambiguity about the physical mechanism driving the observed spectral changes. It is\ncrucial for the authors to clarify whether the spectral dynamics arise predominantly from changes\nin the JT distortion due to exciton-phonon coupling, or from broader electron-phonon interactions\naffected by screening.\nResponse:\nWe thank the reviewer for highlighting this ambiguity. We have carefully revised the\nmanuscript to consistently use 'exciton-phonon coupling' when discussing the interaction\nbetween the core-exciton and phonons, and reserve 'electron-phonon coupling' for general\nvalence band processes. The reduction in the incoherent loss signal is attributed to\ntransient screening that suppresses the Jahn-Teller distortion of the core-exciton complex.\nThis causal sequence is now more clearly stated in the revised Sections 3 and 4.\nIn our study, the parameter R reflects the intensity of the phonon sideband associated with\nvibronic scattering at the carbon K edge under resonant conditions. This sideband arises\nfrom the coupling between the core-exciton—formed by the strongly localized 1s core hole\nand a photoexcited electron in the σ∗ conduction band—and zone-centre optical phonons,\nprimarily of E symmetry. Therefore, the relevant interaction driving the spectral changes\n2g\nin our experiment is exciton-phonon coupling, not generic electron-phonon coupling.\nTo avoid ambiguity, we have revised the manuscript throughout to consistently use the\nterm \"exciton-phonon coupling\" when referring to the physical mechanism underlying\nthe observed vibronic features.\nThe discussion of the Jahn-Teller distortion, which is mediated by the core-exciton,\nfurther supports this assignment: the distortion originates from the symmetry-breaking\ninteraction between the core-exciton and lattice vibrations, as described in the literature\n(e.g., \\cite{Feng.2020}).\nMoreover, the observed reduction in R under photoexcitation is interpreted as a decrease\nin exciton-phonon coupling strength, resulting from enhanced screening of the core-hole\npotential by the photoinjected electron-hole plasma. This screening weakens the\nlocalization and binding energy of the exciton, thereby reducing its ability to distort the\nlattice and generate multiple phonon excitations.\nWe have updated the relevant sections of the manuscript to reflect this clarification and\nhave included a dedicated note in the Supplementary Information outlining the excitonic\norigin of the fitted spectral features.\n2. Ambiguity in spectral origin: the manuscript sometimes leaves unclear whether the changes in\nspectra with detuning or pump delay arise from modifications to the JT distortion or from\nscreening effects, making interpretation difficult for readers.\nResponse (see also the discussion at point 1):\nwe appreciate the Reviewer’s careful reading and fully acknowledge the need to clarify the\nspectral origin of the changes observed with detuning and pump delay.\nThe concern regarding the distinction between effects driven by Jahn-Teller (JT) distortion\nand those resulting from screening is well taken.\nIn our study, changes in the inelastic spectral weight and its temporal evolution are\ninterpreted primarily in terms of screening of the core-exciton by the photoinduced hot\nelectron distribution. This enhanced screening reduces the exciton binding energy,\nweakens its spatial localisation, and consequently diminishes the strength of exciton-\nphonon coupling responsible for the vibronic sidebands.\nThe reduction in vibronic intensity (quantified by the parameter R is thus an indirect\nsignature of screening and not a direct probe of JT distortion dynamics per se.\nHowever, it is important to note that the JT distortion is mediated by exciton-phonon\ncoupling. Therefore, the suppression of the JT-induced lattice distortion under\nphotoexcitation is a consequence of the reduced exciton-phonon coupling strength. The\ntwo effects—screening and JT suppression—are not independent, but causally linked:\nscreening weakens the exciton, which in turn reduces its ability to distort the lattice\nvia the JT mechanism.\nTo address the Reviewer’s concern and improve clarity, we have:\n• Revised the relevant sections in the manuscript to explicitly trace the causal chain:\nphotoexcitation → enhanced screening → weakened exciton → reduced JT\ndistortion and phonon coupling.\n• Added clarifying remarks in the Discussion section and in the caption of Figure 3\nto make the physical interpretation transparent.\n• Included a schematic summary in the Supplementary Information to illustrate how\ndetuning and pump delay affect the excitonic state and its coupling to phonons\nthrough screening. Must be included.\nWe hope these revisions make the interpretation of the spectral changes clearer to the\nreader and resolve the ambiguity highlighted by the Reviewer.\nAmbiguity in spectral origin\nWe thank the Reviewer for raising this important point regarding the interpretation of the\nspectral changes. We agree that distinguishing between the effects of Jahn-Teller (JT)\ndistortion and screening is crucial for a clear understanding of the data.\nIn our experiment, the multi-phonon spectral structure observed in the RIXS spectra\noriginates from the Jahn-Teller distortion associated with strong exciton-phonon\ncoupling in the core-excited state. This structure is well established in the literature and\nreflects the displacement of the excited carbon atom from its equilibrium position due to\ncoupling with optical phonons.\nThe pump-induced changes to this structure—namely the suppression of the phonon\nsidebands—are primarily attributed to modifications in the electronic screening\nenvironment caused by the photoinduced electron-hole plasma. This screening reduces\nthe strength of the exciton-phonon coupling, effectively weakening the JT distortion and\naltering the potential energy surface experienced by the core exciton.\nRegarding detuning, it plays a complementary role: when the photon energy moves away\nfrom resonance, the intermediate state becomes less excitonic and more delocalised,\nreducing the strength and visibility of the phonon-coupled features. This energy-dependent\neffect also modulates the apparent JT distortion, though in a static (non-dynamical)\nfashion.\nTo clarify:\n1. The origin of the phonon progression is the JT distortion due to exciton-phonon\ncoupling.\n2. The modulation of this structure upon pumping reflects screening-induced\nsuppression of the exciton-phonon interaction.\n3. The detuning dependence reflects the resonance condition of the RIXS\nintermediate state and how effectively it couples to phonons.\nWe have revised the relevant sections of the manuscript to clarify these distinctions and\nimprove the interpretative framework for the reader.\n3. Novelty claims:\nThe authors state that this is among the first demonstrations of time-resolved RIXS. However, to\nmy knowledge, multiple recent reviews and studies have demonstrated tr-RIXS probing\ndynamical processes and phase transitions in various materials. Additionally, electron-phonon\ncoupling in graphite has been extensively studied previously. The present work’s novelty lies\nprimarily in demonstrating the time-domain suppression of incoherent exciton-phonon related\nfeatures via photoinduced screening, which is sometimes obscured in the manuscript’s framing.