Indirect tail states formation by thermal-induced polar fluctuations in halide perovskites

Halide perovskites possess enormous potential for various optoelectronic applications. Presently, a clear understanding of the interplay between the lattice and electronic effects is still elusive. Specifically, the weakly absorbing tail states and dual emission from perovskites are not satisfactorily described by existing theories based on the Urbach tail and reabsorption effect. Herein, through temperature-dependent and time-resolved spectroscopy on metal halide perovskite single crystals with organic or inorganic A-site cations, we confirm the existence of indirect tail states below the direct transition edge to arise from a dynamical Rashba splitting effect, caused by the PbBr6 octahedral thermal polar distortions at elevated temperatures. This dynamic effect is distinct from the static Rashba splitting effect, caused by non-spherical A-site cations or surface induced lattice distortions. Our findings shed fresh perspectives on the electronic-lattice relations paramount for the design and optimization of emergent perovskites, revealing broad implications for light harvesting/photo-detection and light emission/lasing applications.

The authors should tone down the paper and work out exactly what is novel about their study. This would also mean that the big claims about the far reaching impact of their findings would need to be toned down. Additional detailed comments that need addressing: 1) The abstract and the beginning are written terribly, like a sales-piece. Phrases like "enormous potential for various impactful deep tech applications" have no place in a serious scientific article. There are many of such phrases and buzzwords, and also many spelling mistakes. Also terms like "giant SOC" suggest technical terms, but here giant is presumably just used as synonym for large. 2) On p.3, when discussing the various differences between SCs and TFs, the authors should cite works for each of the examples. 3) In several places do the authors claim that the indirect bandgap would be beneficial for photovoltaics. This is only true if the devices are limited by the mobility of the charge carriers. As shown by Rau & Kircharz (DOI: 10.1021/acs.jpclett.7b00236), this is not the case for perovskites, where a completely direct bandgap would lead to higher efficiency. 4) When discussing Figure 1d, the authors do not give a reason as to why they do not see the lowenergy peak in the thin films. Presumably, the absorption is just too weak? 5) For the same figure, why is the EQE shape so strange? Ie, why is there a peak right at the bandedge? 6) Far too little detail is given about the experimental details. Basic measures, e.g. how big are the single crystals, what is the difference in the two crystals shown in the SI for each material, what is the geometry of the photodetector etc. are omitted. 7) One of the nicest findings of the paper is the difference in the dynamics of the two peaks. The indirect peak has slower dynamics at low T and identical dynamics at RT. Can the authors expand on the interpretation, for example calculate how much of the emission they expect to be in the direct/indirect peak at a certain T, form the energy difference and the phonon DOS. 8) From the ARPES measurements on MAPbBr3 one would suggest the Rashba splitting to reside mainly in the valence band (doi.org/10.1103/PhysRevLett.117.126401), yet from the DFT calculations here, and from the schematic figures, the authors suggest that the conduction band is more split. Can you explain that discrepancy? 9) In Figure 4 b & c the authors compare different single crystals, but never tell us what the difference is! 10) Towards the end of the paper the authors speculate on the indirect gap to be beneficial for exciton dissociation. It is not clear to me how their interpretation makes sense. They claim that because the electron relaxes into the indirect CBM. How would that help to dissociate the exciton? Only if one changes the delocalization in real space would the binding energy be reduced, and I do not see how this could be done by thermalization into the CBM.
Reviewer #3 (Remarks to the Author): Please find attached file.
Reviewer #4 (Remarks to the Author): In NCOMMS-18-05870 the authors report an experimental, optical spectroscopic study on halide perovskites where the interplay between thermal atomic displacements and electronic properties is investigated. By means of temperature dependent photoluminescence and reflection measurements, the authors reach the conclusion that strong spin-orbit coupling combined with symmetry breaking due to thermal fluctuations cause tail states in the conduction band (Due to a Rashba effect). These tail stats are expressed as a dual peak in the photoluminescence spectra.
The study is comprehensive and has merit. The findings are important and deserve publication. Yet, there are several issues that must be resolved prior to publication: 1. The authors claim that the dual peaks in the photoluminescence are ntrinsic to the crystal. Though they provide some evidence for their claim, there are evidence to the contrary. In DOI:10.1021/acsnano.6b02734. Tilchin et al report the temperature dependent PL and absorption of MAPbBr3 single crystals. In their data, the low energy peak is considerably less pronounced than here (compared to figure 3A at 45 K). The aforementioned paper is not cited by the authors (I am sure it was not ignored but missed). I am also aware of other unreported data (presented in conferences) where the low energy peak is even less pronounced. I wonder how this fact coincides with the authors interpretation. This point must be addressed in the text.
2. I am not sure why the authors suggest that the Rashba splitting (that, the best of my understanding, is responsible for the low energy peak) occurs exclusively in the conduction band. To the best of my experimentally measured (DOI:10.1103/PhysRevLett.117.126401) for the valance band.
3. Moreover, the Rashba splitting should be symmetrical around the gamma point (unlike what is depicted in figure 3d and 4e) and as the authors point out, creates an indirect band gap. On this point two issues are not clear to me: a.How come the photoluminescence from the indirect gap is so efficient that it has the same order of magnitude of the direct band gap photoluminescence? b. If low energy photoluminescence does indeed result from thermally induced Rashba splitting, shouldn't one expect an overlay of a distribution of split bands -meaning effectively broadened bands eventually -instead of a clear discrete split band?

