Momentarily trapped exciton polaron in two-dimensional lead halide perovskites

Two-dimensional (2D) lead halide perovskites with distinct excitonic feature have shown exciting potential for optoelectronic applications. Compared to their three-dimensional counterparts with large polaron character, how the interplay between long- and short- range exciton-phonon interaction due to polar and soft lattice define the excitons in 2D perovskites is yet to be revealed. Here, we seek to understand the nature of excitons in 2D CsPbBr3 perovskites by static and time-resolved spectroscopy which is further rationalized with Urbach-Martienssen rule. We show quantitatively an intermediate exciton-phonon coupling in 2D CsPbBr3 where exciton polarons are momentarily self-trapped by lattice vibrations. The 0.25 ps ultrafast interconversion between free and self-trapped exciton polaron with a barrier of ~ 34 meV gives rise to intrinsic asymmetric photoluminescence with a low energy tail at room temperature. This study reveals a complex and dynamic picture of exciton polarons in 2D perovskites and emphasizes the importance to regulate exciton-phonon coupling.

We thank all reviewers for the generally positive and valuable comments to improve the manuscript. We have performed substantial new experiments and addressed questions and concerns raised by reviewers in the revised manuscript. Following the questions and comments, we made the following corrections and improvements point by point in response.
The manuscript has been improved significantly. The responses are in red and revisions are in blue.
Reviewer #1 (Remarks to the Author): In this manuscript, Tao and coauthors report a unique intermediate exciton-phonon coupling regime in two-layer CsPbBr3. Such exciton polarons gives rise to intrinsic asymmetric photoluminescence with a low energy tail at room temperature and are only momentarily self-trapped by lattice vibrations. The conclusions are supported by static and time-resolved optical spectroscopy and detailed analysis. The manuscript is well organized and this topic is important to this community. I believe that this manuscript can make a contribution to the field, especially for STE related optoelectronic devices. Therefore, I would like to recommend its publication after the authors successfully addressed the following my concerns.

Response:
We sincerely thank reviewer for the positive comments on this interesting study.
My main concern for this manuscript is that the energy level of self-trapped states is higher than that of free excitons but without providing enough evidence. In view of the weak emission of self-trapped excitons, if the energy level of the self-trapped states is around 35 meV above that of free excitons, the population of self-trapped excitons should be very low.
Under such case, we did not expect to observe the self-trapped exciton emission. In addition, the emission spectrum should be equally broadened rather than only exhibit a long energy tail.

Response:
We appreciate reviewer for raising the important question about the relative energy level of self-trapped exciton and the free exciton. This is also the key finding of this study which has not been illustrated before. The conclusion that the energy level (NOT the transition energy) of self-trapped states is higher than that of free excitons is mainly evidenced by 1) the temperature-dependent PL spectra where the tail emission is thermally activated at high temperature and 2) further rationalized by the Urbach-Martienssen rule pointing to an intermediate exciton-phonon coupling strength and a metastable STE state with higher energy than free exciton.
We only observe STE emission at room temperature but not at low temperature, opposite to conventional low energy defect PL which is stronger at lower temperature. In the studied 2D perovskites, free-exciton and self-trapped exciton can achieve thermal equilibrium before their radiative/nonradiative recombination at room temperature, which is evidenced by wavelength-independent PL decay kinetics and sub-picosecond conversion observed in TA measurement. According to Boltzmann distribution, neglecting DOS/degeneracy difference, the self-trapped exciton population is estimated to be 28% of free exciton population at room temperature with an energy level difference of 35 meV. Therefore, the STE population is not that low and could be observed at room temperature PL spectra in this system. On the other hand, if we assume STE state is lower in energy than free exciton, we would expect stronger STE emission than free exciton thus a more asymmetric PL spectra at low temperature, opposite to experimental results.
As can be seen from Figure 4a, the lowest energy configurations of free exciton state and self-trapped exciton state are different, depending on the coupling constant. In our case (left panel), although the STE state is believed to be higher in energy that FE state, the optical transition energy (PL energy) of STE is still lower than that of FE. Therefore, STE emission is much lower and only contribute to the lower energy tail (note the configuration displacement in horizontal axis). In fact, similar low energy emission tail from metastable STE has previously been observed in PbI 2 with σ = 1.48, close to F-S boundary (σ c = 1.64 in 3D) and thermal equilibrium between FE and metastable STE is established before emission process. (Solid State Commun. 56, 101 ,1985;Solid State Commun. 59, 209 ,1986). Under such case, it is impossible to form self-trapped excitons under the excitation energy smaller than that of free excitons. Nevertheless, the authors excited 2L CsPbBr3 with a low energy pulse (with a center at 2.75 eV and a high energy cutoff at 2.83 eV) to selectively excite the absorption tail and still can observe the long emission tail, suggesting that this long emission tail might not be from the self-trapped states.