\nThe authors should revise their novelty claims accordingly.\nResponse: We agree with the reviewer’s observation. In the revised manuscript, we clarify\nthat while tr-RIXS has been previously demonstrated, the novelty of our work lies in its\nspecific application to time-domain suppression of vibronic sidebands in graphite, a regime\nnot previously studied.\nWe fully acknowledge that in the past decade, a number of impactful time-resolved RIXS\n(tr-RIXS) studies have successfully addressed ultrafast dynamics of spin, charge, and\norbital excitations—particularly in strongly correlated transition-metal systems such as\ncuprates, iridates, and vanadates. These contributions have laid the groundwork for\nexpanding tr-RIXS into a broadly applicable tool in condensed matter physics.\nIn response to the Reviewer’s observation, we have carefully revised the manuscript to\nclarify the novelty and scope of our work, avoiding any implication that our contribution\nrepresents the first use of tr-RIXS as a general technique. Instead, we now state explicitly\nthat our study presents the first time-resolved RIXS experiment resolving phonon-\nsideband dynamics at the carbon K-edge, and more specifically, the first observation\nof the ultrafast modulation of exciton-phonon coupling due to photoinduced\nscreening in a light-element, weakly screened material such as graphite.\nThis distinction is now clearly articulated in the revised Introduction and Conclusions\n(highlighted in red in the manuscript), where we situate our study in the context of the\nlimited number of tr-RIXS works that have targeted bosonic excitations. While phonon-\nrelated features in graphite have been previously investigated in equilibrium using various\nspectroscopies, our work goes further by probing how exciton-phonon interactions\nevolve in the transient regime, in response to changes in electronic screening induced\nby femtosecond optical excitation.\nImportantly, the primary objective of our study is not to extract the static exciton-\nphonon coupling constants, but to reveal how this coupling is dynamically modified\nin time, shedding light on the interplay between charge carrier screening and vibronic\nstructure in a regime that is uniquely accessible through ultrafast core-level\nspectroscopies.\nWe thank the Reviewer again for encouraging us to refine the framing of our contribution,\nwhich we believe is now more precise and clearly contextualized within the state of the art.\n4. Suitability for Nature Communications:\nWhile the data are valuable, I am not currently convinced the manuscript meets the threshold for\npublication in Nature Communications without addressing the above issues, especially clarity\nand novelty. Improvement in the discussion of exciton vs electron phonon coupling and stronger\njustification of the unique insight provided by their experimental approach would significantly\nenhance the manuscript.\nGeneral comments:\n• Citation clarity could be improved. For example, line 136 cites six references on JT distortion,\nbut the exact source of the quoted JT magnitude (line 139) is not explicitly referenced, forcing\nreaders to track through earlier citations.\nResponse: we have added the reference about the magnitude of the JT dynamical\ndistortion: Ma, Y. et al. Core excitons and vibronic coupling in diamond and graphite.\nPhys. Rev. Lett. 71, 3725–3728 (1993).\nSpecific comments:\nIntroduction:\n1. Line 72: The authors use the term “radiation-matter interactions.” This phrasing is unusual in\nthe community, which typically uses “light-matter interactions.” Do the authors intend to include\nnon-photon radiation (e.g., alpha, beta particles)? If not, “light” might be a clearer choice.\nResponse: Thank you for the suggestion. We agree that \"light-matter interactions\" is\nmore accurate in this context and have accordingly revised the text\n2. Line 88: Referring to photoexcited carriers as an “electron-hole plasma” is not accurate here,\nas plasma usually implies a state of free charges at high density. Consider revising this wording.\nResponse: We appreciate this observation. The term has been replaced with “hot\nelectrons” to more accurately reflect the nature of the photoexcited carriers in our\nexperiment.\nFigure 1:\nFig. 1c:\na. The authors claim an energy resolution of 350 meV. How was this determined? The off-\nresonance peak appears broader than 350 meV, which raises questions about the actual\nresolution.\nResponse to Reviewer Comment a:\nWe thank the Reviewer for pointing out the need to clarify how the energy resolution was\ndetermined. The nominal energy resolution of ~350 meV was measured independently\nusing the elastic peak from diffuse scattering of the FEL beam off a silicon crystal\nsurface, as shown in the figure now attached to this rebuttal letter (Figure 1S in the\nSupplementary Materials).\nThis calibration was performed off-resonance, far from any absorption edge, to avoid\ndistortions due to self-absorption, core-hole lifetime effects, or other resonant phenomena.\nMoreover, the use of a clean, crystalline silicon surface, as opposed to the peeled graphite\nsample, ensures minimal surface roughness and extrinsic broadening, which is essential\nfor an accurate determination of the resolution. The graph in figure R3 presents a\ncomparison between the spectral distribution of the FEL pulse as recorded by the online\nTARDI spectrometer (blue curve, vertically offset and shown in a narrow energy window)\nand the corresponding spectrum measured via diffuse scattering on a silicon surface using\nthe XES355 spectrometer (green and red curves). The red dashed line illustrates the ideal\nenergy response of the XES355, while the green curve represents the actual measured\nlineshape, which includes the instrument's energy resolution and intrinsic count statistics.\nWe would also like to clarify that the spectra shown in the manuscript were subject to mild\nsmoothing to improve the visibility the spectral features (see figure R4, where dotted\ncurves represent raw data, continuous lines the smoothed spectra ). This smoothing\ninevitably leads to some broadening of the elastic line, but it is applied uniformly across all\ndata and does not reflect the actual instrumental resolution. Therefore, the energy\nresolution was not determined from the data shown in the main manuscript figures.\nTo further support this clarification, we include in the figure attached below both raw and\nsmoothed graphite spectra (the same data already included in Figure 2 in the\nmanuscript), acquired on-resonance and off-resonance. This comparison clearly shows\nthat the smoothing does affect the width of the elastic peak but does so consistently across\nthe dataset. The raw off-resonance elastic peak, measured on the silicon surface, is the\nreference used for determining the experimental resolution of 350 meV.\nWe have added a brief description of the resolution calibration procedure in the\nSupplementary Material (A1).\noff-res. pump-probe\noff resonance spectra\n-4 -2 0 2\nEnergy loss (eV)\nFigure R3 off-resonance pump(red\ncurve) and unpumped (black curve).