Ultrafast nematic-orbital excitation in FeSe

The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In iron-pnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have as-yet-unconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time-, energy-, momentum- and orbital-resolved photo-emission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strong-excitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavily-damped oscillation. This short-life nematicity oscillation is seemingly related to the imbalance of Fe 3dxz and dyz orbitals. These phenomena show critical behavior as a function of pump fluence. Our real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice.

Reply to the Reviewer #1: The presented results are interesting and on a timely subject of nematic order and its origins in FeSe.
However, while the data is clearly presented, the analysis and in particular the conclusions that the authors draw from their data remains mostly speculative and semi-quantitative. While the experimental data may contain information that may lead to new insights about FeSe, the present manuscript does not sufficiently flesh out and justify any novel insights. I suggest that the authors point out more clearly what are the novel insights into FeSe that follow from their non-equilibrium study. Therefore, the paper is not of sufficient interest for the general reader (beyond the ultrafast community) and I cannot recommend publication of the manuscript in its present form at Nature

Communications.
We sincerely thank Reviewer 1 for carefully reading our manuscript and giving us important suggestions and comments. By answering to all his/her questions and comments as described below, we believe that the conclusion of our work and the derived novel insights are now much more clearly presented.

1) For example, the author's analysis on the origin of the oscillatory behavior in \Delta kFy remains rather inconclusive. The authors write what they think is not the origin (optical phonons, order parameter oscillation), but not what they think the origin is.
We thank the Reviewer for his/her important comment. As the Reviewer pointed out, the discussion on the oscillatory behavior in kFy was rather inconclusive. The most important aspect is that the observed antiphase oscillation of kFx and kFy, as shown in Fig. 2f, is the direct representation of Pomeranchuk-type Fermi surface oscillation. To make this point clear, we added the description below in line 8, page 4.
The observed anti-phase oscillation of kFx and kFy rather directly represents the Pomeranchuk-type oscillation of FS 29 , being intensively discussed as the fundamental excitation in the electronic nematic state. Accordingly, we added new reference number 29 as following.
[29] Pomeranchuk, I. Ia. On the stability of a Fermi liquid. J. Exp. Theor. Phys. 8, 361 (1959) In addition, we modify the discussion part. As described in the previous manuscript, electronic Raman scattering measurements [PNAS 113, 9177 (2016)] reported the critical behavior in the nematic susceptibility with the XY-symmetry for FeSe. By further referring to another recent study [arXiv:1710.09892], we can more deeply discuss the similarities between the nematic dynamics obtained by the electronic Raman scattering and our TARPES. In the Raman scattering study, the critical enhancement of nematic susceptibility and corresponding quasi-elastic peak (QEP) in the XY spectrum are observed in the tetragonal phase, on cooling toward the structural transition temperature (Ts). It implies the presence of the critical nematic fluctuation in T > Ts. On cooling below T < Ts, on the other hand, the QEP Raman intensity rapidly diminishes, and a gap opens in the XY spectrum indicating the sudden suppression of low-energy excitations [Fig. 1(b) in arXiv:1710.09892]. On further cooling below the superconducting transition temperature (Tc), they find a peak appearing at 3.6 meV, which they assign to the nematic resonance mode acquiring the coherence in the superconducting state. First we note that the energy of this nematic mode (3.6 meV) is fairly close to that of the Pomeranchuk-type FS oscillation (3.1 meV for 220 J/cm 2 ) obtained by TARPES, thus suggesting the similarity in the origin. Nevertheless, we have to also note that our measurements are done in the non-superconducting state (T ~ 20 K > Tc), where the coherent nematic mode does not exist. Our present interpretation is that the observed short-life FS oscillation should be associated with the QEP (i.e. nematic fluctuation) in the Raman study, since the T-dependence of QEP is very similar to the F-dependence of kFy oscillation; apparent only in F > Fc, and suddenly disappears in F < Fc. The nematic fluctuation should be of course incoherent in nature, however, we consider that by instantaneously triggering the dissolution of the nematic state, it can appear as the heavily-damped oscillatory response in the non-equilibrium time domain.
With these facts, we believe that we can offer the specific microscopic picture of the nematic excitation / fluctuation (i.e. the Pomeranchuk-type FS oscillation accompanying the orbital redistribution), which has been long discussed in the community due to its ubiquitous nature, but without being well identified.
To account for the Reviewer's advices, we modified the sentences in line 4, page 6 of the revised manuscript.
The nematic-orbital excitation obtained in the present TARPES shows a striking resemblance with the nematic dynamics in thermal equilibrium as probed by the recent Raman scattering measurements. 15,30 The electronic Raman spectra of XY symmetry (X and Y are coordinates along the crystal axes of the tetragonal setting) show the characteristic quasi-elastic peak (QEP) evolving toward Ts on cooling the temperature (T), discussed in terms of nematic susceptibility enhancement. 15,30 The QEP rapidly diminishes at T < Ts, on the other hand, and a gap opens in the XY Raman spectra thus indicating the suppression of low-energy nematic excitations (Ref. 30). These behaviors are reminiscent of the nematic-orbital excitation observed by TARPES, where the peculiar slowing behavior shows up in F > Fc, and the excitation itself suddenly disappears in F < Fc. The XY Raman spectrum further reveals a peak at 3.6 meV in the superconducting state (T < Tc), which is interpreted in Ref [30] as the nematic resonance mode acquiring the coherence by the superconducting gap opening. This energy scale is fairly close to that of the damped kF oscillation (3.1 meV) observed by TARPES near Fc, thus suggesting the similarity in its origin. With these facts, we presently consider that the nematic-orbital excitation obtained by TARPES should be associated with the QEP (i.e. nematic fluctuation) in the Raman study. The nematic fluctuation is incoherent in nature, however, by instantaneously triggering the dissolution of the nematic state, it may be appearing as the heavily-damped oscillatory response in the time domain.
We also added the reference number 30 as follows.

2) Another example, is the origin of the different behavior of the orbital occupations, and in
particular the discontinuous jump of t_ret at threshold. The main explanation (orbital flipping) that the authors offer to the reader, which is that orbital occupations oscillate between xz and yz, is not justified in the manuscript. In particular, based on the authors explanations, one would expect some effect of the orbital flipping to be visible in the yz occupations as well. Could authors please describe and clarify in more detail the process they call 'orbital flipping' and how they conclude that it occurs?
We thank the Reviewer's valuable suggestion. We agree that our interpretation of orbital-dependent carrier dynamics regarding tret should be more carefully and precisely explained. Here we would like to emphasize that tret is nearly identical to tp/2 (i.e. half of kF oscillation period) for all pump fluences (F > Fc). For the kF oscillation, we note that the transient FS at tp/2 is more elliptical than that expected without the oscillatory response. Such an overshoot of the nematicity should also appear in the orbital dependence of the carrier dynamics. In the process relaxing back from C4 isotropic to C2 nematic ground state, the electrons at the band top (black rectangles in Fig. 1 b,d) change their orbital characters from "degenerate xz/yz" to "predominantly xz". According to this consideration, we interpret that the retarded maximum in I(t) for xz should correspond to the orbital redistribution from yz to xz orbital ( Fig. 4a), accompanied by the overshoot of the FS nematicity at tp/2.
In this scenario, just as the Reviewer pointed out, there should be the counterpart decrease in the yz intensity at around tret. However, we could not observe clear evidence for the anomalous dynamics in the yz occupation. Since we are looking at the unoccupied state (7.5  2.5 meV above EF), there is always the decaying component of photoexcited electrons relaxing toward E < EF, appearing as the rapid decrease of intensity with the time constant of ~850 fs (fairly close to tret at F = 220 Jcm -2 ). The counterpart decrease expected in I(t) for yz may be overlapped by this process, thus making it difficult to be separately observed.
Through the above discussion, we have come to modify the term 'orbital flipping' to 'orbital redistribution', which should be more precisely representing the phenomena involving the change in the relative xz and yz occupations.
We added the sentences below in line 21 page 5 of the revised manuscript.
We note that the transient FS at tp/2 ( tret) is more elliptical than that expected without the oscillatory response. Such an overshoot of the nematicity in FS should also appear in the orbital-dependent carrier dynamics. In the process relaxing back from C4 isotropic to C2 nematic ground state, the electrons at the band top (black rectangle in Fig. 1 b,d) change their orbital characters from "(nearly) xz/yz degenerate" to "predominantly xz". The retarded maximum in I(t) for xz can be thus regarded as an indication of the orbital redistribution from yz to xz (Fig. 4a). The synchronized responses in the FS oscillation and orbitaldependent carrier dynamics thus represent the nematic-orbital excitation.
According to this modification, we revised the words "orbital flipping" into "orbital redistribution" in line 21, page 7 of the revised manuscript.