Response:
We appreciate reviewer for raising the important question about the excitation of self-trapped state. We agree with reviewer that self-trapped states are with excited state configurational landscape. Within the framework of Frank-Condon principle with vertical transition only, the possibility of a transition being directly excited from electronic ground state depends on the relative ground state population at a certain lattice configuration (which is further determined by phonon population and temperature).
For materials such as white light emitting perovskites with strong exciton-phonon interaction where STE state dominates the excited state properties, STE state is accompanied with large lattice configuration displacement compared to FE state (Holstein-like STE, red curve and transition below). In this case, the ground state population at STE configuration is very small at room temperature thus the direct vertical excitation of STE from ground to excited states is negligible.
In our case of 2L perovskites, exciton-phonon coupling strength is in intermediate regime and PL emission is still dominated by FE emission. The lattice configuration change is not large and the ground state at STE configuration is accessible due to the soft, anharmonic, and dynamically disordered perovskite lattice at room temperature (green curve and transition below). Therefore, the STE transition can be excited at room temperature, as shown by PL (Fig. 2) and TA (Fig. 3) Lett. 2018Lett. , 3, 2030Lett. −2037. If large amount of surface dangling bonds/defects is present, a distinct stokes-shifted broadband trap emission, instead of near band emission with a low energy exponential tail, would be observed as reported in previous literatures (ACS Energy Lett. 2020, 5, 2149−2155Nat Commun 11, 2344,2020 and more importantly, stronger defect-related tail emission would show up at lower temperature. The absence of stokes-shifted broadband emission at room temperature and less tail emission at lower temperature suggest surface dangling bonds are well passivated and surface trap emission doesn't play a role. We also measure the PLQY of our 2D perovskites as reviewer suggested using two methods. The PLQY for 2L CsPbBr 3 is estimated to be about 38% with perylene in ethanol solution as the standard reference (QY=94%, J. Phys. Chem. 1968, 72, 9, 3251-3260) and to be about 40% by comparing the measured PL decay rate (0.313 ns -1 ) with reported radiative rate (0.123 ns -1 ) (Nano Lett. 2018, 18, 8, 5231-5238 Although the 3D perovskite with a diatomic layer can be regarded as a two-dimensional material, there are still differences in structure compared with 2D perovskite we usually investigate (such as (BA)2PbI4, (PEA)2PbI4), especially the difference of organic chains.
In previous reported literature (Nat. Commun. 2019, 10, 806), the slope of (BA)2(MA)Pb2I7 (σ≈0.7) is obviously smaller than that in this manuscript, indicating a stronger exciton-phonon coupling strength. This difference indicates that the organic chain may affect the coupling of excitons and phonons. Therefore, I suggest the authors to clearly illustrate this difference in their manuscript. Another possible reason for their smaller σ is that they did not measure the absorption spectra at different temperatures to fit Urbach tail, resulting in larger fitting errors. In addition, the surface depletion field might also affect the Urbach tail.
The authors are suggested to comment this in their manuscript.