Reviewer #1 (Remarks to the Author):
In this work the authors carried temperature dependent PL studies on metal halide bromide crystals. Independent of the cation ion the find 2 emission peaks. Both peaks originate from bimolecular processes. The energy difference between the lower and higher energy peak increases with temperature, again more or less independent of the cation. Thin films show only a single emission close to the high energy peak of the single crystal. The authors try to interpretive these data by employing the Rashba model. This model, basically explained in figure 4e has been used in previous theoretical and experimental studies to explain results on metal halide perovskites. As such the present work is not very new. As claimed in the present abstract by the authors, this model is also able to explain all PL observations. Unfortunately not much evidence is given why Rashba splitting is the mechanism explaining their results. Therefore I cannot advise publication in its present form. Below I summarize some doubts I have regarding their interpretation.
Response: We thank the reviewer for his valuable time and comments. We acknowledge that the significance and novelty of the findings in our original manuscript may not have been adequately highlighted, which could have affected his views. Indeed, Rashba splitting have been theoretically and experimentally observed in several reports as pointed out by the reviewer. However, detailed understanding of the origin(s) of the splitting effect is still lacking with only a few experimental reports. Most reports simply attributed the Rashba splitting to arise from the breaking of the centro-symmetry of the lattice by the A-site cation. In our work, we uncover new insights into the origins of the Rashba effect in lead halide perovskites. Firstly, we discerned the static effects from organic cations and surface effect. Most importantly, we found that the thermal induced polar fluctuation is the main cause of the Rashba splitting at room temperature. Consequently, unlike the Urbach tail states in conventional polar semiconductors, the indirect nature of the tail states of lead halide perovskites give rise to novel optical properties like dual emission peaks. To further confirm the thermal polar fluctuation and indirect tail states formation, we have also performed new studies involving temperature-dependent low-frequency Raman scattering measurements and correlate with molecular dynamics (MD) simulations. We now have direct evidence of the thermal polar fluctuation and its relationship with the dual emission. We are therefore confident that the quality and novelty of our revised manuscript will meet the stringent standards of Nature Communications.
(1) Comparison the PL of Cs, Ma and Fa perovskite is a very logical choice in view of the huge differences in the cation motion. In Figure 3b they show deltaE as function of the temperature. One would not expect that these dependencies would follow the same trends for the different cations. Apart from different motional freedom of the cation also phase changes (possibly via cation motion) would have profound effects on the splitting. No explanation is given here.
Response: We thank the reviewer for his comments and important suggestions. The band structures near the band edges are dominated by PbX 6 octahedra, i.e., the CBM comprises of the Pb p orbital and the VBM is the anti-bonding state of Pb s and X p orbitals. The energy levels of MA, FA, and Cs is far away from the band edges. Hence, it is expected that changing the A-site cations will not significantly alter the band edge properties and their dependence on temperature. The temperature-dependent trends of the ΔE in lead-bromide perovskites reflect the thermal deformation of the PbBr 6 octahedra, which is directly related to the occupation number of Pb-Br phonons.
One may expect the A-site cation motion can efficiently couple to PbBr 6 octahedra deformation, and may work indirectly on the observed temperature-dependence of the ΔE.  (Nat. Comm., 7:11755, (2016)), rather than through a mixing of A-site cation phonon modes with the Pb-Br modes.
To validate this further, we performed molecular dynamics simulations to obtain the atomic root-mean-square displacements: where N is the number of the equivalent atoms, r i -r 0i is the displacement of the i th atom from its equilibrium position r 0i , of MAPbBr 3 and CsPbBr 3 in cubic phase at 500 K as shown below in Figure R1. MAPbBr 3 temperature dependent ΔE in the 3D perovskites studied here. Even though we observed abrupt band gap changes of both Peak 1 and Peak 2 positions near phase-transition points as shown in Figure 1e. However, their energy difference ΔE is still much affected, as it is only directly related to the PbBr 6 deformation as discussed above.
In response, we added discussion in Page 11, Line 9 from the bottom.
"Although the inorganic and organic A-site cations have different vibrational characteristics, our findings show that they do not play an important role in determining the temperature-dependent Rashba splitting. Their phonon frequencies are not coupled to the Pb-Br frequencies to collectively influence the temperature trend of the splitting. To further validate this, we compared the root-mean-square displacements: where N is the number of the equivalent atoms, r i -r 0i is the displacement of the i th atom from its equilibrium position r 0i . The time-dependent trends of each atoms in (2) Various causes are presented for the Rashba effect: including cation motion, thermal lattice distortion but also surface defects. In view of the fact that the authors measured films and crystals for perovskites with different cations, it would be logical that some of these possible causes could be omitted. However this is not discussed at all.
Response: The Rashba splitting originates from the centro-symmetry breaking of the perovskite lattice. These include (a) static centro-symmetry breaking, e.g., by the non-spherical A-site cation, surface distortion and (b) dynamical symmetry breaking as we discussed in the manuscript by atomic vibration. In the manuscript, we observed in real crystals (including the polycrystalline films and single crystals), none of these causes can be omitted. For example, for the symmetric CsPbBr 3 SC at low temperature when thermal effect is not involved, the splitting effect is still non-zero, this implies the surface effect is present (26 meV for the SC used in the fitting). In addition, the effect of A-site organic cation is obvious, as we always observe a higher value of the splitting effect for MAPbBr 3 compared to CsPbBr 3 . In response to the reviewer, we made a few statements in the revised manuscript (Page 9, Line 1 from the bottom): "MAPbBr 3 generally possess a higher static distortion compared to the other two by around 10 meV, which should be due to the centrosymmetry breaking by MA cations. Furthermore, it is interesting to note without thermal distortion at low temperature, CsPbBr 3 SCs exhibits a static splitting of around 26 meV, implying the contribution of surface distortion is significant in causing Rashba splitting at low temperature." (3) A similar unspecified remark is mentioned in the abstract line 28 (and not mentioned at other places): indirect 'Urbach-like' states. What are those states?
Response: Previously, the term indirect 'Urbach-like' states was used to refer to the novel tail states in lead-halide perovskites sharing characteristics of both indirect band gap states and Urbach tail states. The conduction band minimum is momentum mismatched with respect to the valence band maximum (hence indirect), and they are largely from the lattice fluctuation (similar as the origin of Urbach tail states). To avoid confusion to the readers, we cautioned the use of this term. We now refer to these states as 'indirect tail states' instead of 'indirect Urbach-like' states for greater clarity. We have corrected all the terms and included an explanation in the manuscript.
(4) Seems that something is wrong of the color coding of Figure 2F. In the present case not much difference is found for the two emission peaks, while in the text they mention the there are huge changes.
Response: there is no color problem in Figure 2f. The huge difference of the PL kinetics occurs at low temperature (165 K). But the PL dynamics is almost identical at room temperature.
(5) In the orthorhombic phase of MaPbBr 3 a huge broad emission peak is observable above 600 nm, which is unfortunately cut off, which is probably related to radiative process 6 in Figure 4e.
Response: Yes, there is a broad emission around 600 nm for MAPbBr 3 SC. However, for CsPbBr 3 and FAPbBr 3 , we did not observe this broad emission. The emission also disappears after the temperature is elevated to beyond the phase transition temperature (~150 K). So the emission is most probably attributed to the interaction of the MA cation and the carriers, i.e., the dipolar polaron emission, or carriers trapped by MA cations. The exact origin of this emission is still unknown, but we can generally rule out the relevance of this emission to the concept we discussed in this manuscript.
Reviewer #2 (Remarks to the Author): The authors describe spectroscopic measurements of bromide-based lead halide perovskite single crystals with different organic cations (Cs, MA, FA) and study in detail the sub-bandgap states. They vary the temperature, excitation density and wavelength, and morphology, and find that the below bandgap feature present in PL and absorption in linked to the indirect transition generated via the Rashba effect. Generally, the data is interesting and the interpretation in many places makes sense. However, the writing is very bad in some places, and the paper is oversold in others. Also, many findings are not as novel as the authors claim they are. Thus, while the paper should be published, and might be suitable for Nature Communications, mayor revisions are necessary, both in writing and interpretation. My main concern is the claim of novelty. Response: We thank the reviewer for the careful reading, useful comments and precious suggestions. We appreciate that the reviewer shares our enthusiasm of our findings and feels that the manuscript is suitable for Nature Communications after revisions. We do sincerely apologize for our excitement depicted in the overenthusiastic style of writing. We have since corrected it. However, we respectfully disagree with the reviewer about the novelty of the work. Indeed, as highlighted by the reviewer, Rashba splitting effects have been experimentally observed in a few literature reports. However, there are still significant gaps in understanding the origin of the Rashba splitting effects. Only the MA system is studied in all of the following works: doi:10.1039/C6EE03474H, doi:10.1038/nmat4765 and doi.org/10.1103/PhysRevLett.117.126401 and the origin of the splitting effect is attributed to the centro-symmetric breaking by the non-spherical organic cation.
Here in our manuscript, we systematically investigated the splitting effect by varying the A-site cations, temperature and crystalline size. We observed that the A-site cations actually play only a small role in determining the splitting effect (~ 10 meV). Instead, thermal-induced polar fluctuation dominates the splitting at room temperature. This contrasts with all those previous reports. The novelty of our manuscript are: (1) We elucidated the origin of the Rashba splitting effects in great detail. (2) We discerned the contribution to the Rashba splitting by A-site cations, surface effect and thermal fluctuation. (3) We found the thermal fluctuation is the most important contribution in causing the Rashba splitting at room temperature for high quality crystals, rather than A-site cations or surface distortion. (4) This thermal fluctuation induced dynamical Rashba effect give rise to indirect tail states in lead-halide perovskites that are not present in other semiconductors. These states have profound effects on the carrier properties in lead halide perovskites such as low e-h recombination coefficient, long carrier lifetime, high ASE threshold, high exciton-dissociation efficiency etc, that satisfactorily explains the observed phenomena in the literature.
Furthermore, now we have provided new evidence of the thermal polar fluctuation and its intimate relation with the dual emission characteristic by analyzing the zero-frequency Raman data which is a signature of the lead-halide polar fluctuation. We observed the congruence of the temperature dependence of the splitting effect and the lattice polar fluctuation. We acknowledge that the significance and novelty of the findings in our original manuscript may not have been adequately highlighted, which could have affected the reviewer's view. We admit in the previous version, the novelty of the findings in our manuscript was not highlighted, which may affect the reading and the judgment. We have since revised the manuscript and improved the writing style of the manuscript. We are confident that the quality and novelty of our revised manuscript will meet the stringent standards of Nature Communications.
Additional detailed comments that need addressing: 1) The abstract and the beginning are written terribly, like a sales-piece. Phrases like "enormous potential for various impactful deep tech applications" have no place in a serious scientific article. There are many of such phrases and buzzwords, and also many spelling mistakes. Also terms like "giant SOC" suggest technical terms, but here giant is presumably just used as synonym for large.
Response: We thank the reviewer for their precious comments on the writing. We have revised the manuscript accordingly: "optoelectronic properties with enormous potential for various impactful Deep Tech applications" has been changed to "amazing photophysical properties with enormous potential for various optoelectronic applications." "…giant SOC…" has been changed to "…large SOC…"  (2017).