\ndotted curves represent raw data,\ncontinuous lines the smoothed spectra\nFigure R4 Energy resolution calibration of the XES355\nspectrometer. The blue curve shows the spectral profile of the FEL\npulse as measured by the online TARDI spectrometer, plotted in\nthe restricted 294.15--294.31~eV range. The red dashed curve\ncorresponds to the expected XES355 response, obtained by\nconvolving the TARDI spectrum with a Gaussian kernel\nrepresenting the known XES355 resolution. The green curve shows\nthe measured elastic diffuse scattering line from a silicon wafer\nusing the XES355 spectrometer. This direct comparison confirms\nthat the overall spectral broadening in XES355 is dominated by its\ninstrumental resolution (FWHM 340 meV).\nb. Line 167 states a source bandwidth of ~60 meV, which seems contradictory to the 350 meV\nresolution claim. Please clarify this discrepancy.\nResponse: we thank the reviewer for pointing out this apparent discrepancy. The 60 meV\nbandwidth mentioned in line 167 refers to the intrinsic spectral width of the FEL pulse,\nwhich is a property of the source. This value is consistent with the Fourier-limited\nbandwidth of the seeded FERMI pulses and is measured for each single pulse using the\nTARDI online spectrometer [Malvestuto et al., Rev. Sci. Instr. ].\nHowever, the energy resolution of the experiment is determined not only by the source\nbandwidth but also by the instrumental resolution of the XES355 spectrometer, which\nbroadens the detected features. In our case, the XES355 was characterized using diffuse\nscattering from a silicon surface, yielding a total observed FWHM of 350 meV for the elastic\nline. After deconvolving the independently measured FEL bandwidth (∼63 meV), the\nintrinsic resolution of the XES355 spectrometer is estimated to be ∼344 meV. This value\nreflects the actual resolving power of the spectrometer under the experimental geometry.\nTo clarify this, we now explicitly distinguish between the source bandwidth (∼60 meV) and\nthe spectrometer-limited experimental resolution (∼350 meV) in the revised text. A detailed\ncomparison between the TARDI and XES355 measurements is shown in the\nSupplementary Information.\nc. The “on-resonance” asymmetric peak shows small oscillations that do not match phonon\npeaks in the high-resolution reference [12]. Could the authors comment on their origin?\nResponse: we thank the reviewer for this observation. The small oscillations visible on the\n\"on-resonance\" asymmetric peak are not related to real phonon excitations. Instead, they\nare an artifact arising from counting noise in the measured spectrum. These fluctuations\nbecome more apparent after applying smoothing procedures, which we used to improve\nvisualization of broad spectral features. The oscillations have no physical significance and\nare not reproducible across independent measurements.\n• Fig. 1d: The colored pulses/arrows lack explanation in the caption and seem randomly\nassigned. Adding clear labels and descriptions would improve reader understanding.\nResponse\nWe thank the Reviewer for pointing out the ambiguity regarding the color-coded arrows in\nFigure 1d. We agree that the absence of explicit labels and descriptions in the original\ncaption may hinder the reader’s understanding of the excitation and scattering processes\ndepicted.\nTo address this, we have thoroughly revised the caption for Figure 1d to explicitly\ndescribe the meaning of each arrow:\n• The green solid arrow represents the optical pump excitation, resonantly\ndriving the π→π∗ transition at the M saddle point of the Brillouin zone.\n• The blue dashed arrow depicts the X-ray probe excitation, corresponding to\nthe transition of a 1s core electron into the unoccupied σ∗ conduction band states\nat the Γ point.\nThese revisions ensure that the schematic is now fully self-contained and interpretable\nwithout ambiguity. We hope this resolves the issue and improves the clarity of Figure 1d.\n• Line 197: The statement about “anomalous valence quasiparticle lifetimes” attributed to a\nphonon bottleneck and band structure deserves further elaboration. What specifically is\nanomalous, and how does graphite’s band structure produce this behavior?\nResponse: the term “anomalous” refers to the observation that valence quasiparticles in\ngraphite can exhibit unusually long lifetimes in specific regions of the Brillouin zone,\nparticularly near the M point, in contrast to the short lifetimes typically expected due to\nrapid electron-electron and electron-phonon scattering.\nThis behaviour arises from a phonon bottleneck effect, which is strongly influenced by\nthe peculiar topology of graphite’s electronic band structure. Specifically, at energies\nbelow ~1.5 eV, the joint density of states for electron-hole pair creation at large momentum\ntransfer is suppressed, owing to the semimetallic nature and the Dirac-like dispersion near\nthe K and H points. In such a regime, decay pathways requiring large momentum transfer\n(i.e., involving high-qq phonons or interband transitions) are energetically or kinematically\nunfavourable.\nFurthermore, the long screening length in graphite favours small-q (i.e., low-momentum)\nelectron-electron and electron-phonon scattering. However, for quasiparticles near saddle\npoints (such as the M point), decay via small-qq scattering is inefficient because the\navailable phase space for low-energy excitations at small momentum is limited. As a result,\nthese quasiparticles lack efficient relaxation channels, leading to longer lifetimes than\nwould be expected in more typical metallic or semiconducting systems.\nThis effect has been documented in both experimental and theoretical studies (e.g., Refs.\n[Xu 1996, Breusing 2011, Spataru 2001, Piscanec 2004]), and represents a deviation from\nthe usual expectation that quasiparticle lifetimes decrease monotonically with energy due\nto increased scattering phase space. We have now expanded the discussion in the\nmanuscript accordingly to clarify this point. (lines 211-220)\nFigure 2:\nThe static and pumped RIXS spectra (on and off resonance) are well presented. The authors\nattribute the asymmetric on-resonance lineshape to exciton-phonon coupling, which diminishes\noff resonance and upon pumping due to screening.\nLine 313: The phrase “diminishing impact of the photoexcitation as photon energy deviates from\nresonance” is ambiguous. Does this mean the screening effect weakens, the sensitivity to\nexciton-phonon coupling reduces off resonance, or the exciton is less effectively excited?\nClarification is needed.\nResponse: we acknowledge that the wording was ambiguous and have revised the text\nto accurately reflect the intended meaning.\nIn this context, “photoexcitation” refers to the optical pump pulse that generates a non-\nequilibrium charge distribution in the valence and conduction bands.\nThe core-resonant probe pulse used in the RIXS process is tuned across the XAS\nresonance, and its detuning (Ω) determines the effective RIXS scattering time and the\nstrength of the core-exciton response.\nAs the probe photon energy is tuned away from the resonance, the system becomes\nless sensitive to exciton-phonon coupling for two reasons:\n1. The core-exciton is less efficiently formed off-resonance, and the process\nbecomes dominated by more delocalised particle-hole excitations with weaker\ncoupling to phonons.\n2. The shorter effective RIXS scattering time at larger detuning reduces the\nprobability of observing scattering processes involving slower lattice dynamics,\nsuch as phonon emission.