Response:
We appreciate reviewer for raising the question about the organic chain effects on the exciton-phonon coupling strength which indeed is really very interesting and important.
As reviewer pointed out, ligand organic ligands could affect exciton-phonon coupling strength in 2D perovskites. The organic ligands for our CsPbBr3 is oleylaminium (OLA), which has same functional binding group but is longer than BA or PEA ligands. A recent literature (J. Phys. Chem. Lett. 2020, 11, 20, 8565-8572) show some preliminary data of ligand effect on exciton phonon coupling, which requires further investigation. The ligand effect would be our next step. I am afraid we cannot say too much about this topic now, without any results.
The literature (Nat. Commun. 2019, 10, 806) reviewer mentioned proposed a stronger exciton-phonon coupling strength in (BA) 2 (MA)Pb 2 I 7 and assigned the low energy PL peak to STE. However, this is still under strong debate. For example, recent two literatures point out that extrinsic defects such as halide vacancies and surface defects are responsible for the broadband emission peak in PEA 2 PbI 4 (ACS Energy Lett. 2020Lett. , 5, 2149Lett. −2155Nat Commun 11, 2344,2020. Again, without performing experiments on this sample, we cannot comment too much. As for the steepness constant for (BA) 2 (MA)Pb 2 I 7 in Nat. Commun. 2019, 10, 806, the σ 0 is estimated about 0.7 (left panel below), which seems to be too small compared to critical value of 2D case i.e. σ c =1.42. Such low σ 0 would indicate a lowest energy STE state where all excitons should localize to, especially at low temperature. However, their PL spectra show a dominant free exciton emission with only a PL tail (right panel below). As we have stated clearly in revised manuscript, the Urbach tail and the degree of steepness can be easily contaminated by the light scattering in measurements and extrinsic defects/disorders in samples. This can significantly lower σ 0 value and doesn't reflect the true σ 0 due to intrinsic exciton-phonon interaction in a material. "For 2D perovskites, there have been a few attempts to probe the exciton-phonon interaction from the absorption tail. However, the Urbach tail and the degree of steepness can be easily contaminated by the light scattering in measurements and extrinsic defects/disorders in samples, which could significantly underestimate σ 0 . Extracting the intrinsic σ 0 due to exciton-phonon interaction requires a careful measurement on a high-quality sample."

Revisions
3) page 17, top, we added: "Our results above are based on oleylaminium-capped CsPbBr3 2D perovskites. Changing surface ligand to e.g. BA, PEA or halide to I, Cl will likely affect exciton-phonon coupling strength thus exciton behavior, which will be our following study." 4) page 17, middle, we added: "However, we also note the origin about low energy broadband emission in BA-or PEA-PbI 4 2D perovskites is still under highly debate. Whether it's from intrinsic STE or surface defects requires further careful experiment investigation." Considering that the size of the sample is only 20 nm, which is much smaller than the collection size of a spectrometer, the signals emitted from the edge and surface of the sample both are collected. Given the larger proportion of the edge surface, it is important to consider the influence of the edge state luminescence. If surface/edge states are dominating in the material, it may be difficult to identify them by power-dependent spectrum solely.

Response:
We thank reviewer for raising the important question on the influence of edge/surface state luminescence. We agree with reviewer that with a large proportion of the edge/surface in our sample, edge state luminescence could play a role. However, we didn't observe the signature of edge state emission in our samples at both room temperature and low temperature. Previous studies (e.g. ACS Nano 2019, 13, 1635−1644) have shown that the edge state is extrinsic and forms where the adjacent layers partially merge together with the help of water molecular. The edge state is broad with lower energy and shows large stokes shift with longer lifetime compared to intrinsic state, which was not observed. On the other hand, although our sample is only 20 nm, the surface/edge is well passivated during NPs synthesis and a high PL QY (38%) was determined for these sample.