3) In several places do the authors claim that the indirect bandgap would be beneficial for photovoltaics.
This is only true if the devices are limited by the mobility of the charge carriers. As shown by Rau & Kircharz (DOI: 10.1021/acs.jpclett.7b00236), this is not the case for perovskites, where a completely direct bandgap would lead to higher efficiency. Reply: We thank the reviewer for highlighting the nice theory paper by Rau & Kircharz, which we have unfortunately missed out. The reference provides a deep physical discussion about the efficiency change when introducing an indirect band gap slightly below the direct band gap. In the radiative limit, they concluded that there will not be any benefit with such an indirect gap. We have revised the manuscript by adding lines in Page 16, Line 3: "This ensures long carrier diffusion lengths favorable for charge extraction in a solar cell with relatively low carrier mobility. On the other hand, for high and balanced carrier mobilities such as in optimized lead halide perovskites, it may not help to increase the ultimate efficiency in the radiative limit. 52 " 4) When discussing Figure 1d, the authors do not give a reason as to why they do not see the low-energy peak in the thin films. Presumably, the absorption is just too weak? Reply: We thank the reviewer for point this out. Indeed, for thin films with ~ 100 nm thickness, the absorption from the indirect transitions is insignificant as the indirect absorption coefficient is typically < 10 3 cm -1 . It will require a thick film of several microns to get sufficient light absorption. For emission profiles, the low-energy PL intensity is highly dependent on the crystalline quality, as shown in Figure 2a. This is due to the carrier distribution and e-h recombination coefficient that is sensitive to the Rashba splitting, doping and other local environmental effects, etc. In general, the high energy peak (Peak 1) is direct but with less carrier occupation; while the low energy peak (Peak 2) is slightly indirect but with higher carrier occupation. Hence, in some case, the two peak intensity can be comparable. In view of the reviewer's comment, we have included a few lines in Page 5, Line 1 from the bottom: "…indicating band edge emission in the TF. The Peak 2 is absent in TF due to its weak absorbing and emitting nature. The EQE…"

5) For the same figure, why is the EQE shape so strange? i.e, why is there a peak right at the bandedge?
Response: The peak at around 560 nm in EQE near the direct band edge is evidence of the indirect tail states. The peak corresponds to the tail-state absorption by the Rashba splitting. Since it originates from an indirect transition, light can penetrate deep and excite the bulk of the crystal. Carriers generated can drift/diffuse to the respective electrodes and be collected. The distinct peak indicates (1) the transition is weak and (2) the carriers generated are delocalized. Above the direct band edge, the transition is direct. The photo-carriers are mainly generated near the front side of the crystal and therefore only one type of the carriers is predominantly collected. Hence, the difference in the EQE shape for these two cases of indirect tail states and direct band edge transistions.
In response, we revised the manuscript accordingly in Page 5, Line 3: "MAPbBr 3 SC based photo-detector shows high efficiency near Peak 2, indicating weak transition and delocalized nature of the excited species. The absorption is weak, so the light can easily penetrate deep into the crystal to reach the back side. Both types of carriers can therefore be collected at their respective electrodes. Another requirement for the efficient collection of carriers near Peak 2 is that they should be highly delocalized (free carriers) with long diffusion lengths." Response: We thank the reviewer for the comment. There is no difference in the two crystals in Figure S1. They are from the same batch. The single crystals used in our experiments have typical size of around 2-3 mm × 2-3mm × 0.5-1 mm. In our measurements, we did not find any obvious difference between the bigger and the smaller crystals. The photo-detector is made by placing a MAPbBr 3 SC (~ 0.5 mm) on Ga electrode and then evaporating a 28 nm thick Au electrode. The EQE is measured with 40nW/cm 2 light intensity and 4V bias. We have revised the manuscript accordingly in the experimental part.