\nTherefore, although the optical pump remains unchanged, its effect becomes less visible\nin the RIXS spectrum because the probe is no longer sampling a regime in which the\ncore-exciton–phonon interaction is strong or spectroscopically accessible.\nWe have revised the sentence in the manuscript accordingly, from line 380.\n• The pump-probe delay time shown in Fig. 2d is not specified and should be clearly stated.\nResponse:\nwe thank the Reviewer for this helpful observation. In the revised manuscript, we have\nclarified this point. The panel previously referred to as Figure 2d now appears as panel a\nof the new Figure 3. The pump–probe delay time at which the pumped spectra were\nmeasured (150 femtoseconds) is now explicitly stated in both the main text (line 296) and\nin the updated caption of Figure 2, ensuring full clarity for the reader.\nThe discussion inconsistently refers to changes in the incoherent spectral weight (R) as due to\nexciton-phonon coupling in some places, but attributes it to electron-phonon coupling in the Eq. 1\ndiscussion (line 343). This contradiction is confusing and should be resolved. Additionally, while\nscreening should reduce exciton binding energy and lifetime, the authors assume an unchanged\nexciton lifetime in the nonequilibrium state (line 337), which appears inconsistent.\nResponse:\nWe thank the Reviewer for carefully pointing out two important issues:\n1. The inconsistent terminology in our manuscript regarding “exciton–phonon” versus\n“electron–phonon” coupling, particularly in relation to the spectral weight changes\ndescribed by parameter R;\n2. The assumption of an unchanged exciton lifetime in the nonequilibrium state, despite\nthe expectation that photoinduced screening could reduce the exciton binding energy\nand hence its lifetime.\nWe address both concerns below and describe the revisions made to the manuscript to\nimprove clarity and consistency.\n1. Exciton–Phonon vs Electron–Phonon Coupling\nWe agree with the Reviewer that the terminology must be used precisely. The parameter\nR represents the intensity of the inelastic phonon sideband in the RIXS spectrum, which\narises from coupling between the core-exciton and lattice vibrations. The appropriate\nphysical mechanism governing this process is therefore exciton–phonon coupling,\nrather than generic electron–phonon coupling.\nWe acknowledge that the use of “electron–phonon coupling” in the context of Equation 1\n(in the previous manuscript version, line 343) was imprecise and potentially misleading.\nEquation 1 is derived from the single-site model introduced by Ament et al., where the\nlattice couples to the local charge density of the core-excited intermediate state.\nAccordingly, the coupling is more accurately described as exciton–phonon in nature.\nWe have now revised the manuscript to use “exciton–phonon coupling” consistently in all\nrelevant discussions.\nWe note that while this distinction is now gaining traction in the literature, past RIXS studies\nhave often referred to the extracted coupling constants in terms of electron–phonon\ncoupling, especially in the context of superconductivity or many-body renormalisation\neffects. However, as emphasized in a recent review by Gilmore et al. (Phys. Chem. Chem.\nPhys., 2022), “the coupling constant extracted from a RIXS measurement is better viewed\nas exciton–phonon coupling than the usual electron–phonon coupling initially sought.” This\nreflects a growing consensus in the field, particularly when interpreting RIXS spectra under\nstrong resonance conditions, such as those involving core-excitons with well-defined\nsymmetries.\nWe hope this clarification resolves the apparent inconsistency and improves the\nconceptual clarity for the reader.\n2. Assumption of fixed exciton lifetime in the pumped state\nThe Reviewer also raises an important point about the assumption of a constant exciton\nlifetime in the photoexcited state. While screening by the hot electrons may reduce the\nbinding energy of the core-exciton, it is important to distinguish between the exciton\nbinding energy and the core-hole decay lifetime.\nIn our analysis, the effective lifetime used in the fitting model refers to the core-hole\nlifetime (represented by the parameter Γ), which is dominated by atomic Auger decay and\nradiative recombination processes involving the deeply bound 1s core orbital. These\nprocesses are largely unaffected by photoinduced changes in the valence carrier\npopulation, particularly at the moderate excitation fluences used in this experiment.\nTherefore, we have kept Γ fixed in both pumped and unpumped conditions, in order to\nisolate and interpret changes in the exciton–phonon coupling strength, represented by\nthe parameter M in our model. A more comprehensive treatment including lifetime\nbroadening effects would require higher-resolution data and a multi-parameter global fit,\nwhich goes beyond the scope of the present study.\nTo address this point, we have added a clarification in both the manuscript and\nSupplementary Information.\nSummary of Revisions in the Manuscript\n• All references to “electron–phonon coupling” in the context of Equation 1 and the fitting\nof R have been replaced with “exciton–phonon coupling” for consistency.\n• An explicit statement has been added explaining why Γ is held constant in the fits, and\nwhy this is a reasonable assumption given the nature of the core-excited state and the\nspectral resolution of our data.\n• A clarifying citation to Gilmore et al. (PCCP 2022) has been included to support our\ninterpretation of RIXS as a probe of exciton–phonon coupling.\nWe thank the Reviewer again for raising these important issues, which have helped us\nimprove the precision and clarity of the manuscript.\nFigure 3:\nLine 432: The off-resonance dynamics are attributed to thermal modification of interplanar\ndistances, supported only by the timescale (330 fs). This explanation is insufficiently developed.\nCould other mechanisms (e.g., optical phonons) contribute? The authors should expand or\nqualify this interpretation.\nResponse: we thank the Reviewer for this insightful observation. We agree that the\ninterpretation of the off-resonance dynamics as arising solely from thermal modification of\ninterplanar distances, based primarily on the observed 330 fs timescale, was insufficiently\ndeveloped in the original manuscript. We now clarify and expand this interpretation, as\nrequested.\nIn the off-resonance regime (i.e., for large detuning Ω≳ 1 eV), the effective RIXS scattering\ntime is below ~2 fs, which is too short for the system to probe slower lattice distortions such\nas those associated with vibronic coupling or Jahn-Teller effects. The absence of overtone\nsidebands and the full overlap of pumped and unpumped spectra in this regime confirm\nthat excitonic contributions are no longer spectroscopically accessible.\nThe observed dynamics at long delays (with a characteristic timescale of ~330 fs) are\ninstead attributed to thermal effects—specifically, the adiabatic response of the lattice to\nenergy transfer from the photoexcited electron-hole plasma to the phononic subsystem.\nThis assignment is consistent with time-resolved diffraction studies on graphite and related\nmaterials, which report similar sub-picosecond timescales for the onset of lattice expansion\nand contraction processes following ultrafast optical excitation (see e.g., Harb et al. 2011,\nCarbone et al. 2008).