3) Identifying tp^{-1} with the equilibrium quantity \Gamma from Raman scattering in Ref.[15]
simply because both timescales are approximately (3 meV)^{-1} is not justified either. Since one of the main conclusions of the paper, which is that the electronic nematic dynamics is uncoupled from the lattice (which seems reasonable), is based on this identification, this must be underpinned with theory/analysis more thoroughly.
We thank the Reviewer for the valuable suggestion. We agree that there is no strong justification on directly comparing \Gamma of QEP in static Raman studies with the present tp -1 . From the result we believe there is some unknown relationship between them, however, at present we lack any theoretical support. For this reason, we modified the part describing the similarity in the behaviors of nematic dynamics obtained by Raman studies and TAPRES, as mentioned in Reply 1). Regarding the timescale, we now compare tp -1 (3.1 meV) with the peak energy of the nematic resonance Raman mode (3.6 meV) appearing in the superconducting state (arXiv:1710.09892), to discuss its possible similarity in the origin. Regarding the critical (F-linear) behavior, we simply focus on the T-linear behavior of the inverse of the QEP Raman intensity (interpreted as the nematic susceptibility), suggesting the critical enhancement of the nematic fluctuation toward the electronic nematic transition at T0 ~ 20 K (much below Ts = 90 K) [PNAS 113, 9177 (2016)]. The critical behavior of tp −1 toward F  40 Jcm −2 , i.e. much smaller than Fc, may be reflecting that the base temperature of the TARPES measurements (20 K) is close to T0. This similarity suggests that the dynamics of the nematicity in TARPES is seemingly electronic and thus decoupled from lattice.
Regarding the decoupling of the electronic system from the lattice, we also added some discussion based on the transient electronic / lattice temperatures, as we will discuss in Reply 5).
According to the above discussion, we revised the sentences below in line 1, page 7.
In F < Fc, as already mentioned, the kF oscillation as well as the anomaly in the xz orbital response disappear, and 1 −1 becomes constant. In the XY Raman spectrum, the critical T-linear behavior was found in the inverse of the QEP intensity above Ts (Ref. 15). By the detailed analysis of the Curie-Weiss-like T-dependent nematic susceptibility in the form of |T -T0| -1 , 15 the authors derived the bare electronic nematic transition temperature T0 that should describe the ideal nematic transition purely driven by electrons without any influence of lattice. For FeSe, T0 was estimated to be far below Ts,i.e. 8 K,20 K (Ref.15) and 30 K (Ref.31).
The critical behavior of tp −1 and 1 −1 toward F  40 20 Jcm −2 , i.e. much smaller than Fc, may be reflecting that the base temperature of the TARPES measurements (20 K) is close to T0. This scenario is also consistent with the initial photo-response of kFy with small threshold (< 30 Jcm −2 , see Fig. 2c). These results indicate that the electronic nematiciy in the initial ultrafast regime (~120 fs) shows the flexible photo-reaction by decoupling from the lattice.

4) Another minor question is related to the meaning of kF in non-equilibrium. The electronic
distribution function is clearly broadened and may not even be thermal. Looking at Fig.1(b), it looks as if there should be a substantial (systematic) error bar being associated with extracting kF in non-

equilibrium, but the data in panel (d) contain no error bars.
We thank for the Reviewer's important advice. As he/she mentioned, we are measuring the electronic state in non-equilibrium. However, in our time-region of interest (t > 120 fs), the electronic distribution obeys the Fermi-Dirac function with the elevated electronic temperature [will be discussed in 5)]. In this situation, we can safely obtain kF by fitting the momentum distribution curves at EF. Regarding the errors, we fully agree that we should clearly indicate the error bars of kFy in Fig. 2d. We apologize for missing this information. Here we added the error bars estimated from the fitting analysis of the MDCs using a Lorentz function as shown in Fig. R1. For example, the error bars for F = 430 J/cm 2 were estimated to be  0.0011 Å -1 at t = −400 fs,  0.0017 Å -1 at t = 120 fs and  0.0013 Å -1 at t = 4000 fs, respectively. As can be seen, this modification does not severely affect the context of the manuscript. According to this modification, we modified Fig. 2d in the revised manuscript as follows.
5) It would be useful if authors try to estimate the hypothetical final temperature of the electronic system based on the energy they deposit into the system, and compare this with T_S.
We thank for the Reviewer's valuable suggestion. To answer this important issue, here we directly estimate the electronic temperature (Te) from the fitting analysis of the momentum-integrated EDCs. In general, Te should be estimated by using the momentum-integrated EDC spectrum which represents the total density of states multiplied by the Fermi-Dirac function further convoluted by the instrumental resolution function, as performed in the previous TARPES [PRB 89, 115126 (2014)]. We integrated the EDCs of ARPES on xz from 0.0 Å -1 to 0.17 Å -1 along ky, and fitted by a FD function convoluted by the gaussian of energy resolution (20 meV), assuming the constant density of states neat EF (Fig. R2a). After the photoexcitation of 220 Jcm −2 , Te reaches 88 2 K at 120 fs. Then, it shows a rapid decrease in < 1 ps and remains nearly constant at 45 K for t > 3000 fs (Fig. R2b), which is considerably lower than Ts = 90 K.
According to the two-temperature model [J. Exp. Theor. Phys. 66, 375 (1974)], elevated Te approaches a constant value after the rapid relaxation via the electron-lattice coupling. There, the quasiequilibrium state is realized, where the temperatures of electrons and lattice become equivalent. This behavior has been indeed discussed in the ultrafast optical measurements of the iron-based superconductors [Nature Communications 5, 3229 (2014)]. The maximum lattice temperature is thus expected to be ~45 K in the present TARPES case. These analyses suggest that the electronic nematic order gets dissolved in the ultrafast regime while the lattice well maintains the orthorhombicity. With this, one of our main conclusion "the electronic nematic dynamics is uncoupled from the lattice" is well supported. According to the new data analysis regarding the estimation of Te, we added the discussion below in line 11, page 7.
Our analysis on the transient electronic temperature (Te) (Supplementary section 7) indeed shows that Te immediately reaches 88 2 K at 120 fs and then decreases in less than 1 ps (Fig. S6a, b). For t > 3 ps, it becomes nearly constant at ~45 K, indicating the realization of quasi-equilibrium state where the temperatures of electrons and lattice become equivalent through the electron-lattice coupling 32 . The maximum lattice temperature is thus much lower than Ts (= 90 K), showing that the lattice stays orthorhombic.
We also added the reference number 32.
According to this modification, the discussion below in line 24, on page 6 of the previous manuscript was removed.
Being at T  T0, the nematic FS may lose its C2 property even by a weak photo-excitation that never raises the electron temperature close to Ts, where the nematicity starts to decrease in thermal equilibrium (19). If this is the case, the electronic nematicity at least in this initial ultrafast regime (~120 fs) should be decoupled from the lattice.
We also added the supplementary section 7 with the supplementary Fig. S6 as following.