7) One of the nicest findings of the paper is the difference in the dynamics of the two peaks. The indirect peak has slower dynamics at low T and identical dynamics at RT. Can the authors expand on the interpretation, for example calculate how much of the emission they expect to be in the direct/indirect peak at a certain T, form the energy difference and the phonon DOS.
Response: We thank the reviewer for his valuable comments to help us improve the manuscript. Conventionally, one would expect the hot carrier relaxation process assisted by phonons to be ultrafast (within tens to hundreds of femtoseconds; even for low temperature), which are several orders faster than the radiative recombination rate. It will be normal to see the lifetime is the same (like what we observed at room temperature 295 K) as the population exchange rate between the high-lying and low-lying states is rapid. Hence, it is very strange to see that the PL lifetimes can be different for Peak 1 and Peak 2 at 165 K and other low temperatures. We noticed a few publications proposed the so-called large polaron effect and phonon bottleneck effect that impedes hot carrier relaxation in MAPbBr 3 as in MAPbI 3 and FAPbI 3 (e.g., Nat. Photonics, 10, pages 53-59 (2016), Nat. Comm., 6:8420 (2015), Nat. Comm. 8:14120 (2017)). This effect occurring on long timescales up to a few nanoseconds, may be one reason of the slow population exchange at low temperature. However, at current stage, the mechanisms are a matter of intense debate. Hence, we are unable to propose a model that could perfectly explain the observed phenomena that ranges from sub-ps to few ns. Further clarifications are needed. Response: In principle, both CBM and VBM can have Rashba splitting effects. The CBM is dominated by Pb p orbital, while the VBM is comprised of the anti-bonding states of Br p orbital and Pb s orbital. As Pb is larger than Br (Z=82 vs. Z=35), it is expected that the CBM have a much higher splitting effect than VBM. For example, in calculating the instantaneous band structure in Figure 3c at 300 K, we found the maximum Rashba splitting occurs in Γ-Y direction with a value 1.365 eV Å at CBM. On the other hand, VBM shows negligible splitting with maximum value of only 0.22 eV Å. ARPES can only measure the VBM characteristics. It is reasonable to infer that the CBM should have a much higher splitting than the VBM if it could be measured. In response, we added a few lines in Page 8, Line 5: "The Rashba band splitting at the VBM has been directly verified with angle-resolved photo-electron spectroscopy. 14 The effect should be stronger at the CBM according to DFT calculations because the atomic number of Pb (Z = 82), which constitutes the conduction orbitals, is much larger than Br (Z = 35)."

9) In Figure 4 b & c the authors compare different single crystals, but never tell us what the difference is!
Response: We thank the reviewer for pointing out this potential ambiguity. The different crystals ferent to three different MAPbBr 3 crystals made in the same batch. Even though the fabrication conditions are the same, the PL characteristics at different points can vary significantly at 77 K. The PL characteristics however can vary significantly at 77 K. The. This implies different surface distortion at different points or different samples may introduce different Rashba splitting effect at low temperature that causes the PL difference.
To avoid ambiguities, we revised the manuscript in Page 15: "…splitting at low temperature (77 K). Note the SCs used in these measurements were prepared under the same conditions. Different surface distortions among different crystals and points may account for the different Rashba splitting effect and PL properties at low temperature. These results suggest the ease of lattice distortion and the associated change of the indirect tail states play a significant role in the emissive properties (PLQY, dual peaks, etc) of lead halide perovskites. The presence…"

10) Towards the end of the paper the authors speculate on the indirect gap to be beneficial for exciton dissociation. It is not clear to me how their interpretation makes sense. They claim that because the electron relaxes into the indirect CBM. How would that help to dissociate the exciton? Only if one changes the delocalization in real space would the binding energy be reduced, and I do not see how this could be done by thermalization into the CBM.
Response: Thanks the reviewer for pointing out this. After reconsideration, we would like to caution our original statement. However, the efficient exciton dissociation may be still relevant to the thermal structural fluctuation in the lead halide perovskite system. The inorganic lattice fluctuation is essential for determining the efficient charge separation in lead halide perovskites with or without organic cations (J. Phys. Chem. C 2017, 121, 26648−26654;Nano Lett. 2015, 15, 248−253;Phys. Chem. Chem. Phys.,2015, 17, 9394). In response, we deleted the previous speculative part and revised the manuscript by adding the new discussion: "We interpret that the photogenerated charges are rapidly separated due to electrostatic potential fluctuation coupled to the inorganic lattice dynamics. The organic cations which were believed to be critical in causing potential fluctuation and charge separations previously, 66,67 may not be essential as H.
Uratani and K. Yamashita demonstrated through MD simulations. 68 " In this paper authors are trying to revised their interpretation of results based on few new experimental findings. Many of their argument fails to their own statements put up into abstract and introduction of paper. In general, in this paper authors are trying to put up a model based on co-existence of direct and indirect bandgap in perovskite semiconductor as an origin of observation of double emission peak. They argued in introduction that there are puzzling results and explained using various models and many time morphology was held responsible for these observations. Which I found is the case even for them where they comment that double emission peak observation is possible in their SCs due to good quality of crystal, which is backed up showing higher decay time as compare to their own previous results, However, there are reports which has also used similar technique to grow SCs and got lifetime higher or comparable to reported in this paper but still shows single emission peak in perovskite single crystals. Introduction should align with their results and discussion. I noted few things which needs attention from authors.
Response: We thank the reviewer for the comments. However, we respectfully disagree with his comments that our findings are not consistent with literature reports. Unfortunately, the reviewer has not provided any specific reference to this. Below are some data from the literature that reported single emission peak (Figure d,e,f), while others showed two peaks (Figure a,b,c). We wish to highlight that for those reports showing single peak, the single peak is in fact not symmetric. One needs to carefully examine the peak to notice the tail at the low-energy side (Figure d,e,f). These observations are in agreement with our findings that there is a weak low energy peak, whose intensity is relatively weak and subdued by the strong main peak at room temperature. Figure R2. The emission profiles of MAPbBr 3 single crystals in the literature.

Abstract is too general in the form of perspective instead of communication paper and fail to give the flavor on content of paper.
Response: We thank the reviewer for pointing this out. We have modified the abstract accordingly.