\nHowever, we agree that additional phonon-related mechanisms may contribute to\nthe observed dynamics. In particular, the rapid population of strongly coupled optical\nphonons (SCOPs), which occurs on sub-100 fs timescales, could influence the transient\nspectral weight through anharmonic coupling to acoustic modes or thermal expansion\neffects. These SCOPs are known to dominate energy relaxation pathways in graphite\nwithin the first picosecond (Kampfrath et al. 2005, Caruso et al. 2020).\nTo reflect this broader perspective, we have revised the manuscript text (line: 606).\nWe hope this expanded interpretation addresses the Reviewer’s concern and provides a\nmore complete picture of the dynamics observed in the off-resonant regime.\nIf the authors address the above points and clarify their interpretation and novelty claims, this\nmanuscript would be significantly improved.\nWe thank the reviewers for their constructive and thoughtful comments. We have revised\nthe manuscript to address all concerns, including restructuring figures, clarifying\nterminology, expanding theoretical justification, and improving contextualization with prior\nwork. Below, we provide detailed responses to each point."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I feel like my questions were adequately addressed and the readability of the manuscript has been notably improved. I will leave it to the other referees to determine if their comments have been adequately addressed.", "reviewer_2": "We thank the authors for a careful revision and detailed responses. The inclusion of the full spectra is appreciated and helps in assessing the low-energy spectral features. While we appreciate the methodical innovation of the study, we had two major concerns. The experimental energy resolution raises questions about how phonon information can be uniquely and quantitatively extracted in the way claimed in the text. The Ament model has been shown to have major qualitative failures in how it can describe the low-energy spectra of graphite. To be publishable, the manuscript either needs to substantiate its claims of quantitatively tracking electron phonon coupling (i.e., quoting numbers) or it needs to directly say that it can only obtain qualitative trends and not quantitative information with its current data quality and model.\nThis requires many changes in the manuscript, but just to highlight a few, the text says:\n“This approach enables direct access to mode-specific vibronic dynamics under nonequilibrium conditions and uncovers a transient regime in which exciton-lattice interactions are strongly modulated\nby the screening environment.”\nWe disagree that this work is mode-specific. The spectrum has been explicitly shown in prior work to contain multiple\ndifferent phonons at different momenta, which are clearly not resolved here.\n“Our results broaden the applicability of time-resolved RIXS as a tool for quantifying exciton-phonon coupling dynamics”\nWhile the RIXS community would very much like to be able to quantitatively extract exciton phonon coupling, there have been prior works directly testing this idea that have shown that the approach used does not yield quantitatively valid couplings.\nThe same problems remain at many places in the text., particularly where numbers are quoted.\nWe’d like to raise some further concerns about the methodology along the same lines as the prior report:\n1) The manuscript extracts three quantities from RIXS data to narrate the story: the elastic line intensity scaling factor r, the\nexperimental inelastic spectral weight R, and its theoretical version based on Ament’s model. The first two are effectively\nunderdetermined without a valid estimate of the tr elastic line intensity. In the authors’ response to our previous 5), they\nmention “applying the same scaling to both elastic and inelastic parts”. Yet this is still unsubstantiated since the\nphonon contamination at 0 eV would vary as a function of detuning and pumping. The elastic part and phonon overtones both\ndepend on absorption cross section but can also be scattered off several other channels. Simple scaling between off and on-\nresonance introduces an apparent systematic error.\n2) We remain concerned about the usage of the single-mode Ament’s model, in view of the existing intensive study of the\nsame objects in PRL 125, 116401 (2020) and PRX 11, 041052 (2021). Both studies show explicitly that the phonon features\nseen in C K-edge compose of modes mixing, and state the limitation of Ament’s model in this case. Although the authors\nstate that “The Ament model is applied only to the total inelastic spectral weight and not to the decomposition into individual\nphonon modes or overtones.” We do not see any reason why the model should be trusted to describe the total intensity as a\nfunction of incident energy if it does not describe the shape of the spectrum as a function of energy loss. For example, how\nwould the sum of the red and green curves in Fig. R2A compare with the raw data in black?\n3) A few minor suggestions:\na) Maintain consistent panel labeling across all figures.\nb) In Fig. 4a, tau denotes the fast decay timescale and tau_s in b and c represents the effective scattering time. This notation\nis inconsistent with, for example Fig. 2b and lines 422–428.\nc) It is preferable to include in the main text the q probed in this experiment. This information shall also play a role in\ndetermining the phonon coupling mechanism.\nd) The symbol for detuning changes inconsistently in Section A.3, from \\Omega to \\Delta\nOverall, the current version of this manuscript rests on over-simplified assumptions in the face of resolution-hindered data,\nand has not yet demonstrated persuasively, that the interpretation together with the quantitative treatment of the inelastic\nspectra weight is valid. We suggest a further revision focusing on a validated elastic line extraction, and a model-adequacy\ncheck.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_4": "Round 2\nThe authors have addressed most of my comments, and I thank them for their efforts. Below I include some minor edits and\nencourage another grammar pass. However, I remain unsatisfied with the discussion of the off-resonant dynamics shown in\nFig. 4a. I find the discussion of a “thermally-drive adiabatic modification of interlayer lattice spacing” on a 100 fs timescale to\nbe incorrect and/or potentially misleading, and would like further clarification.\n• L67-69: Well specifically the excitonic hole would be localized (core) but the excitonic electron part of the wavefunction\nwould be delocalized, right?\n• L167-168: “This process generates a photoexcited hot electrons…” (grammar).\n• L578: The authors should clarify what is being plotted as DR/R, as this commonly refers to reflectivity measurements.\n• L606-611: I still do not agree with the authors’ conclusion here. Off resonance, the authors attribute the dynamics of Fig. 4a\nto a “thermally-driven adiabatic modification of interlayer lattice spacing”, but, to my knowledge, 330 fs is not the right time\nscale for this.