1) Page 5, top, we revised:
"The PL quantum yield (QY) is measured to be ~ 38%, which is comparable with the highest reported PLQY (49%) of 2L CsPbBr 3 and suggests high sample quality."

2) Page 7, bottom, we added:
"This is also not expected for surface/edge state emission which was observed previously in 2D perovskites and characterized with lower energy and longer PL lifetime compared to free exciton emission."

3) Page 9, top, we added:
"This temperature dependent behavior of LE emission cannot be ascribed to surface/edge-related states which should yield more pronounced LE emission at lower temperature." Within a certain power range, for example, two orders of magnitude in this manuscript, LE and FE have a similar linear law, which can eliminate the suspicion of external defects.
However, previous report reveals that the luminescence peak under the band gap of the two-dimensional perovskite has a different power dependence from the free exciton only under strong excitation light, and the luminescence peak under the band gap is also attributed to STE (Sci. Adv. 2020, 6, eaay4900). Therefore, the range of the excitation intensity should be enlarged to check that.

Response:
We thank reviewer pointing this out. Following reviewer's suggestion, we enlarged the excitation intensity range and the results are shown in manuscript below. Both PL spectra and the ratio between FE and STE emission remain same by varying the excitation power over the range of four orders of magnitude. This result strongly implies that the tail emission is intrinsic to 2D perovskites without saturation, in line with our assignments to the meta-stable STE state emission.

Revisions:
We revised the Figure.2b with a much broader excitation power range and revised the content accordingly.
I donot think it is proper to call such 2L CsPbBr3 as 2D RP perovskites. The authors are suggested to provide evidence that their samples are indeed 2L in thickness. More characterizations on morphology and crystalline quality of their samples should be provided.

Response:
We thank reviewer for raising this question. The synthesized 2D perovskites is (100)-oriented and can be viewed as dimensional reduction of 3D perovskite lattice. The (100)-oriented 2D perovskites can be further classified into RP and DJ phase according to the charge of the spacer cation (J. Am. Chem. Soc. 2019, 141, 3, 1171-1190. Since the spacer cation in the synthesized 2D perovskites is single charged (protonated oleylamine), we call them 2D RP perovskites. Actually, this kind 2D perovskite NPs can be reversibly assembled into ordered superstructure, i.e. multi-layered RP perovskite we usually investigate (JACS 2019 141 (33), 13028-13032). This sample can be best viewed as unstacked or exfoliated RP perovskites.
We are sorry that we can not directly see the 2L structure with TEM instrument we can access. Obtaining this kind of high-resolution image is very challenging for perovskites Ratio As because of their rapid structural degradation under electron beam exposure (Science 2020, 370, eabb5940). Even by a short time exposure for low resolution imaging, we already observed some local structure damage and Pb formation (the black dots on image). Instead, we rely on optical measurements to characterize the sample thickness and crystalline quality.
The relationship between the absorption/emission peak and the layer number has been well established in previous literatures (e.g. Nano Lett. 2018, 18, 8, 5231-5238). Due to quantum confinement effect along vertical direction, the strong and sharp absorption/emission peak of 2D perovskites shows a one-to-one unique and precise correspondence with layer number, which provides a facile and precise way to determine the layer number. The NP we use in this study corresponds to the absorption/emission peak of 2L CsPbBr 3 . The absence of any other absorption/emission peaks also suggests that our synthesized NPs are of high monodispersed.
The crystalline quality of our samples can also be inferred from the high QY of NPs. (~ 38%) There are some typos, e.g. page 9 'Previous studies on 2D lead halide perovskites also have show …' should be 'shown'.

Response:
We are sorry about the typos and have corrected them in the revised manuscript.
Reviewer #3 (Remarks to the Author): In this manuscript, the authors mainly use temperature-dependent PL spectra and TA spectra to investigate the exciton activities in 2D lead halide perovskites, and the momentarily interconversion between free and self-trapped exciton polaron gives rise to intrinsic asymmetric photoluminescence with a low energy tail. There are no new testing techniques, theories, and mechanisms to address the conclusion. However, the result is interesting and valuable to the research of 2D perovskite materials. Before further consideration, the following questions must be fully addressed.