Whole PL needs to be fitted with Guassian peaks to show whether they need 2 or 3 Gaussians to get physics out?
Response: We thanks the reviewer for the raising this point. The whole PL spectra were fitted using Voigt (including Gaussian + Lorentz) functions. In response, we added one line in Page 5: "…Figure 1e shows the temperature-dependent PL peak positions of CsPbBr 3 , FAPbBr 3, and MAPbBr 3 SCs versus their TF counterparts extracted with Voigt function…" 3. How does Peak1 and peak2 position changes individually with respect to temperature is missing? Though more suitable would be fit the Guassians and then analyze.
Response: The individual peak 1 and 2 position changes can be found in Figure 1e. The temperature-dependent positions of Peak 1 and Peak 2 are extracted by fitting the PL spectra with Voigt functions. The Voigt function is more suitable than Gaussian function as homogeneous broadening and inhomogeneous broadening may both play a role in determining the linewidth of the PL spectra.
4. Peak2 vs Peak1 splitting seems to be asymmetric, though both of them have lattice-dilation and electron-phonon interaction?
Response: We thank the reviewer for the comment. The effects of lattice-dilation and electron-phonon interaction on the band gap of lead halide perovskites are complicated. Previous studies focused on the abnormal development of Peak 1 with temperature that is opposite to the Varshni relation (e.g., Phys.Chem. Chem.Phys. 2014, 16, 22476). They observed a blue-shift of the band gap (Peak 1) with increased temperature, i.e., the lattice-dilation effect dominates in lead halide perovskites, in contrast to conventional inorganic semiconductors such as Si, GaAs. However, this anomalous behavior can now be explained based on our findings of the indirect tail states below the direct band gap, which is strongly dependent on electron-phonon interaction and red-shifts with elevated temperature. For example, Peak 2 of CsPbBr 3 between 77 K and 300 K (without any phase transition) can be well-fitted by the Varshni equation: where E 0 =2.32 ± 0.01 eV, α=4.9 ± 0.5 × 10 -4 eV/K, β = 190 ± 60 K. The energy difference between Peak 1 and Peak 2 is proportional to the phonon occupation number. That means, in lead halide perovskites, the fundamental gap (Peak 2) is also determined by both lattice-dilation and electron-phonon interaction effects. The electron-phonon interaction effect was not found previously because it results in indirect transitions with weak absorption coefficient that was not discerned. In view of the reviewer's question, we have added a few lines on Page 5, Line 13: "However, Peak 2 exhibits red-shift with increasing temperature, which can be well-fitted by the Varshni equation for most inorganic semiconductors accounting for the electron-phonon coupling effect ( Figure   S3)." And we added the figure below to the supporting information Figure S3. Figure R3. The temperature-dependent Peak 2 fitted with the Varshni equation.

How does their FWHM changes as a function of temperature for these Gaussians?
Response: The FWHM for Peak 1 and Peak 2 follows the same trend. The peaks were fitted with Voigt function and the FWHM was defined as: FWHM=sqrt(wG 2 +wL 2 ), where wG and wL are the Gaussian and Lorentz linewidths, respectively. Figure R4 a shows the FWHM of a typical CsPbBr 3 SC, in which an LO phonon energy of around 20 meV can be globally extracted. For SCs, the Peak 2 FWHM may also be changed by reabsorption effect, so we turned to the FWHM of the films, i.e., the MAPbBr 3 film (1 M concentration) with obvious double peaks, which still shows very similar trend with temperature. This indicates the two peaks' broadening shares the same scattering mechanism dominated by Pb-Br LO phonon scattering at elevated temperatures (Nat. Comm. 7:11755 (2016)). In response, we have revised the manuscript accordingly in Page 10, Line 5: "…The fitted values of E ph are 12-18 meV, which corresponds well with the broadening of the PL peaks (Figure S7), and is attributed to the Pb-Br LO phonon modes (Pb-Br-Pb bending and Pb-Br stretchings). 29,47 " And inserted Figure R4 as Figure S7 in the SI.
6. Instead of showing the TRPL for whole by separating faster and slower components, authors should compare TRPL due to each single Gaussian peak by deconvolution of the PL. Response: We thank the reviewer for the useful comment. For MAPbBr 3 thin film at room temperature, the population exchange between the two bands are much faster than the recombination, so the dynamics are identical between the two bands. We cannot separate them using any deconvolution method. For the dynamics at low temperature, due to slower population exchange (which is possibly related to slow hot carrier cooling in perovskites), we can separate the two band dynamics using non-negative matrix factorization method to decompose the two band dynamics as shown below: Figure R5. The deconvolved TRPL profiles and dynamics of MAPbBr 3 thin film at 165 K using non-negative matrix factorization (NMF) method.
In response, we have used Figure R5 as Figure 2e-f and revised the main text accordingly in Page 9: "We employed the non-negative matrix factorization (NMF) method to deconvolute the TRPL data at 165 K. The deconvoluted effective lifetimes are around 110 ± 10 ns and 1540 ± 50 ns for Peak 1 and 2, corresponding to the recombination through the direct transitions and indirect transitions, respectively. At room temperature, both peaks show identical bi-exponential decay, indicating fast population exchange between the upper direct bands and lower indirect bands by phonon scattering."  Fig 3a, ratio of peak1 to peak2 for Cs is in contrast to other two, where according to their model indirect peak has more PL than FA and MA based SCs, why? Response: At this low temperature, the relative peak intensities are now sensitive to the excitation density. As shown in Figure R6 below, the low-energy PL peak relative intensity increases with excitation density. This is probably due to the slow population exchange at the two bands at low temperature as discussed above. Figure R6. Intensity-dependent PL profiles of CsPbBr 3 at 45 K.
With our newer results, we have removed figure 3a from the original manuscript and relegated it to the supporting info. However, it does not discount our claims.
8. Fig. 3b shows the slope for spilt energy vs T is independent of molecular cation, which is very surprising and cannot be explained using model described by authors where lattice dynamics of these three system has to be different. However, reabsorption model can explain it in good way considering equivalent parameters in terms of absorption coefficient, thickness of samples, lattice dilation properties and possible scattering factor.
Response: We thank the reviewer for raising the important question. However, we respectfully disagree with the view about the reabsorption model. Our reasons are as follows: The band structures near the band edges are dominated by PbX 6 octahedra, i.e., the CBM is comprised of Pb p orbital and the VBM is the anti-bonding state of Pb s and X p orbitals. The energy levels of MA, FA, and Cs is far away from the band edges. Hence, it would be expected that the changing of the A-site cations will not alter much of the band edge properties and their dependence on temperature. The temperature-dependent trends of the ΔE in lead-bromide perovskites reflect the thermal deformation of the PbBr 6 octahedra, which is directly related to the occupation number of Pb-Br phonons.
One may expect the A-site cation motion can efficiently couple to PbBr 6 octahedra deformation, and may work indirectly on the observed temperature-dependence of the ΔE. However, we did not observe any Energy (eV) 0.1 μJ cm -2 0.2 μJ cm -2 0.4 μJ cm -2 0.8 μJ cm -2 1.6 μJ cm -2 3.2 μJ cm -2 frequencies of Cs, MA or FA phonons coupled to Pb-Br modes to change the ΔE in our observation. This is consistent to that only the Pb-Br LO phonon modes via Fröhlich coupling contributes to the electron-phonon scattering and PL broadening in 3D perovskites (Nat. Comm., 7:11755, (2016)), rather than an mixing of A-site cation phonon modes. A few recent published theoretical works also support our assumptions here. For example, Uratani and Yamashita compared the molecular dynamics of CsPbI 3 , FAPbI 3 and MAPbI 3 , in which they observed similar lattice fluctuation and efficient charge separation (J. Phys. Chem. C 2017, 121, 26648−26654). McKechinie et al predicted similar spin splitting effect in CsPbI 3 and MAPbI 3 (arXiv:1711.00533v1).
To verify this, we also simulated the root-mean-square atomic displacements of MAPbBr 3 and CsPbBr 3 in cubic phase at 500 K as shown in Figure R1 above. The RMSDs at 500 K for MAPbBr 3 atoms are (MA: 0.95Å, Pb: 0.51 Å, Br: 0.86 Å), and for CsPbBr 3 atoms are (Cs: 0.74 Å, Pb: 0.54 Å, Br:0.65 Å). From this, we believe the change of A-site cation from Cs to MA may not significantly change the PbBr 6 octahedra dynamics.
The reabsorption factor can be well excluded as we discussed the high quality thin film part in the main text. For thin film on the order of 200 nm, it is impossible to yield any significant reabsorption, while we can still get Peak 2.
In response, we added discussion in Page 11, Line 9 from the bottom. "Although the inorganic and organic A-site cations have different vibrational characteristics, our findings show that they do not play an important role in determining the temperature-dependent Rashba splitting. Their phonon frequencies are not coupled to the Pb-Br frequencies to collectively influence the temperature trend of the splitting. To further validate this, we compared the root-mean-square displacements:

This is known that there is good amount of scattering in these crystals and temperature dependent lattice expansion, both of these factors can influence their calculation of reabsorption model, as this is one of the strong model to explain the dual emission peak in literature as referred by authors as well.
Response: Reabsorption effect is an important factor that may contribute to the optical behavior of the thick single crystal. However, it is not sufficient to explain the observed phenomena in thin films as discussed in Figure 2 in the manuscript. Similar double PL peaks were also reported for MAPbI 3 thin films before (Energy Environ. Sci., 2017, 10, 509). The thin films look very smooth by eye and from the AFM images ( Figure R7) The RMS are 4.8 nm, 4.8 nm, 7.7 nm and 6.5 nm for thin films with 0.25 M, 0.5 M, 0.75 M, and 1 M precursor concentration, respectively. It is unlikely the scattering effect play an important role. The absorption coefficient measured is also in good agreement with other reports using ellipsometry (Nat. Comm., 6:7961 (2015)). We fully considered the reabsorption effect as the possible reason of the double peaks; however, it fails to explain the observed phenomena satisfactorily.
In response, we have added a few lines in Page 7, Line 13: "-free electron-hole recombination. Furthermore, the optical scattering related artefacts are not likely to occur in the TFs as they look very smooth from AFM images with typical RMS less than 8 nm in 10 µm × 10 µm region ( Figure S5). These observations hint at a common origin as those in SCs." And insert Figure R7 as Figure S5 in the SI. Figure R7. AFM images MAPbBr 3 films prepared with varied precursor concentration.

Authors claim about Rashba splitting is indirect, where unusual polaronic effects and defect tolerant perovskite semiconductors can make these interpretations illusive. A more direct approach needed for this big claim. (doi:10.1038/nphys675)
Response: Our claim about the Rashba splitting is strongly supported by many theoretical and experimental works. Direct approaches such as magneto-optical measurements have been applied to observe the PL fine structures of CsPbBr 3 nanostructures due to the Rashba effect at extremely low temperature (Nano Lett., 2017, 17, 5020−5026;Nano Lett., 2017, 17, 2895−2901. Another powerful technique angle-resolved photoemission spectroscopy (ARPES), has also been used to observe clear signature of the valence band splitting in MAPbBr 3 single crystal due to the Rashba effect (Phys. Rev. Lett., 117, 126401 (2016). Furthermore, we have performed temperature-dependent Raman scattering measurements from which we can observe clear temperature-dependent trend of the zero-frequency Raman signifying the polar fluctuation of lead halide perovskites. We observed direct correlation between the dual emission (splitting effect) and the thermal polar fluctuation as shown below: The polar fluctuation becomes stronger as the increase of temperature. The zero-frequency mode intensity undergoes a similar increase fashion with that of the energy splitting. Figure R8. (a) Temperature-dependent low-frequency Raman spectra of CsPbBr 3 SC. (c) Temperature-dependent relative intensity of the zero-frequency mode.
In lead halide perovskites, the (large) polaronic effects are often mentioned and are responsible for their defect tolerance and screened scattering.(e.g., J. Phys. Chem. Lett. 2015, 6, 4758−4761, Sci. Adv. 20173: e1701217) In this manuscript, we do not attempt to prove whether the photo-excitation in lead halide perovskites is free carrier or polaron (carrier dressed with lattice deformation). In the lead halide perovskites whose lattices are apt to deform, it is very probable that the photo-excited carriers can form polarons. However, we note that whether free carrier or large polaron in lead halide perovskites does not contradict the band splitting effect. If the photo-excitations are treated as polarons, the polaron bands are still possible to be split in the presence of the Rashba effect.
Lastly, one may argue there is the coexistence of free carrier and polaron, and that the high-energy peak is due to free carrier whilst the low-energy peak is from polaron. However, our optical signatures can generally rule out this case. For example, the weak tail state absorption edge is consistent with the low-energy PL peak. We know from polaron theory that it is the quasi-particle of excited carriers with the perturbed lattice, so that it could not have ground-state absorption signature near the band gap. It implies the low-energy PL peak could not be due to polaron emission, either. In addition, if the low-energy peak is understood as from polaron, as temperature increases, the polaron should be expected to ionize to a free electron and renormalized phonons (Phys. Rev. B, (12), 5472, (1975)). That is, the energy difference between the free carrier and polaron should reduce with temperature.
In response, we have inserted the Raman spectra related discussion in the main text and SI.  (9), 5609 (1995). Although we cannot quantify the absorption coefficient using the diffuse reflectance spectroscopy, it provides information where the fundamental absorption edge is. The factors the reviewer mentioned can indeed affect the measured tail absorption, but we can generally exclude them through careful measurements. For example, (i) the scattering that is not relevant to the band gap usually behaves as a flat background, which can be simply removed. (ii) The cryostat effect can be excluded as we compared the diffuse reflectance spectra measured with and without the cryostat and we did not observed any difference. (iii) Since we used diffuse reflectance spectroscopy to measure the absorption edge in SC, there is inevitable weak absorption from sub-gap defect states. However, we observed the slope of the absorption edge shows a temperature-dependence, which is a typical signature of thermal fluctuation induced tail states ( Figure R9). Hence, it is reasonable to conclude that we were measuring the tail state absorption.