\n• The time-scale of electron dynamics in graphite has been extensively measured and documented:\no Electron-electron scattering: fluence dependent, 10 fs timescale\n  Ulstrup, Søren, et al. \"Ultrafast electron dynamics in epitaxial graphene investigated with time-and angle-resolved\nphotoemission spectroscopy.\" Journal of Physics: Condensed Matter 27.16 (2015): 164206.\n  Gierz, Isabella, et al. \"Snapshots of non-equilibrium Dirac carrier distributions in graphene.\" Nature materials 12.12 (2013):\n1119-1124.\no Time to electron-bath thermalization: fluence dependent, 10-100 fs\n  Na, MengXing, et al. \"Establishing nonthermal regimes in pump-probe electron relaxation dynamics.\" Physical Review B\n102.18 (2020): 184307.\no Electron-SCOP scattering: fluence dependent, 100 fs timescale (here we have a non-thermalized lattice)\n  Na, MengXing, et al. \"Direct determination of mode-projected electron-phonon coupling in the time domain.\" Science\n366.6470 (2019): 1231-1236.\n  Yang, Jhih-An, et al. \"Novel electron-phonon relaxation pathway in graphite revealed by time-resolved Raman scattering\nand angle-resolved photoemission spectroscopy.\" Scientific Reports 7.1 (2017): 40876.\no Anharmonic phonon decay and lattice thermalization: 10-100 ps timescale.\n  Stern, Mark J., et al. \"Mapping momentum-dependent electron-phonon coupling and nonequilibrium phonon dynamics with\nultrafast electron diffuse scattering.\" Physical Review B 97.16 (2018): 165416.\n• In my opinion, only after lattice thermalization could one discuss a thermally-driven adiabatic modification of the interlayer\nspacing.\n• In Harb et al. the effect of laser induced strain was measured on the order of 10 ps.\n• In Carbone et al. 2008 the effect of lattice expansion is reported to be 7 ps.\no Here an initial contraction is on shorter timescales at very high fluences\n• In Carbone 2010, the author writes:\no “The photoinduced dynamics of carriers and lattice in graphite can be summarized as follows: The thermalization of the\ninitial fs electronic excitation takes 10–30 fs. During this time-scale the electronic structure is out of equilibrium and the\ncarrier temperature can reach several hundreds of degrees Kelvin. This process has been experimentally investigated by\nmeans of photoemission [13], THz [12] and optical pump probe experiments [1], while the modification of the electronic\nwavefunction has been recently investigated theoretically in [26]. In this period (0–100 fs) the electronic structure cannot be\ndescribed by standard LDA methods. During the electrons thermalization, emission of strongly coupled optical phonons\ntakes place because of graphite anisotropic band structure [27], [11]. These phonons are mainly in-plane vibrations of the\ncarbon ions (hard modes, 30 fs period) as well as a slower (700–1 ps period) c-axis shearing motion of the planes. During\nthe time between 100 and 500 fs, the electronic excitation relaxes back to equilibrium. The ultrafast compression reported in\n[5] begins in this time-scale and continues for about 2–3 ps.”\n• It’s possible the authors are referring to this ultrafast compression in their discussion, but this is not a thermal or adiabatic\nprocess, but an effect that seems to occur at very high (pre-ablation) fluences. Furthermore, I would note that the cartoon in\nFig. 4c does not reflect this, but rather seems to be a lattice expansion.\n• Still, beyond the timescale, I don’t see a reason why this ultrafast compression should be the most likely candidate to\nexplain the off-resonant behavior of Fig.4a.\n• L632: The authors could cite some TR-ARPES works here (see above)."}, "author_response": "General comment before addressing issues (1) and (2)\nWe thank the reviewer for the careful assessment and for clearly articulating the two central\nconcerns. We took these comments seriously and used them to sharpen both the scope\nand the message of the manuscript. In the revision:\n• We remove all mode-specific and quantitative claims. We no longer attempt to\nextract mode-resolved or numerical exciton-phonon coupling values. Throughout\nthe text and SI we now state explicitly that, at the present energy resolution, our\nanalysis yields qualitative trends only.\n• We tighten the methodology for determining the integrated inelastic weight (R):\ninstead of relying on a single scaling, we now present three independent\nnormalization schemes (zero-loss alignment, XAS-normalized spectra, and XAS-\nscaled reference) and show that they converge to the same detuning trend. This\ndirectly addresses the concern about 0-eV contamination and absorption-\ndependent channels and removes the possibility of a systematic error tied to a\nsingle assumption.\n• We redefine the role of the Ament model. It is used solely as a phenomenological\nenvelope for the integrated inelastic response versus detuning—never to\nreproduce loss-line shapes or to claim mode selectivity. To demonstrate model\nagnosticism at our resolution, the SI now includes both single-mode and two-mode\nenvelopes, which produce similar detuning dependencies of the integrated weight.\n• We revise wording across the abstract, introduction, results, and conclusions (red\ncoloured text in the manuscript) to reflect this scope. Statements previously\nimplying “mode-specific” or “quantitative” extraction have been removed or\nreplaced by language emphasizing qualitative changes in exciton–phonon\ncoupling. The primary message is now clearly framed as a pump-induced reduction\nof the integrated inelastic weight at the C K-edge σ resonance, interpreted as a\nqualitative signature of decreased exciton–phonon coupling under nonequilibrium\nconditions.\n• We also implement the reviewer’s stylistic requests (consistent panel labels and\nnotation, clarified (q) range, uniform detuning symbol) and add cross-references in\nthe SI for transparency.\nWith these changes, the manuscript presents a transparent, methodology-robust\nqualitative result that we believe addresses the reviewer’s concerns and strengthens the\npaper.\nWe’d like to raise some further concerns about the methodology along the same lines as the\nprior report:\n1) The manuscript extracts three quantities from RIXS data to narrate the story: the elastic line intensity scaling factor r, the\nexperimental inelastic spectral weight R, and its theoretical version based on Ament’s model. The first two are effectively\nunderdetermined without a valid estimate of the tr elastic line intensity. In the authors’ response to our previous 5), they\nmention “applying the same scaling to both elastic and inelastic parts”. Yet this is still unsubstantiated since the\nphonon contamination at 0 eV would vary as a function of detuning and pumping. The elastic part and phonon overtones both\ndepend on absorption cross section but can also be scattered off several other channels. Simple scaling between off and on-\nresonance introduces an apparent systematic error.\nResponse\nWe appreciate the reviewer’s careful methodological point. We agree that, at our\nexperimental energy resolution, the elastic and inelastic contributions cannot be uniquely\nseparated at the zero-loss position. For this reason, in the revised manuscript we do not\nclaim quantitative ExPC values and do not perform mode-specific fits. Instead, we report\nqualitative trends of the integrated inelastic weight (R) versus detuning and pump. In this\ncontext, (R) is used as a proxy (not an absolute cross section) for the total low-loss inelastic\nintensity (sum over unresolved phonon overtones).