Section S7. Estimation of the transient electronic temperature.
Here we estimate the electronic temperature (Te) from the fitting analysis of the momentum-integrated EDCs. In general, Te should be estimated by using the momentum-integrated EDC spectrum which represents the total density of states multiplied by the Fermi-Dirac function further convoluted by the instrumental resolution function. We integrated the EDCs of ARPES on xz from 0.0 Å -1 to 0.17 Å -1 along ky, and fitted by a FD function convoluted by the gaussian of energy resolution (20 meV), assuming the constant density of states neat EF (Fig. S6a). After the photoexcitation of 220 Jcm −2 , Te reaches 88 2 K at 120 fs. Then, it shows a rapid decrease in < 1 ps and remains nearly constant at 45 K for t > 3000 fs (Fig.   S6b), which is considerably lower than Ts = 90 K.
According to the two-temperature model S5 , elevated Te approaches a constant value after the rapid relaxation via the electron-lattice coupling. There, the quasi-equilibrium state is realized, where the temperatures of electrons and lattice become equivalent. This behavior has been indeed discussed in the ultrafast optical measurements of the iron-based superconductors S6 . The maximum lattice temperature is thus expected to be ~45 K in the present TARPES case. These analyses suggest that the electronic nematic order gets dissolved in the ultrafast regime while the lattice well maintains the orthorhombicity. We also added the references below in the supplementary information.
Reply to the Reviewer #2 : The authors present a time-resolved ARPES study of detwinned FeSe, and report on the topic of pump-probe effects of electronic nematicity in this material. This is potentially an interesting study on the out-of-equilibrium effects of electronic nematicity, which would be novel to the field. However, there are several issues that prevent me from recommending publication in its current form.
We sincerely thank Reviewer 2 for evaluating our work and giving us valuable comments. We have now answered all the comments from the Reviewer and added new section of the Supplementary information according to his/her advice.

Could the authors comment on the effect of transient heating? Since the pump pulse necessarily
deposits energy unto the sample, which very likely heats the sample up, it is hard to disentangle whether the observed disappearance of nematicity is due to intrinsic excitation out of this electronic phase at a temperature below T_S or simply the effect of having raised the electronic temperature to above T_S in this material. The transient heating would also have a fluence dependence where beyond a critical fluence the sample would always be pumped above T_S, and a saturation of the change in kf is observed. This is an important issue regarding the argument that the pumped response probes the electronic nematicity decoupled from the lattice degree of freedom because in the case of transient heating the disappearance of electronic nematicity is observed on a tetragonal lattice via raised temperature, and in the case without transient heating the observed disappearance of electronic nematicity is observed on an orthorhombic lattice at base temperature.
We thank for the Reviewer's valuable suggestion. We agree that clarifying the effect of the transient heating is an important issue for correctly understanding the present TARPES results. For discussing the transient heating, it is important to introduce the temperatures for the electronic system (Te) and the lattice system (Tl). In the present case, we can conclude that Te reaches ~Ts (= 90 K) in the ultrafast regime when strongly excited, while Tl is always considerably lower than Ts (i.e. the lattice constantly remains orthorhombic).
This indicates that the electrons are instantaneously decoupled from the lattice, giving rise to the nearly pure dynamics of the many-body electrons system. This is also consistent with the very small F threshold (<< Fc) behavior of kF as seen in Fig. 2c. The estimation of Te is described in the following.
The transient heating should raise both the electronic temperature (Te) and lattice temperature (Tl) after photoexcitation. According to the two-temperature model [J. Exp. Theor. Phys. 66, 375 (1974)] which has been widely applied to the ultrafast dynamics in iron-based superconductors [Nature Communications 5, 3229 (2014)], the responses of Te and Tl are not equivalent until they reach the quasi-equilibrium state through the energy transfer from the electrons to the lattice. This process usually takes few ps depending on the strength of the electron-phonon coupling.
For understanding the transient heating effect, here we directly estimate the electronic temperature (Te) from the fitting analysis of the momentum-integrated EDCs. In general, Te should be estimated by using the momentum-integrated EDC spectrum which represents the total density of states multiplied by the Fermi-Dirac function further convoluted by the instrumental resolution function, as performed in the previous TARPES [PRB 89, 115126 (2014)]. We integrated the EDCs of ARPES on xz from 0.0 Å -1 to 0.17 Å -1 along ky, and fitted by a FD function convoluted by the gaussian of energy resolution (20 meV), assuming the constant density of states neat EF (Fig. R1a). After the photoexcitation of 220 Jcm −2 , Te reaches 88 2 K at 120 fs. Then, it shows a rapid decrease in < 1 ps and remains nearly constant at 45 K for t > 3000 fs ( Fig. R1b), which is considerably lower than Ts = 90 K.
According to the two-temperature model [J. Exp. Theor. Phys. 66, 375 (1974)], elevated Te approaches a constant value after the rapid relaxation via the electron-lattice coupling. There, the quasiequilibrium state is realized, where the temperatures of electrons and lattice become equivalent. This behavior has been indeed discussed in the ultrafast optical measurements of the iron-based superconductors [Nature Communications 5, 3229 (2014)]. The maximum lattice temperature is thus expected to be ~45 K in the present TARPES case. These analyses suggest that the electronic nematic order gets dissolved in the ultrafast regime while the lattice well maintains the orthorhombicity. We also note that the orthorhombicity requires the longer time and higher pump fluence to be fully suppressed. According to the pump-probe Xray diffraction measurement on BaFe2As2, 10 % suppression of the orthorhombicity occurs in 30 ps by F = 3.3 mJ/cm 2 [Struct. Dyn. 3, 023611 (2016)].
Owing to the Reviewer's valuable advice, we believe that one of the main claims "the pumped response probes the electronic nematicity decoupled from the lattice degree of freedom" has become much clearer. According to the new data analysis regarding the estimation of Te, we added the discussion below in line 11, page 7.
Our analysis on the transient electronic temperature (Te) (Supplementary section 7) indeed shows that Te immediately reaches 88 2 K at 120 fs and then decreases in less than 1 ps ( Fig. S6a, b). For t > 3 ps, it becomes nearly constant at ~45 K, indicating the realization of quasi-equilibrium state where the temperatures of electrons and lattice become equivalent through the electron-lattice coupling 32 . The maximum lattice temperature is thus much lower than Ts (= 90 K), showing that the lattice stays orthorhombic.
We also added the reference number 32.
According to this modification, the discussion below in line 24, on page 6 of the previous manuscript was removed.
Being at T  T0, the nematic FS may lose its C2 property even by a weak photo-excitation that never raises the electron temperature close to Ts, where the nematicity starts to decrease in thermal equilibrium (19). If this is the case, the electronic nematicity at least in this initial ultrafast regime (~120 fs) should be decoupled from the lattice.
We also added the supplementary section 7 with the supplementary Fig. S6 below.