Reference for inverted temperature crystallization needs to be relooked.
Reply: We thank the reviewer for pointing out the error. We have updated the references now: "FAPbBr 3 and MAPbBr 3 single crystals were prepared using the reported inverted temperature crystallization (ITC) method. 57

Page 15, line 12 english error.
Response: thanks the reviewer for pointing out the typo. We have deleted the excess "and" in the revised manuscript. "The temperature was and cooled down using liquid nitrogen" has been changed to "The temperature was

Diffuse reflectance as a function of temperature using Nikon microscope in dark field could not really explain how this measurement was performed, more details needed.
Response: We thanks the reviewer for pointing this out. The temperature-dependent diffuse reflectance was measured using a Nikon microscope equipped with a liquid-nitrogen cooled cryostat (Janis). The white light from a tungsten bulb was directed onto the single crystal with 10× objective and the diffused light was collected with the dark field mode. The incident light intensity was calibrated by measuring the reflected light intensity from a quartz substrate and calculated with the as-known quartz refractive indices. Later the diffused light from the single crystals was collected and divided by the incident intensity to get the diffuse reflectance spectra. We have added the details above into the experimental part of the revised manuscript now.

Detector EQE biasing conditions vs illumination direction and applied bias information is missing.
Response: The photo-detector EQE was measured with 40nW/cm 2 light intensity and 4V bias. We have added it in the revised manuscript now.

Considering above comments, I do not feel that this work full-fill the requirement of Nature Communication standard and should be published elsewhere after justifying the above comments.
Reviewer #4 (Remarks to the Author): In NCOMMS-18-05870 the authors report an experimental, optical spectroscopic study on halide perovskites where the interplay between thermal atomic displacements and electronic properties is investigated. By means of temperature dependent photoluminescence and reflection measurements, the authors reach the conclusion that strong spin-orbit coupling combined with symmetry breaking due to thermal fluctuations cause tail states in the conduction band (Due to a Rashba effect). These tail stats are expressed as a dual peak in the photoluminescence spectra. The study is comprehensive and has merit. The findings are important and deserve publication. Yet, there are several issues that must be resolved prior to publication: Response: we sincerely thank the reviewer for the meticulous reviewing and positive evaluation of our work. We are delighted that the reviewer shares our enthusiasm about this work for Nature Communications.  figure 3A at 45 K).

The aforementioned paper is not cited by the authors (I am sure it was not ignored but missed). I am also aware of other unreported data (presented in conferences) where the low energy peak is even less pronounced. I wonder how this fact coincides with the authors interpretation. This point must be addressed in the text.
Response: We thank the reviewer for the comment. Unfortunately, we were not aware of the paper published by Tilchin et al. in ACS Nano. We did notice a few literature works showing less pronounced low-energy peak compared to the high-energy peak ( Figure R2 above). It implies the peak intensity is highly sensitive to the local physical properties of the perovskites. These physical properties such as disorder/defects, lattice distortion and doping can determine the band structure and the carrier distribution at the direct band edge in the presence of the indirect tail states. The electron-hole recombination coefficient at the direct band edge of an indirect bandgap material can be expressed as 49 : where E gi and E gd are the indirect and direct bandgap, respectively, m e and m h are the effective masses of carriers in the conduction band and valence band, respectively. m 0 is the electron mass, h is Planck constant, k B is Boltzmann constant, T is the temperature, e is the elementary charge, c is the light speed in vacuum, n is the refractive index and M c is the number of equivalent minima in the conduction band. The calculated B 1 is sensitive to the exponential term Hence, the sensitivity of the high-energy/low-energy PL intensity is directly related to the direct-indirect bandgap difference, which cannot be satisfactorily explained with other theories. There is no contradiction to our claims.
In response, we have cited the paper mentioned and revised the manuscript in the main text and SI accordingly: determined by the direct-indirect bandgap difference, and therefore can be significantly changed with different surface distortion and defect density. As shown in Figure 4a, we observed a striking difference of the effective e-h recombination coefficients between polycrystalline TFs and SCs (details of the fitting can be seen in Figure S11 and Supplementary Note 4). At room temperature, the effective e-h recombination coefficient of FAPbBr3 TFs approaches 10 -8 cm 3 s -1 which is three orders higher than that of the bulk of the SCs. Similarly, the..." 2. I am not sure why the authors suggest that the Rashba splitting (that, the best of my understanding, is responsible for the low energy peak) occurs exclusively in the conduction band. To the best of my experimentally measured (DOI:10.1103/PhysRevLett.117.126401) for the valance band. Response: We thank the reviewer for the valuable comment. As discussed above in response to the 8 th question by reviewer 2, both CBM and VBM in principle can have Rashba splitting effects. The CBM is dominated by Pb p orbital, while the VBM is comprised of the anti-bonding states of Br p orbital and Pb s orbital. As Pb is larger than Br, it is expected that the CBM have a much higher splitting effect than VBM. For example, in calculating the instantaneous band structure in Figure 3c at 300 K, we found the maximum Rashba splitting occurs in Γ-Y direction with a value 1.365 eV Å at CBM. On the other hand, the VBM shows smaller splitting with maximum value of only 0.22 eV Å, only 20% of that of the CBM. As we know, ARPES can only measure the valence band properties. It would be expected the CBM should have a larger splitting effect than the VBM if it can be measured. To avoid ambiguities, we made a few comments in the revised manuscript. In Page 9, Line 5, we added: "The Rashba band splitting at the VBM has been directly verified with angle-resolved photo-electron spectroscopy. 14 The effect should be stronger at the CBM according to DFT calculations because the atomic number of Pb (Z = 82), which constitutes the conduction orbitals, is much larger than Br (Z = 35)."