Response:
We 1. There are so many formats, grammatical and typo errors in the article. For example, the footnotes in figure captions of Fig. 1 and Fig. S3 are not in the right form. The figure legend of Fig. 2 has two (d), but no (e). There is no Fig. 4 in the manuscript. Some sentences are hard to understand, the English language of this article should be polished thoroughly, and some language errors should be modified.

Response:
We are sorry about typos in manuscript and have corrected them in the revised manuscript. Thank you so much! 2. The reviewer can't see the two layers of CsPbBr3 NPs in Fig. 1a, the authors should provide clearer TEM images of 2L CsPbBr3 and 3L CsPbBr3 to confirm the number of layers.

Response:
We are sorry that we cannot directly see the 2L structure with TEM instrument we can access. Obtaining this kind of high-resolution image is very challenging for perovskites because of their rapid structural degradation under electron beam exposure (Science 2020, 370, eabb5940). Even by a short time exposure for low resolution imaging, we already observed the structure damage and Pb formation. Therefore, instead, we rely on optical measurements to characterize the exact sample thickness and crystalline quality. The relationship between the absorption/emission peak and the layer number has been well established in previous literatures (e.g. Nano Lett. 2018, 18, 8, 5231-5238). Due to quantum confinement effect along vertical direction, the strong and sharp absorption/emission peak of 2D perovskites shows a one-to-one unique and precise correspondence with layer number, which provides a facile and accurate way to determine the layer number. The NP we use in this study corresponds to the absorption/emission peak of 2L/3L CsPbBr 3 . The absence of any other absorption/emission peaks also suggests that our synthesized NPs are of high monodispersed.

Revisions:
Page 4, bottom, we revised: As these atomically thin perovskite NPs are highly susceptible to electron beam damage, we turn to optical measurements to characterize the exact thickness and homogeneity of NPs, which provides a facile and precise approach.
3. Equ. 4 shows the function of the absorption coefficient with photon energy E. However, why do you use Equ. 4 to fit PLE intensity in Fig. 5b? Is it suitable?
Response: We apologize that we didn't make it clear in previous manuscript. As pointed by the reviewer, Equ.4 shows the function of the absorption coefficient with photon energy E. For NPs solution or thin film, light scattering/reflection, instead of real absorption, is hard to avoid, which could hinder the precise measurement of the absorption tail. To minimize these artifacts, we extract the photon-energy dependent absorption tail using PLE spectrum which is proportional to absorption spectrum but has much higher sensitivity and dynamic range.
Basically, PLE is a highly sensitive absorption measurement.
As shown by ( ) = ( ) ( , PLE intensity is given by photon number N at a specific excitation wavelength ( ) which is normalized in PLE measurement, the absorption (in percentage) at and quantum yield (QY) at which can be assumed to be same within such narrow wavelength range. Therefore, PLE profile directly yields absorption profile. 6. The review notice that the authors use the sentences like "The exact nature will be discussed later" and "As we'll show later", which means the manuscript is not in a good arrangement, the logic of the document should be improved.

Revisions
Response：We thank review point this problem out. We have revised the manuscript to make it easier to follow. Thanks again! 7. Are the LE and STE the same thing? If they are the same, please unify them.
Response： We apologize that we didn't make it clear in the manuscript. LE (localized exciton) is a general class of localized exciton suffering localization effects, including intrinsic localization due to exciton-phonon interaction (self-trapped exciton) and extrinsic localization due to defects (trapped exciton). In the beginning, when we discussed the emission spectrum, we observe a low energy tail and at that time, without knowing exact nature, we simply attribute it to LE emission rather than STE emission. Only with more investigation and results, we can reach the conclusion that the LE emission is due to STE and change the notation. We revised the manuscript substantially to make it easier to follow.