Section S7. Estimation of the transient electronic temperature.
Here we estimate the electronic temperature (Te) from the fitting analysis of the momentum-integrated EDCs. In general, Te should be estimated by using the momentum-integrated EDC spectrum which represents the total density of states multiplied by the Fermi-Dirac function further convoluted by the instrumental resolution function. We integrated the EDCs of ARPES on xz from 0.0 Å -1 to 0.17 Å -1 along ky, and fitted by a FD function convoluted by the gaussian of energy resolution (20 meV), assuming the constant density of states neat EF (Fig. S6a). After the photoexcitation of 220 Jcm −2 , Te reaches 88 2 K at 120 fs. Then, it shows a rapid decrease in < 1 ps and remains nearly constant at 45 K for t > 3000 fs (Fig.   S6b), which is considerably lower than Ts = 90 K.
According to the two-temperature model S5 , elevated Te approaches a constant value after the rapid relaxation via the electron-lattice coupling. There, the quasi-equilibrium state is realized, where the temperatures of electrons and lattice become equivalent. This behavior has been indeed discussed in the ultrafast optical measurements of the iron-based superconductors S6 . The maximum lattice temperature is thus expected to be ~45 K in the present TARPES case. These analyses suggest that the electronic nematic order gets dissolved in the ultrafast regime while the lattice well maintains the orthorhombicity. We also added the references below in the supplementary information. We thank the Reviewer for his/her valuable suggestion. As replied to the Comment 1, we analyzed the momentum-integrated EDC of xz using a Fermi Dirac function convoluted with the instrumental resolution.
Regarding the shape of EDCs, we can conclude that they look like the thermally broadened spectra with elevated Te, at least in the t > 120 fs region where we discuss the nematic dynamics in this paper. This is because the electrons usually get quickly thermalized by the electron-electron interaction, typically in 10-100 fs. The peak/ hump structure above EF should definitely appear in a more ultrafast regime (e.g. < ~10 fs), especially when much shorter optical pulses are used (in the present work, the pulse duration is 250 fs). Fig. 3a and 3b, if the pumping excites xz electrons to unoccupied xz states above EF, where do the pumped yz electrons go in panel b? It seems that there is substantial spectral weight depletion after pumping in the yz states. Then where does it go if it cannot go into the unoccupied xz states?

Along the same lines, comparing
We thank the Reviewer for his/her valuable comment. As the Reviewer pointed out, we find substantial spectral weight depletion in the yz states after pumping. While it awaits further investigations, we consider that the photo-excited yz electrons may be partly trapped at the M point. Figure   We also modified the sentence in line 4 page 5 of previous manuscript as following.
As shown in Fig. 3g,h, I(t) of xz exhibits the retarded maximum at tret = 700 fs, whereas the yz electrons show the simple exponential decay similar to the weak-excitation regime, with the initial maximum at ~250 fs.

→
As shown in Fig. 3g,h, I(t) of xz exhibits the retarded maximum at tret = 700 fs, whereas the yz electrons show the exponential decay more or less similar to the weak-excitation regime, with the initial maximum at ~250 fs.

4.
There is an oscillatory component in the delay response for higher fluences. This, if real, would not be due to transient heating. Could the authors discuss more the potential origin of this mode?
We thank the Reviewer for his/her important comment. As the Reviewer pointed out, the discussion on the potential origin of the oscillatory behavior in kFy was rather inconclusive. The most important aspect is that the observed anti-phase oscillation of kFx and kFy, as shown in Fig. 2f, is the direct representation of Pomeranchuk-type Fermi surface oscillation. To make this point clear, we added the description below in line 8, page 4.
The observed anti-phase oscillation of kFx and kFy rather directly represents the Pomeranchuk-type oscillation of FS 29 , being intensively discussed as the fundamental excitation in the electronic nematic state.
Accordingly, we added new reference number 29 as following.
[29] Pomeranchuk, I. Ia. On the stability of a Fermi liquid. J. Exp. Theor. Phys. 8, 361 (1959) In addition, we modify the discussion part. As described in the previous manuscript, electronic Raman scattering measurements [PNAS 113, 9177 (2016)] reported the critical behavior in the nematic susceptibility with the XY-symmetry for FeSe. By further referring to another recent study [arXiv:1710.09892], we can more deeply discuss the similarities between the nematic dynamics obtained by the electronic Raman scattering and our TARPES. In the Raman scattering study, the critical enhancement of nematic susceptibility and corresponding quasi-elastic peak (QEP) in the XY spectrum are observed in the tetragonal phase, on cooling toward the structural transition temperature (Ts). It implies the presence of the critical nematic fluctuation in T > Ts. On cooling below T < Ts, on the other hand, the QEP Raman intensity rapidly diminishes, and a gap opens in the XY spectrum indicating the sudden suppression of low-energy excitations [ Fig. 1(b) in arXiv:1710.09892]. On further cooling below the superconducting transition temperature (Tc), they find a peak appearing at 3.6 meV, which they assign to the nematic resonance mode acquiring the coherence in the superconducting state. First we note that the energy of this nematic mode (3.6 meV) is fairly close to that of the Pomeranchuk-type FS oscillation (3.1 meV for 220 J/cm 2 ) obtained by TARPES, thus suggesting the similarity in the origin. Nevertheless, we have to also note that our measurements are done in the non-superconducting state (T ~ 20 K > Tc), where the coherent nematic mode does not exist. Our present interpretation is that the observed short-life FS oscillation should be associated with the QEP (i.e. nematic fluctuation) in the Raman study, since the T-dependence of QEP is very similar to the F-dependence of kFy oscillation; apparent only in F > Fc, and suddenly disappears in F < Fc. The nematic fluctuation should be of course incoherent in nature, however, we consider that by instantaneously triggering the dissolution of the nematic state, it can appear as the heavily-damped oscillatory response in the non-equilibrium time domain.
With these facts, we believe that we can offer the specific microscopic picture of the nematic excitation / fluctuation (i.e. the Pomeranchuk-type FS oscillation accompanying the orbital redistribution), which has been long discussed in the community due to its ubiquitous nature, but without being well identified.
To account for the Reviewer's advices, we added the sentences below in line 6, page 6 of the revised manuscript.
The nematic-orbital excitation obtained in the present TARPES shows a striking resemblance with the nematic dynamics in thermal equilibrium as probed by the recent Raman scattering measurements. 15,30 The electronic Raman spectra of XY symmetry (X and Y are coordinates along the crystal axes of the tetragonal setting) show the characteristic quasi-elastic peak (QEP) evolving toward Ts on cooling the temperature (T), discussed in terms of nematic susceptibility enhancement. 15,30 The QEP rapidly diminishes at T < Ts, on the other hand, and a gap opens in the XY Raman spectra thus indicating the suppression of low-energy nematic excitations (Ref. 30). These behaviors are reminiscent of the nematic-orbital excitation observed by TARPES, where the peculiar slowing behavior shows up in F > Fc, and the excitation itself suddenly disappears in F < Fc. The XY Raman spectrum further reveals a peak at 3.6 meV in the superconducting state (T < Tc), which is interpreted in Ref [30] as the nematic resonance mode acquiring the coherence by the superconducting gap opening. This energy scale is fairly close to that of the damped kF oscillation (3.1 meV) observed by TARPES near Fc, thus suggesting the similarity in its origin. With these facts, we presently consider that the nematic-orbital excitation obtained by TARPES should be associated with the QEP (i.e. nematic fluctuation) in the Raman study. The nematic fluctuation is incoherent in nature, however, by instantaneously triggering the dissolution of the nematic state, it may be appearing as the heavily-damped oscillatory response in the time domain.
We also added the sentences below in line 1, page 7 of the revised manuscript.
In F < Fc, as already mentioned, the kF oscillation as well as the anomaly in the xz orbital response disappear, and 1 −1 becomes constant. In the B1g Raman spectrum, the critical T-linear behavior was found in the These results indicate that the electronic nematiciy in the initial ultrafast regime (~120 fs) shows the flexibile photo-reaction by decoupling from the lattice.
We also added the reference number 30 as follows.  (2017)]. Since this is considerably shorter than the pulse duration of the present TARPES measurements (250 fs), they seem to be severely suppressed.
To address this point clearly, we add the sentence below in line 6, page 4, as the footnote in reference number 28.
[28] We note that the previously reported A1g optical phonons 25 are absent in the present TARPES data, because of the time resolution (250 fs). We thank the Reviewer 3 for highly evaluating our work and recommending the publication in Nature Communications. We have now answered all the comments from the Reviewer.