\nWhy the off-resonant spectrum is a valid elastic reference: the off-resonant peak (i)\ndisperses linearly with the incident energy (Rayleigh-like, not Raman-like), (ii) is\nsymmetric, and (iii) shows no valence-loss sidebands at our resolution. We therefore use\nit as an operational elastic lineshape. For each resonant spectrum, the off-resonant\nreference is scaled to the same zero-loss intensity; the difference (integrated over a fixed\nloss window) defines (R), a measure of the inelastic weight. We stress that this\nprocedure does not aim to fully separate elastic and inelastic parts, which is not feasible\nhere because of the energy resolution; it provides a consistent measure of change in the\ninelastic weight with detuning and pump.\nAddressing the reviewer’s concern about “applying the same scaling to elastic and\ninelastic parts.”\nTo remove any potential systematic error from a single scaling choice—especially if the\nzero-loss bin contains detuning- or pump-dependent phonon weight—we implemented\nthree independent normalization schemes that bracket the different possibilities for the\nbehavior at 0 eV and explicitly treat absorption. Their exact definitions are given in the SI\nSupplementary Note 5 “Detuning dependence of the inelastic RIXS response”, and their\nside-by-side comparison is shown in Supplementary Figure 6.\n1. Method 1: Elastic-peak alignment\nThe off-resonant reference is scaled to the measured zero-loss level of each\nresonant spectrum, and the difference is integrated over the analysis window.\nWhat it tests: the extreme in which the zero-loss bin is dominated by elastic\nintensity; any phonon weight near 0 eV manifests only as asymmetry away from\nthis baseline.\n2. Method 2: XAS-normalized resonant spectra\nEach resonant spectrum is first normalized by the C K-edge XAS amplitude at\nthat detuning (to factor out absorption), then equalized at zero loss, and finally\ncompared with the unscaled off-resonant reference.\nWhat it tests: a scenario where the absorption cross section, rather than the raw\nzero-loss level, governs the detuning dependence. Critically, this method does\nnot use the resonant zero-loss bin to set the baseline.\n3. Method 3: XAS-scaled reference\nThe resonant spectrum is left untouched; only the reference is scaled by the XAS\nfactor before subtraction and integration.\nWhat it tests: whether zero-loss alignment (Method 1) and absorption scaling\n(Method 3) are operationally equivalent for the integrated trend; it also explicitly\nbrackets any detuning- or pump-dependent phonon contribution at 0 eV, because\nthe resonant zero-loss bin is not used to define the baseline.\nConclusion.\nIn line with the reviewer’s methodological concern, we do not attempt a quantitative\nseparation of elastic and inelastic intensities. Instead, we use three independent,\nabsorption-aware normalizations that converge to the same R(W) trend. This strategy\nremoves the potential systematic error associated with simple off/on-resonance scaling\nand provides a robust qualitative measure of the pump-induced change in the total inelastic\nweight, which we interpret as a qualitative signature of reduced EPC in the σ* regime. For\nall operational details and formulas, please see SI.\n2) We remain concerned about the usage of the single-mode Ament’s model, in view of the existing intensive study of the\nsame objects in PRL 125, 116401 (2020) and PRX 11, 041052 (2021). Both studies show explicitly that the phonon features\nseen in C K-edge compose of modes mixing, and state the limitation of Ament’s model in this case. Although the authors\nstate that “The Ament model is applied only to the total inelastic spectral weight and not to the decomposition into individual\nphonon modes or overtones.” We do not see any reason why the model should be trusted to describe the total intensity as a\nfunction of incident energy if it does not describe the shape of the spectrum as a function of energy loss. For example, how\nwould the sum of the red and green curves in Fig. R2A compare with the raw data in black?\nResponse\nWe thank the reviewer for raising this important point regarding the limitations of the Ament\nsingle-mode model, especially in light of high-resolution studies of graphite at the C K-edge\n[PRL 125, 116401 (2020); PRX 11, 041052 (2021)]. We have carefully revised the\nmanuscript to fully address these concerns.\nFirst and foremost, we now clearly state that our analysis is qualitative and does not aim\nto resolve individual phonon modes or extract quantitative ExPC constants. We do not use\nthe Ament model to fit or reproduce the fine structure of the loss spectrum. Instead, we\nrestrict its use to serving as a phenomenological envelope for the integrated inelastic\nspectral weight R(Ω), as a function of incident photon detuning under both pumped and\nunpumped conditions.\nThis restricted scope is now explicitly stated in the main text and reiterated in the Methods.\nThe previous discussion of the ExPC fit parameters based on single-mode modeling has\nbeen removed.\nWe agree with the reviewer that single-mode displaced-oscillator models are not suited for\nmode-resolved analysis of C K-edge RIXS spectra, particularly under conditions where\nphonon mixing and momentum dispersion are important. Nevertheless, we have included\na detailed supplementary analysis to test whether our integrated metric R(Ω) is sensitive\nto this mode mixing. Specifically:\n• In SI Supplementary Note 3, we compare the theoretical detuning envelopes\ncalculated using both a single-mode Ament model and a two-mode extension,\nadopting parameters consistent with prior literature and convolving the results with\nthe instrumental resolution.\n• As shown in SI Supplementary Figures 3 and 4, both models yield nearly identical\ndetuning trends for the integrated inelastic weight after convolution. This\ndemonstrates that, at the current energy resolution (~350 meV), R(Ω) is a robust\nand resolution-appropriate proxy that is insensitive to detailed phonon composition.\n• Importantly, no fitting is performed; theory and data are shown under identical\ndisplay scaling to illustrate qualitative trends only.\nIn direct response to the reviewer’s question — “How would the sum of the red and green\ncurves in Fig. R2A compare with the raw data in black?” — we provide this comparison in\nSI Supplementary Note 5 and Supplementary Figure 5. At fixed detuning, we overlay: (i)\nthe broadened inelastic envelope, (ii) the elastic line, and (iii) their sum. This composite\nreproduces the overall envelope of the raw spectrum, but again, we do not interpret this as\na validation of lineshape fidelity. The agreement simply reinforces the qualitative role of the\nAment model in tracking integrated inelastic trends, not mode-specific behavior.\nThe reviewer’s comment prompted us to expand the theoretical motivation for using a\nsimplified Einstein-mode envelope in this regime:\n1. Intermediate-state phase space at the σ* resonance: The C K-edge resonance\naccesses highly localized σ* conduction states several eV above E , where core-\nF\nexcitonic effects are strong. In this energy range, the phase space for electron–phonon\n(and therefore exciton-phonon) scattering is highly restricted, favoring small-q optical\nphonons — namely, Γ-point modes like E . Prior literature and core-level calculations\n2g\nsupport this small-q dominance for localized excitations in graphite.