Revisions for Q6 and Q7:
1) we removed the sentence with "The exact nature will be discussed later" and "As we'll show later" and revised content accordingly.

2) In page 5, bottom, added:
"The exact origin about the LE emission, e.g. whether it's intrinsic or extrinsic, is unclear yet." 3) in page 8, middle, we revised: "The intrinsic nature of the asymmetric PL with a low energy tail can be attributed the polaronic effect in lead halide perovskites and we assign the LE emission to STE emission." 8. Could the authors provide the TA spectra at low temperatures? It will help verify and explain why the PL spectra at low temperatures have symmetric shapes.

Response:
We thank reviewer for the suggestion. Following reviewer's suggestion, we measured the TA spectra at low temperature and TA spectra comparison between 80K and 300K are shown below. They show similar features characterized with a dominating ground state bleach (GSB) and two photo-induced absorption (PIA) signals on its wings. The low temperature TA spectra does look narrower and more symmetric compared to that at room temperature, consistent with PL result. The authors have significantly improved their manuscript according to the reviewers' comment. Therefore, I would like to recommend its publication after addressing the following minors.
1) The authors claimed that 'the self-trapped exciton population is estimated to be 28% of free exciton population at room temperature with an energy level difference of 35 meV. Therefore, the STE population is not that low and could be observed at room temperature PL spectra in this system. On the other hand, if we assume STE state is lower in energy than free exciton, we would expect stronger STE emission than free exciton thus a more asymmetric PL spectra at low temperature, opposite to experimental results.' Here the authors assumed that the radiative recombination rate of STE is the same or similar to that of free excitons. Usually, this is not the case. The authors are suggested to validate this.
2) The authors claimed that 'the Urbach tail and the degree of steepness can be easily contaminated by the light scattering in measurements and extrinsic defects/disorders in samples. This can significantly lower σ0 value and doesn't reflect the true σ0 due to intrinsic exciton-phonon interaction in a material.'. Can the authors provide a method to determine the intrinsic excitonphonon interaction of a material? Can the authors illustrate more on the claim 'It is important to note that only the high temperature steepness constant σ0 represents the intrinsic exciton-phonon coupling constant by Equation S6.'? Do those two claims contradict with each other?
Reviewer #3 (Remarks to the Author): In this revision, the authors have tried to address all the questions; however, there are still several important issues that have not been resolved. The issues are given in the following: 1. There are still uncertain and inaccurate data or statements described in the current revision. In particular, the reviewer shares the same concern with other reviewers that the authors haven't provided enough evidence to prove that their samples are indeed 2L in thickness. The topic discussed in this manuscript is the optical properties of 2L, 3L, and bulk perovskites. If the layer number is unclear, then the accuracy of the result will also be affected. At the same time, a thorough check on the reference (Nano Lett. 2018, 18, 8, 5231-5238) is performed, in which the research team there have compared with each spectrum and discussed the difference among them. Nevertheless, in this work here, the authors just provide a single spectrum with no obvious sign to know the layer number is 2 or 3. Also, the absorbance spectra of 3L and bulk materials are not provided, while the difference of the spectra is also not discussed. In this regard, it is not precise and accurate to determine the layer number with the current approach. More convictive characterizations on the morphology and crystalline quality of their samples are essential.
2. The authors said that "absorption and QY at λ which can be assumed to be the same within such narrow wavelength range." However, the reviewer thinks 2.3~2.4 eV, or 2.6~2.7 eV are not narrow wavelength range, the absorption and fluorescence will change dramatically. It is not the typical or classical way to fit the absorption coefficient utilizing the current method.
We thank all reviewers for the generally positive and valuable comments to improve the manuscript. We have addressed questions and concerns raised by reviewers in the revised manuscript. The manuscript has been improved significantly. The responses are in red and revisions are in blue.
Reviewer #1 (Remarks to the Author): The authors have significantly improved their manuscript according to the reviewers' comment. Therefore, I would like to recommend its publication after addressing the following minors.