My only criticism regards the speculative attempt to identify the fluence dependence of the timescales with a critical behavior. Could the author explain what is a quantum critical point? A hypothetic nematic phase that, if decoupled from the lattice, would display a transition temperature of 20 K does not lead to a quantum critical point. On which basis such hypothetical phase would lead to fluctuations affecting linearly the electronic timescale if the fluence overcomes the threshold value?
First we would like to apologize that the statement on the quantum critical point at the last part (line 23, page 6 in the previous version) was perhaps misleading. As he/she pointed out, FeSe shows the nematic phase transition at Ts = 90 K (T0 = 20 K for the hypothetical electronic phase), which is not located at the quantum critical point (QCP). Nevertheless, we believe that the critical behavior of various timescales in the fluence dependence can be discussed in analogy with those appearing in the vicinity of temperature-or any parameter-driven (e.g. pressure, magnetic/electric field, etc) phase transitions. In general, when there is a phase transition at the critical parameter of Pc, the critical phenomenon appears in many physical quantities e.g. susceptibility, correlation length, specific heat, and so on, in the |P -Pc| a form (a: critical exponent). In the present case of FeSe, as reported by Raman scattering studies, the intensity of the quasielastic peak (interpreted as the nematic susceptibility) shows the |T -T0| -1 behavior at T > Ts, thus indicating the critical fluctuation enhancement toward T0 (<< Ts), which quenches below the structural transition Ts [PNAS 113, 9177 (2016)]. The F-dependent time-scales of damped kF oscillation as well as the xz orbital retardation are reminiscent of such behavior, i.e. |F -F0| -1 property with F0 = 40 20 Jcm -2 (<< Fc = 220 Jcm -2 ) at F > Fc, which suddenly disappears in F < Fc. Considering this striking similarity, we conclude that the heavily damped kF oscillation and the xz orbital retardation are associated with the critical nematic fluctuation observed by Raman studies.
Regarding the quantum criticality, we can access the QCP of the nematic phase by replacing 17% of Se with S in Fe(Se,S) system [PNAS 113, 8139 (2016)]. It will be very interesting to study this QCP by TARPES. Near the QCP, the electronic Raman scattering shows a drastic enhancement of the nematic (quantum) fluctuations toward 0 K. In this case, the FS dynamics should be dominated by the enhanced nematic fluctuation also in the very weakly excited conditions, and the threshold fluence Fc is expected to approach zero. For clarifying the dynamics of the electronic nematicity near the QCP, further TARPES measurements on the FeSe1-xSx system are highly desired.
To account for this important issue, we changed the sentence below in line 1, page 8.

Summary of changes;
1. We changed the word "is" into "are" in line 1, page 3.
2. We modified the equation in line 3, page 4 as follows.
[28] We note that the previously reported A1g optical phonons 25 are absent in the present TARPES data, because of the time resolution (250 fs). 5. We added the words "(22 meV)" in line 7, page 4. 6. We modified the words "3 meV for 220 Jcm -2 " into "3.1 meV for 220 Jcm -2 " in line 7, page 4. 7. We changed the sentence in line 8, page 4 in the previous manuscript as following.
It should be also distinguished from amplitude modes of symmetry-broken states 22,28 (i.e. nematic-order in this case), considering that the oscillations are rather lacking in the ordered weak-excitation regime.

→
The observed anti-phase oscillation of kFx and kFy rather directly represents the Pomeranchuk-type oscillation of FS 29 , being intensively discussed as the fundamental excitation in the electronic nematic state. 8. We removed the previous reference number 28 and added new reference number 29.
As shown in Fig. 3g,h, I(t) of xz exhibits the retarded maximum at tret = 700 fs, whereas the yz electrons show the simple exponential decay similar to the weak-excitation regime, with the initial maximum at ~250 fs.

→
As shown in Fig. 3g,h, I(t) of xz exhibits the retarded maximum at tret = 700 fs, whereas the yz electrons show the exponential decay more or less similar to the weak-excitation regime, with the initial maximum at ~250 fs.
10. We modified the words, "orbital flipping" into "retarded maximum in xz component" in line 18, page 5. 11. We added the word "similarly" in line 18, page 5.
13. We added the sentences below in line 21 page 5 of the revised manuscript.
We note that the transient FS at tp/2 ( tret) is more elliptical than that expected without the oscillatory response. Such an overshoot of the nematicity in FS should also appear in the orbital-dependent carrier dynamics. In the process relaxing back from C4 isotropic to C2 nematic ground state, the electrons at the band top (black rectangle in Fig. 1 b,d) change their orbital characters from "(nearly) xz/yz degenerate" to "predominantly xz". The retarded maximum in I(t) for xz can be thus regarded as an indication of the orbital redistribution from yz to xz (Fig. 4a). The synchronized responses in the FS oscillation and orbitaldependent carrier dynamics thus represent the nematic-orbital excitation.
14. We added the sentences below in line 6, page 6 of the revised manuscript.
The nematic-orbital excitation obtained in the present TARPES shows a striking resemblance with the nematic dynamics in thermal equilibrium as probed by the recent Raman scattering measurements. 15,30 The electronic Raman spectra of XY symmetry (X and Y are coordinates along the crystal axes of the tetragonal setting) show the characteristic quasi-elastic peak (QEP) evolving toward Ts on cooling the temperature (T), discussed in terms of nematic susceptibility enhancement. 15,30 The QEP rapidly diminishes at T < Ts, on the other hand, and a gap opens in the XY Raman spectra thus indicating the suppression of low-energy nematic excitations (Ref. 30). These behaviors are reminiscent of the nematic-orbital excitation observed by TARPES, where the peculiar slowing behavior shows up in F > Fc, and the excitation itself suddenly disappears in F < Fc. The XY Raman spectrum further reveals a peak at 3.6 meV in the superconducting state (T < Tc), which is interpreted in Ref [30] as the nematic resonance mode acquiring the coherence by the superconducting gap opening. This energy scale is fairly close to that of the damped kF oscillation (3.1 meV) observed by TARPES near Fc, thus suggesting the similarity in its origin. With these facts, we presently consider that the nematic-orbital excitation obtained by TARPES should be associated with the QEP (i.e. nematic fluctuation) in the Raman study. The nematic fluctuation is incoherent in nature, however, by instantaneously triggering the dissolution of the nematic state, it may be appearing as the heavily-damped oscillatory response in the time domain.
16. We revised the sentences below in line 1, page 7: In F < Fc, as already mentioned, the kF oscillation as well as the anomaly in the xz orbital response disappear, and 1 −1 becomes constant. In the B1g Raman spectrum, the critical T-linear behavior was found in the inverse of the QEP intensity above Ts (Ref. 15). By the detailed analysis of the Curie-Weiss-like Tdependent nematic susceptibility in the form of |T -T0| -1 , 15 the authors derived the bare electronic nematic transition temperature T0 that should describe the ideal nematic transition purely driven by electrons without any influence of lattice. For FeSe, T0 was estimated to be far below Ts,i.e. 8 K,20 K (Ref.15) and 30 K (Ref.31). The critical behavior of tp −1 and 1 −1 toward F  40 20 Jcm −2 , i.e. much smaller than Fc, may be reflecting that the base temperature of the TARPES measurements (20 K) is close to T0. This scenario is also consistent with the initial photo-response of kFy with small threshold (< 30 Jcm −2 , see Fig. 2c).
These results indicate that the electronic nematiciy in the initial ultrafast regime (~120 fs) shows the flexibile photo-reaction by decoupling from the lattice. Fig. 2d. 18. We removed the sentences in line 9, page 6 in the previous manuscript.