\n2. Ab initio EPC analysis at high energy: As shown in panel (c) of Fig. 3 and discussed in\nSI Fig. 4S(a), our first-principles spectral function calculations reveal the strongest\nrenormalization of the σ* band near k ≈ Γ. This renormalization arises from coupling to\nΓ-point optical phonons, in particular the E mode. Contributions from larger-q\n2g\nphonons (K, M) are less pronounced in this intermediate-state manifold. This supports\nthe use of a single dominant mode to qualitatively follow R(Ω).\n3. Energy-dependent EPC channel evolution in graphite and graphene: Theoretical\nstudies [e.g., Margine & Giustino, PRB 90, 014518 (2014); Mazzola et al., PRB 95,\n075430 (2017)] show that the dominant phonon coupling channel depends on the\nexcitation energy. Near the Dirac point, the A1' mode at K dominates; however, at\nhigher energies relevant to σ-like bands, the EPC shifts toward E and ZO phonons.\n2g\nExtrapolating to the σ* resonance (~8 eV above EF), the phase space is most favorable\nfor small-q optical modes, validating a single-mode envelope for tracking R(Ω).\nThis qualitative trend in R(Ω) matters: it reveals how photoinduced screening modifies\nexciton–phonon interactions in real time. While most ultrafast EPC studies focus on low-\nenergy π/π* excitations near E , our work probes the higher-energy σ* manifold, where\nF\nvibronic interactions and phase space constraints differ significantly. The observed pump-\ninduced suppression of R(Ω) is consistent with reduced exciton–phonon coupling under\ntransient screening, a central finding of our study.\nTo conclude, we have thoroughly addressed the reviewer’s concerns:\n• The Ament model is not used to interpret phonon lineshapes or extract mode-\nresolved quantities.\n• Its use is limited to qualitatively modeling the detuning dependence of integrated\ninelastic weight.\n• We provide both theoretical and physical justification for the single-effective-mode\napproximation at the σ* resonance.\n• Comparisons between one- and two-mode models, and overlays with experiment,\nare now provided in the SI to transparently demonstrate robustness.\nWe believe that the revised manuscript now clarifies the scope, assumptions, and\nimplications of the modeling strategy, while maintaining a rigorous and realistic\ninterpretation of the data in light of current energy resolution constraints.\nNewly introduced references (as cited in manuscript/SI)\n• Ishioka et al., \"Ultrafast electron–phonon decoupling in graphite,\" Phys. Rev. B 77,\n121402 (2008).\n• Pomarico et al., \"Nonequilibrium dynamics and electron–phonon coupling in\ngraphene,\" Phys. Rev. B 95, 024304 (2017).\n• Margine & Giustino, \"Two-gap superconductivity in heavily -doped graphene: Ab\ninitio Migdal-Eliashberg theory\" Phys. Rev. B 90, 014518 (2014).\n• Mazzola et al., \"Strong electron–phonon coupling in the σ band of graphene,\"\nPhys. Rev. B 95, 075430 (2017).\n• Pan, Y. et al., \"Momentum-Resolved Signatures of Carrier Screening Effects on\nElectron–Phonon Coupling in MoS2,\" ACS Nano 19, 11381–11389 (2025).\n• Erhardt, N. G. et al., \"Ultrafast Nonequilibrium Enhancement of Electron–Phonon\nInteraction in 2H-MoTe2,\" Phys. Rev. Lett. 135, 146904 (2025).\n3) A few minor suggestions:\na) Maintain consistent panel labeling across all figures.\nWe have carefully reviewed and updated all figure labels in both the main text and the SI\nto ensure full consistency in panel naming and referencing.\nb) In Fig. 4a, tau (t) denotes the fast decay timescale and tau_s (t) in b and c represents the\ns\neffective scattering time. This notation is inconsistent with, for example Fig. 2b and lines 422–428.\nWe acknowledge the inconsistency and have corrected the notation throughout the\nmanuscript. In the revised version, tau consistently refers to the fast decay time extracted\nfrom the delay-dependent RIXS dynamics (Fig. 2b), while tau_s is used to denote the\neffective scattering time of the intermediate state (as shown conceptually in Fig. 3). These\ndefinitions are now clearly stated in the figure captions and main text to avoid ambiguity\nc) It is preferable to include in the main text the q probed in this experiment. This information shall\nalso play a role in determining the phonon coupling mechanism.\nWe thank the Reviewer for this helpful suggestion. We have clarified in the Experimental\nsection that the experimental geometry at the carbon K-edge (30° incidence and ~90°\nscattering angle) results in a small momentum transfer, ∣q⃗∣∼0.26 A˚−1. This corresponds\nto a region near the Brillouin zone center, consistent with dominant contributions from G-\npoint optical phonons. This observation supports our modeling strategy based on zone-\ncenter exciton–phonon coupling and justifies the use of an effective Einstein-mode\nenvelope in the analysis of detuning-dependent dynamics.\nd) The symbol for detuning changes inconsistently in Section A.3, from \\Omega to \\Delta\nWe thank the reviewer for spotting this inconsistency. We have corrected the symbol usage\nacross the entire manuscript and SI to consistently use W as the detuning variable, aligning\nwith its definition in the main text and equation references.\nOverall, the current version of this manuscript rests on over-simplified assumptions in the face of resolution-hindered data,\nand has not yet demonstrated persuasively, that the interpretation together with the quantitative treatment of the inelastic\nspectra weight is valid. We suggest a further revision focusing on a validated elastic line extraction, and a model-adequacy\ncheck.\nResponse to Reviewer #2\nWe thank the reviewer for the supportive comments and are pleased that the additional\nnormalization checks, the phenomenological use of the Ament model, and the softened\nquantitative statements clarified our interpretation of the pump-induced EPC changes.\nWe appreciate the recommendation for acceptance.\nResponse to Reviewer #3\nWe thank the reviewer for their contribution to the evaluation of our work\nResponse to Reviewer #4\nWe thank the reviewer for the positive assessment and recommendation for publication.\nWe have corrected the minor inconsistency in the styling of “tr-ARPES”: the acronym is\nnow written consistently as “tr-ARPES” throughout the manuscript, including at the\nlocations corresponding to former lines 588 and 594."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have substantially revised the manuscript to address our two major concerns. They provide additional\nnormalization checks converging on the same detuning trend as in Fig. S5. The inelastic weight is tested with an envelope\nproduced by the Ament’s model, in a phenomenological rather than quantitative sense. The authors have softened the\nquantitative statements about the pump-induced EPC change and focus more on the qualitative trend. We feel the revision is\nmore appropriately scoped and recommend acceptance.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_4": "The authors have satisfied my questions, and I support the manuscript's publication.\nI note one minor inconsistency in the styling of \"TR-ARPES\" in lines 588 and 594."}, "author_response": ""}]

Decision letter