Response:
We sincerely thank reviewer for the positive comments on our revised manuscript.
1)The authors claimed that 'the self-trapped exciton population is estimated to be 28% of free exciton population at room temperature with an energy level difference of 35 meV. Therefore, the STE population is not that low and could be observed at room temperature PL spectra in this system. On the other hand, if we assume STE state is lower in energy than free exciton, we would expect stronger STE emission than free exciton thus a more asymmetric PL spectra at low temperature, opposite to experimental results.' Here the authors assumed that the radiative recombination rate of STE is the same or similar to that of free excitons. Usually, this is not the case. The authors are suggested to validate this.

Response:
We appreciate reviewer for raising the important question about the radiative recombination rate difference between STE and FE.
We completely agree with reviewer that the radiative recombination rate should be different for STE and FE. Unfortunately, we cannot quantify them by directly measuring them. They show same PL decay kinetics (Fig. 2c) due to fast thermal equilibrium between them.
Under quasi-thermal equilibrium condition, the LE/FE emission intensity ratio obeys the equation (3) in the main text, the full mathematical derivation can be found in previous literature discussing the ratio between STE and FE emission intensity in white-light emitting perovskites at a given temperature (Chem. Sci.,2017, 8, 4497-4504 The key is that the absolute fraction of STE doesn't matter. Instead, the temperature dependence matters. Less STE emission from FE at lower temperature indicates higher STE energy. Revisions: Page 9, middle, we added "We note the relative PL intensity is also affected by the radiative rate constant, which unfortunately cannot be easily determined since they show identical PL decay kinetics under thermal equilibrium (Fig. 2c)." 2) The authors claimed that 'the Urbach tail and the degree of We sincerely thank reviewer for the careful reading and constructive comments which help to improve the manuscript significantly.
The issues are given in the following: 1. There are still uncertain and inaccurate data or statements described in the current revision. In particular, the reviewer shares the same concern with other reviewers that the authors haven't provided enough evidence to prove that their samples are indeed 2L in thickness. The topic discussed in this manuscript is the optical properties of 2L, 3L, and bulk perovskites. If the layer number is unclear, then the accuracy of the result will also be affected. At the same time, a thorough check on the reference (Nano Lett. 2018, 18, 8, 5231-5238) is performed, in which the research team there have compared with each spectrum and discussed the difference among them. Nevertheless, in this work here, the authors just provide a single spectrum with no obvious sign to know the layer number is 2 or 3. Also, the absorbance spectra of 3L and bulk materials are not provided, while the difference of the spectra is also not discussed. In this regard, it is not precise and accurate to determine the layer number with the current approach. More convictive characterizations on the morphology and crystalline quality of their samples are essential.

Response:
We appreciate reviewer for the suggestion to provide more evidence to prove our sample thickness. We completely understand reviewer's concern about the layer thickness. Indeed, the layer thickness is very important.
In the revised manuscript, following reviewer's suggestion, we plotted the absorption and emission spectra of our 2L and 3L samples together and also compared with literature results systematically to distinguish their thickness ( Fig. S4 and  3. The effect of the luminescence from defects and edges is not fully considered and still unclear in the current revision.

Response:
We appreciate reviewer for raising the important question about the effect of the luminescence from defects and edges. We agree with reviewer that distinguishing these extrinsic effects from intrinsic self-trapped exciton emission is very important to draw a correct conclusion. As reviewer suggested, we added some discussion in previous submission and add more discussion in this revised manuscript.
We distinguish the self-trapped exciton emission and defects/edges emission by several measurements. If the luminescence from defects and edges contributes substantially or dominates the emission tail, it should also manifest in temperature dependent PL spectra and kinetics. However, our experimental results are opposite to those expected for defects or edges.