We added the error bars in
Being at T  T0, the nematic FS may lose its C2 property even by a weak photo-excitation that never raises the electron temperature close to Ts, where the nematicity starts to decrease in thermal equilibrium (19). If this is the case, the electronic nematicity at least in this initial ultrafast regime (~120 fs) should be decoupled from the lattice.
19. We added the discussion below in line 11, page 7.
Our analysis on the transient electronic temperature (Te) (Supplementary section 7) indeed shows that Te immediately reaches 88 2 K at 120 fs and then decreases in less than 1 ps (Fig. S6a, b). For t > 3 ps, it becomes nearly constant at ~45 K, indicating the realization of quasi-equilibrium state where the temperatures of electrons and lattice become equivalent through the electron-lattice coupling 32 . The maximum lattice temperature is thus much lower than Ts (= 90 K), showing that the lattice stays orthorhombic. 20. We modified the words, "orbital flipping" into "orbital redistribution" in line 21, page 7. 21. We modified the sentences below in line 1, page 8. 22. We also added the references as follows.

Section S7. Estimation of the transient electronic temperature.
Here we estimate the electronic temperature (Te) from the fitting analysis of the momentum-integrated EDCs. In general, Te should be estimated by using the momentum-integrated EDC spectrum which represents the total density of states multiplied by the Fermi-Dirac function further convoluted by the instrumental resolution function. We integrated the EDCs of ARPES on xz from 0.0 Å -1 to 0.17 Å -1 along ky, and fitted by a FD function convoluted by the gaussian of energy resolution (20 meV), assuming the constant density of states neat EF (Fig. S6a). After the photoexcitation of 220 Jcm −2 , Te reaches 88 2 K at 120 fs. Then, it shows a rapid decrease in < 1 ps and remains nearly constant at 45 K for t > 3000 fs (Fig.   S6b), which is considerably lower than Ts = 90 K.
According to the two-temperature model S5 , elevated Te approaches a constant value after the rapid relaxation via the electron-lattice coupling. There, the quasi-equilibrium state is realized, where the temperatures of electrons and lattice become equivalent. This behavior has been indeed discussed in the ultrafast optical measurements of the iron-based superconductors S6 . The maximum lattice temperature is thus expected to be ~45 K in the present TARPES case. These analyses suggest that the electronic nematic order gets dissolved in the ultrafast regime while the lattice well maintains the orthorhombicity. 24. We added the references below in the supplementary information.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): As said in my previous report, the manuscript "Ultrafast nematic-orbital excitation in FeSe" contains an interesting and thorough experimental study of the dynamics of electronic nematicity after photoexcitation at optical frequencies in FeSe. My main concern was regarding the analysis, modeling and interpretation of the experimental data and which new physical insights are obtained from this study. The revised manuscript addresses most of my concerns, in particular regarding the analysis part.
The revised manuscript now includes results of the transient electronic "temperature" after photoexcitation (extracted from fitting EDCs for xz orbitals). This confirms that the lattice remains below the nematic transition T_s while the electronic temperature reaches a temperature T \approx T_s shortly after/during the pump (after 120 fs). At longer times, the electronic temperature saturates at T=45 K, which is well below T_s. Wording of the manuscript has also been improved at various locations, making the manuscript more readable. The figures contain a lot of information, but are well organized and clearly arranged.
The interpretation and modeling aspect of the work is certainly improved but still rather speculative. On the positive side, this may trigger further studies on the subject. Overall, I am not a strong advocate for publication of the manuscript in Nature Communication, but I still support it, because this TARPES study is a very useful addition to the literature on FeSe that will stimulate further research on the subject, both in and out of equilibrium.
Before publication, I urge the authors to revise the discussion about comparison to Raman study, in particular, regarding the comparison with Raman results in the superconducting state. While a comparison to equilibrium Raman studies is a good starting point, it is too simplistic to associate certain excitations they find with modes seen in Raman in equilibrium simply based on similar energy scales. The reason is that in the TARPES experiment, the system is far from equilibrium, where entirely new physics may appear that is absent in (or close to) equilibrium, where the Raman study is performed. Furthermore, various possible excitations are nearby in energy and interactions and nonlinearities cannot be neglected out of equilibrium. Phonons, both acoustic and optical, are also present (and nearby in energy) and their effect is not discussed in much detail in the manuscript. It is not convincing that the (oscillation) timescale t_p, which authors extract from the xz photoelectron dynamics in the normal state (above superconducting Tc), should be associated with the Raman resonance mode observed only in the superconducting state (analogously to the neutron resonance mode). This discussion should be substantially revised before publication.
Further, I would suggest that authors discuss the potential impact of phonon dynamics on their observations, in particular, given that the optical phonon frequency they mention (22 meV \equiv 0.2 ps) is also in the range of timescales/energy scales under investigation. Since the orbital content of the Fermi pockets is linked to the state of the lattice, phonon excitations may strongly affect the electronic carrier distribution in n_{xz} and n_{yz} orbitals as well. Since the pump is in the optical range, it is expected that optical phonons will also be excited. As their timescales is comparable to the few ps timescales observed in the experiment, it is not obvious that their effect can be neglected.
Minor questions that the authors should consider are: 1) Which fluence F is used in Fig.2 (a, b)? 2) Would it be possible to add a y-axis scale to Fig. 2 (d)?
Reviewer #2 (Remarks to the Author): The authors have answered all questions in detail and I am satisfied with the modifications. The manuscript has been much improved and I am happy to recommend its publication.
One comment regarding the asymmetry between xz and yz after pumping in the weak fluence regime ( Fig. 3a and b). It seems that what the authors put in the response to be rather important, that there is an asymmetric scattering channel for xz and yz between Gamma and M in the nematic state, which could be the reason for the missing yz spectral weight at Gamma after pumping. At least this seems consistent with the equilibrium ARPES results (and perhaps even the STM result) on FeSe in that the electron pocket carrying xz at M has been missing while the observed electron pocket is dominated by yz. Could it be useful to include a sentence in the main text pointing out this difference of behavior between xz and yz, if not the potential interpretation, at least a statement of the experimental observation?
Reviewer #3 (Remarks to the Author): This article represent the first clear signature of electronic oscillations related to a nematic phase. As explained by the author the monitored mode can be detect even if the nematic order does not hold long range coherence. The high quality data on detwinned crystals are hard to obtain and demand strong experimental effort. Being an expert in time resolved ARPES, I could say that this article is more interesting than several recent works published in Science or Nature and that target just the ultrafast community. I am satisfied by the reply of the authors to my comment about quantum criticality. However the final discussion of the article is too speculative. I support publication in Nature Comm. but I encourage the authors fix the following issues: a) It would be good to state that the 1/|T-T_c| behavior is expected from Gaussian fluctuations and not does not provide information about the universality class and critical exponents. a) The dynamical scaling observed when the system is weakly perturbed and the temperature approach T_c is conceptually different the one observed when approaching the fluence to a threshold value. The authors may rather consider non-equilibrium criticality to the explain their data. c) On the base of the data that I have seen, there is no reason to claim that the excitation of nematic order is decoupled to the lattice. On one hand, the conjecture of an underlying electronic transition at lower temperature is badly posed. Indeed, it is the relevant coupling to the lattice that defines the experimetal T_c. On the other hand, the observed critical fluence is not particularly small and also corroborates a significant coupling to the lattice. As a consequence the authors should revise missleading statements as "These real-time observations reveal the nature electronic nematic excitation decoupled from the underlying lattice.
Reply to the Reviewer #1: We sincerely thank Reviewer 1 for positively evaluating our manuscript and giving us important suggestions and comments. By answering to all his/her questions and comments as described below, we believe that the discussion part is improved. This discussion should be substantially revised before publication. Further, I would suggest that authors discuss the potential impact of phonon dynamics on their observations, in particular, given that the optical phonon frequency they mention (22 meV ¥equiv 0.2 ps) is also in the range of timescales/energy scales under investigation. Since the orbital content of the Fermi pockets is linked to the state of the lattice, phonon excitations may strongly affect the electronic carrier distribution in n_{xz} and n_{yz} orbitals as well. Since the pump is in the optical range, it is expected that optical phonons will also be excited. As their timescales is comparable to the few ps timescales observed in the experiment, it is not obvious that their effect can be neglected.
We agree that the present comparison between the TARPES and electronic Raman scattering is somewhat speculative, and more detailed discussion on non-equilibrium critical phenomenon is certainly necessary. Nevertheless, the theoretical basis for such discussion is still severely lacking, and developing it may be beyond the scope of this paper. We strongly hope our work will stimulate the future investigations.
According to the Reviewer's advice, we removed the sentences describing the direct comparison between the observed Fermi surface oscillation and the nematic collective Raman mode in the superconducting state (line 14, page 6 in the previous manuscript), and added some discussion to stress the above point (line 20, page 7 in the present manuscript) .
We removed the statement (line 14, page 6 in the previous manuscript): "The XY Raman spectrum further reveals a peak at 3.6 meV in the superconducting state (T < T c ), which is interpreted in Ref [30] as the nematic resonance mode acquiring the coherence by the superconducting gap opening. This energy scale is fairly close to that of the damped k F oscillation (3.1 meV) observed by TARPES near F c , thus suggesting the similarity in its origin." We added the discussion (line 20, page 7 in the present manuscript): "This behavior is seemingly related to the critical nematic fluctuation, nevertheless, future theoretical studies on non-equilibrium critical phenomena are highly necessary." We also agree with the possible importance of the optical / acoustic phonon dynamics in relation to the nematic-orbital excitations detected by TARPES. Regarding the coherent A 1g optical phonon mode (22 meV, 190 fs) as reported by several TARPES studies [Science 357, 71 (2017).], however, it is fairly difficult to observe in the present experimental setup utilizing the pump pulse of ~170 fs FWHM. Since this pulse duration is very close to the time period of the A 1g optical phonon mode, the oscillatory response may be cancelled out even though the total time resolution itself is not so bad (250 fs). To fully understand the nematic excitation in association with phonons, more systematic time-resolved measurements on electrons and lattice (TARPES, ultrafast x-ray & electron diffraction, etc) with shorter pulses are highly desired. To discuss these points, we added some descriptions as follows.
We added some description on A 1g phonons (line 9, page 4): "The time scale of the oscillatory response (1.4 ps, 3.1 meV) is considerably slow as compared to the coherent A 1g optical phonon (190 fs, 22 meV) which is known to strongly couple to the electronic state in this system [24][25][26] . Their potential interplay is unfortunately hidden in the present TARPES data, possibly due to the duration of the pump pulse (170 fs) comparable to the time period of A 1g mode (190 fs) that tends to vanish the coherent oscillation." We added some description on future perspective (line 2, page 8): "Systematic time-resolved diffraction measurements will also help understanding the possible interplay among the nematic excitation and the optical / acoustic phonons. 25, 34 " We accordingly added new reference #34 as follow.
Minor questions that the authors should consider are: 1) Which fluence F is used in Fig.2 (a, b)?
We thank for the Reviewer's advice. The fluence for the Fig. 2(a,b) is 220uJ/cm 2 . We added the information in the caption of Fig. 2(a,b).

2) Would it be possible to add a y-axis scale to Fig. 2 (d)?
We thank for the Reviewer's suggestion. The y-axis scale bar was shown in Fig.2(d) but it was perhaps too thin. We added the zero label and y-axis scale for each curve.
Reply to the Reviewer #2: We thank Reviewer 2 for highly evaluating our work and recommending the publication in Nature Communications. We have now answered the comments from the Reviewer.
One comment regarding the asymmetry between xz and yz after pumping in the weak fluence regime ( Fig. 3a and b). It seems that what the authors put in the response to be rather important, that there is an asymmetric scattering channel for xz and yz between Gamma and M in the nematic state, which could be the reason for the missing yz spectral weight at Gamma after pumping. At least this seems consistent with the equilibrium ARPES results (and perhaps even the STM result) on FeSe in that the electron pocket carrying xz at M has been missing while the observed electron pocket is dominated by yz. Could it be useful to include a sentence in the main text pointing out this difference of behavior between xz and yz, if not the potential interpretation, at least a statement of the experimental observation?
We thank Reviewer 2 for his/her valuable suggestion. We added the sentences regarding the origin of the asymmetry between xz and yz after pumping in the weak fluence regime to the new reference Reply to the Reviewer #3: We thank Reviewer 3 for highly evaluating our work and giving us valuable comments. We have now answered all the comments from the Reviewer.
However the final discussion of the article is too speculative. I support publication in Nature Comm. but I encourage the authors fix the following issues: a) It would be good to state that the 1/|T-T_c| behavior is expected from Gaussian fluctuations and not does not provide information about the universality class and critical exponents.
We agree with the Reviewer's statement and revised the description as the following.
We revised the statement in line 22, page 6 as follows.
"the critical T-linear behavior was found in the inverse of the QEP intensity above T s (Ref. 15)."  "the T-linear behavior was found in the inverse of the QEP intensity above T s (Ref. 15), indicative of the Gaussian fluctuation evolving in this regime." b) The dynamical scaling observed when the system is weakly perturbed and the temperature approach T_c is conceptually different the one observed when approaching the fluence to a threshold value. The authors may rather consider non-equilibrium criticality to the explain their data.
We agree that the present comparison between the TARPES and electronic Raman scattering is somewhat speculative, and more detailed discussion on non-equilibrium critical phenomenon is certainly necessary. Nevertheless, the theoretical basis for such discussion is still severely lacking, and developing it may be beyond the scope of this paper. We strongly hope our work will stimulate the future investigations.
According to the Reviewer's advice, we added some discussion to stress the above point (line 20, page 7 in the present manuscript) .
We added the discussion (line 20, page 7 in the present manuscript): "This behavior is seemingly related to the critical nematic fluctuation, nevertheless, future theoretical studies on non-equilibrium critical phenomena are highly necessary." c) On the base of the data that I have seen, there is no reason to claim that the excitation of nematic order is decoupled to the lattice. On one hand, the conjecture of an underlying electronic transition at lower temperature is badly posed. Indeed, it is the relevant coupling to the lattice that defines the experimetal T_c. On the other hand, the observed critical fluence is not particularly small and also corroborates a significant coupling to the lattice. As a consequence the authors should revise missleading statements as "These real-time observations reveal the nature electronic nematic excitation decoupled from the underlying lattice." We thank for the Reviewer's valuable comments. We agree that the experimental T c (i.e. T s = 90 K) in this case mostly reflects the degree of coupling to the lattice, and the discussion on  (2016)]. In these studies, the mean-field transition temperature of the Curie-Weiss-like nematic susceptibility is also understood as the electronic transition temperature. There could be some remaining debate on the strict theoretical validity of the models and/or the accuracy of electronic (mean-field) transition temperature estimated by the extrapolation at T > T s . However, now that extensive discussions are made through these publications in the Fe-superconductor community, we think that it is worth noting and comparing them with our present result. To more carefully describe these issues, we modified the text as follows.
We modified the text (line 22, page 6): "In the XY Raman spectrum, the T-linear behavior was found in the inverse of the QEP intensity above T s (Ref. 15), indicative of the Gaussian fluctuation evolving in this regime. Similarly, the elastoresistivity measurement had also revealed the existence of electronic nematic fluctuation at T > T s interpreted as the Curie-Weiss-like nematic susceptibility. 31 Through the analysis of the T-dependent nematic susceptibility in the form of |T -T 0 | -1 , the authors discuss the mean-field transition temperature T 0 in terms of the ideal nematic transition purely driven by electrons without any influence of lattice. 15,31 " Regarding our present TARPES data, we discuss the F-dependence in analogy with the T-dependent critical behavior. One of the "threshold" F c = 220 μJcm -2 , where the completely circular Fermi surface is attained at 120 fs, should naively correspond to the experimental T c (90 K).
"Another threshold" we are considering here is the F (< 30 μJcm -2 , as explained in line 8, page 7) where the finite dissolution of nematicity starts to be observed in the ultrafast regime (Fig. 2c). By the pump fluence of F ~ 30 μJcm -2 , the electron temperature should only rise up to 45 K, where the change of Fermi surface nematicity is negligible in the equilibrium state. This tells us that in the ultrafast regime (~120 fs), the Fermi surface nematicity is seemingly decoupled from the lattice. We also note that according to the two-temperature model, the electron temperature is strongly deviated from the lattice temperature in the ultrafast regime (< 1 ps). To make this point clearer, we revised the text as follows.
We revised the text in the abstract: "These real-time observations reveal the nature of the electronic nematic excitation decoupled from the underlying lattice."  "These real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice." We also added the word "instantly" in line 18, page 7 in the present manuscript.

Summary of changes
1. We revised the sentence in the abstract as follows.
"These real-time observations reveal the nature of the electronic nematic excitation decoupled from the underlying lattice."  "These real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice." 2. We removed the sentence below in line 5, page 4 in the previous manuscript.
Such an oscillatory response of nematic FS for F > F c is not likely attributed to the usual coherent phonons [24][25][26]28 , since the energy of optical phonons in FeSe (~22 meV) is much higher than the observed oscillation (3.1 meV for 220 μJcm -2 ).
3. We added some description on A 1g phonons inline 9, page 4.
"The time scale of the oscillatory response (1.4 ps, 3.1 meV) is considerably slow as compared to the coherent A 1g optical phonon (190 fs, 22 meV) which is known to strongly couple to the electronic state in this system [24][25][26] . Their potential interplay is unfortunately hidden in the present TARPES data, possibly due to the duration of the pump pulse (170 fs) comparable to the time period of A 1g mode (190 fs) that tends to vanish the coherent oscillation." 4. We modified the sentences below in line 8, page 6 in the present manuscript as follows.
The nematic-orbital excitation obtained in the present TARPES shows striking similarities with the nematic dynamics in thermal equilibrium as probed by the recent Raman scattering measurements.  Now we discuss the nematic-orbital excitation obtained in the present TARPES by comparing with the nematic dynamics in thermal equilibrium as probed by the recent Raman scattering measurements. 5. We removed the sentences below in line 14, page 6 in the previous manuscript.
The XY Raman spectrum further reveals a peak at 3.6 meV in the superconducting state (T < T c ), which is interpreted in Ref [30] as the nematic resonance mode acquiring the coherence by the superconducting gap opening. This energy scale is fairly close to that of the damped k F oscillation (3.1 meV) observed by TARPES near F c , thus suggesting the similarity in its origin. With these facts, we presently consider that the nematic-orbital excitation obtained by TARPES should be associated with the QEP (i.e. nematic fluctuation) in the Raman study.
6. We revised the statement in line 22, page 6 as follows.
"In the XY Raman spectrum, the critical T-linear behavior was found in the inverse of the QEP intensity above T s (Ref. 15). By the detailed analysis of the Curie-Weiss-like T-dependent nematic susceptibility in the form of |T -T 0 | -1 , 15 the authors derived the bare electronic nematic transition temperature T 0 that should describe the ideal nematic transition purely driven by electrons without any influence of lattice."  "In the XY Raman spectrum, the T-linear behavior was found in the inverse of the QEP intensity above T s (Ref. 15), indicative of the Gaussian fluctuation evolving in this regime. Similarly, the elastoresistivity measurement had also revealed the existence of electronic nematic fluctuation at T > T s interpreted as the Curie-Weiss-like nematic susceptibility. 31 Through the analysis of the T-dependent nematic susceptibility in the form of |T -T 0 | -1 , the authors discuss the mean-field transition temperature T 0 in terms of the ideal nematic transition purely driven by electrons without any influence of lattice. 15,31 " 7. We added the word "instantly" in line 18, page 7 in the present manuscript. 8. We revised the sentences in line 20, page 7 in the present manuscript as follows.
which is seemingly related to the critical nematic fluctuation  This behavior is seemingly related to the critical nematic fluctuation, nevertheless, future theoretical studies on non-equilibrium critical phenomena are highly necessary. 9. We added the word "Experimentally," in line 24, page 7 in the present manuscript.
10. We added the sentence below in line 2, page 8 in the previous manuscript.
Systematic time-resolved diffraction measurements will also help understanding the possible interplay among the nematic excitation and the optical / acoustic phonons. 25,34 11. The previous reference #28 was removed.
12. We added the sentences to new reference #29 in line 22, page 4, as follows