Moreover, the Rashba splitting should be symmetrical around the gamma point (unlike what is depicted in figure 3d and 4e) and as the authors point out, creates an indirect band gap. On this point two issues are not clear to me:
Response: We thanks the reviewer for the valuable comment and pointing out the potential ambiguity in our schematic. For lead halide perovskites with organic cations, the splitting may be asymmetric due to different interaction of the organic cation and the octahedra at different directions (as seen the band structure below for MAPbI 3 ). For more generality, we have corrected this in the revised manuscript by aligning the CBM and VBM around the R point for a typical Rashba splitting effect.
Rashba effect lifts the spin-degeneracy and creates Fermi surface consisting of two concentric circles with opposite chiral spin textures. In lead halide perovskites, both conduction band and valence band have Rashba effect. However, since Pb is heavier than Br, it is expected the SOC effect is more severe at the CBM which is comprised of Pb p orbital than the VBM which is comprised of Br p orbital and Pb s orbital. The difference of the Rashba effect can lead to a slight momentum mismatch of the CBM with respect to the VBM. Therefore, the consequence is spin-split indirect band gap is formed. This was illustrated in APL Materials 4, 091501 (2016); doi: 10.1063/1.4955028 and as shown in Figure R10. In this calculation paper, the splitting effect is more severe at R->M direction compared to R->Γ direction, which leads to an asymmetric CBM that resembles our earlier schematic. Figure R10. Electronic band structure of CH 3 NH 3 PbI 3 . From APL Materials 4, 091501 (2016).
In response, we changed the schematic of Figure 3d to: a. How come the photoluminescence from the indirect gap is so efficient that it has the same order of magnitude of the direct band gap photoluminescence?
Response: We thank the reviewer for the interesting comment. The indirect PL intensity can reach the same order of magnitude of the direct gap PL due to a few reasons: (a) More carrier population at the low-lying indirect bandgap than at the high-lying direct bandgap. This is due to Fermi-Dirac distribution: In response, we have added in the part "Implications for light emission applications." of the revised manuscript: "It is reasonable that the low-lying indirect emission peak can be as prominent as the direct one when more carriers reside at the indirect tail than in the direct band, and the phonon-mediated momentum mismatch is relatively small, i.e. relatively strong Fröhlich coupling may also assist the crystal momentum transfer in an indirect emission process. 29,54 "

b. If low energy photoluminescence does indeed result from thermally induced Rashba splitting, shouldn't one expect an overlay of a distribution of split bands -meaning effectively broadened bands eventuallyinstead of a clear discrete split band?
Response: We thank the reviewer for this interesting question. There are three factors that determine the photoluminescence intensity.
(1) The probability to find an electron at certain energy. The lower energy, the higher electron occupation probability.
(2) The density of states at certain energy. Thermal fluctuation tends to create a distribution of density of states below the band gap. Hence, the lower energy, the less density of states.
(3) The momentum matching conditions between the conduction and valence bands. Hence, the larger the Rashba splitting, the less probable the momentum matching can be reached. Thermal-induced Rashba splitting creates a distribution of split bands. For the split bands with large thermal polar distortion, the electron occupation probability is high, but the density of states and momentum matching is reduced, and vice versa ( Figure Rx). Therefore, a maximum transition can occur near the equilibrium position, creating a peak-like PL structure below the direct emission peak. In response, we have added in the part "Implications for light emission applications." of the revised manuscript: "The presence of thermal polar fluctuations and their associated indirect tail states can lead to the dual emission phenomena that were not observed in conventional polar semiconductors with an Urbach tail. Strictly speaking, the second emission peak at elevated temperature with thermal fluctuation should correspond to the energy position when the product of the density of the carriers and the transition probability reaches its maximum." techniques, to name a few, angle-resolved photoemission spectroscopy, circular photogalvanic effect, magneto-PL, etc.
We agree the experiments under magnetic field can be an important and straight-forward technique to prove the Rashba effect, as those done in DOI: 10.1021/acs.nanolett.7b02248. However, we note that such splitting by magnetic field is insignificant even with a 8T strong field -i.e., a splitting of only ~1.2 meV is observed. Therefore, it will be impractical to discern any change of the PL for our large-scale single crystals, which have typical PL full-width half maximum (FWHM) on the order of tens of meV.
An alternative approach is to use circular-polarized laser pulses to excite the single crystals and detect their spin-related properties. The Rashba effect lifts the degeneracy of the band edges (here mainly CBM for APbBr 3 ), forming two split spin valleys ( Figure R1). The spin-flipping could thus be slowed down for carriers in the valleys due to a barrier formed between the two valleys with opposite spin. A circular-polarized (left-circular σ + , right-circular σ -) excitation near the band edge will selectively excite one of the valleys. The ensuing PL will retain the helicity of the excitation depending on the timescales of the spin-flipping and recombination/transport. Figure R1. Schematics of the Rashba split bands and selective excitation with circularly-polarized light.
Herein, for our new experiments, we excite the lead halide perovskite single crystals with circularly polarized laser pulses and detect the circularly polarized PL. There is an obvious difference in the intensity of the PL under different optical pumping helicity near the band edge, indicating the presence of two valleys that can be selectively excited. Typical right circularly polarized (σ -) PL spectra of MAPbBr 3 SC following optical excitation with left (σ + ) and right (σ -) circularly-polarized laser pulses at with 532 nm, 473 nm, and 400 nm lasers at 77 K are shown in Figure R2. With 532 nm pumping, the PL helicity is most prominent, which becomes reduced with 473 nm excitation and is negligible with 400 nm excitation. These results indicate that when the photocarriers are generated near the band edge, the carrier spin is preserved due to the potential barrier formed between the two spin valleys. Without the Rashba effect and the formation of two spin valleys, the strong SOC in lead halide perovskites will lead to an ultrafast spin-flipping and negligible PL helicity. Similar results can be obtained for CsPbBr 3 SC ( Figure R2 d- spin-current of MAPbI 3 SC that follows the optical pumping helicity, the so-called circular photogalvanic effect. Therefore, we are very confident that our results provide strong evidence of the formation of spin-valleys and the Rashba effect in lead halide perovskites. Figure  In response, we have added the following contents in the main text (Started from Page 9, Paragraph 2) and inserted Figure R2 d-f into the supporting information ( Figure S7).: We further confirmed the formation of the split spin valleys through demonstrating the PL helicity that depends on the excitation light helicity at cryogenic temperature. The experimental schematic is shown in Figure 3a. If there are spin-split bands due to the Rashba effect, we can selectively excite these bands using circular-polarized optical pumping. To exclude any instrumental polarization-dependent response, we kept the same detection polarization and only varied the incident polarization only. Figure 3b displays typical right circularly-polarized (σ -) PL spectra of MAPbBr 3 SC upon left (σ + ) and right (σ -) circularly-polarized excitation with 532 nm laser at 77 K.
It can be clearly observed that the PL helicity follows that of the optical pumping, a signature of the optically pumped valley polarization. The degree of circular polarization of the PL is defined as: 48,49 ( ) ( ) ( ) ( ) where I(σ + ), I(σ -) are the PL intensity with left-and right-circular optical pumping, respectively. P at Peak 2. The latter has a much slower rate compared to that of the spin-flipping, smearing out all the polarization information. P also drops significantly when the excitation wavelength is changed from near-resonance to off-resonance. For example, P decreases to 3% and 0% with 473 nm and 400 nm optical-pumping, respectively. This is attributed to the potential barrier formed between the two spin-split bands that preserves the initial photo-carrier spin with near-resonance excitation. Similar results were obtained for CsPbBr 3 SC ( Figure S7)   "While this manuscript contains some interesting findings, it cannot be published as the main conclusions are (partially) based on a misinterpretation of spectroscopic measurements.
The authors report a difference in band gap for MAPbBr single crystals and thin films. However, a recent paper in Nature Communications showed very clear evidence that the optical band gap for MAPbBr in single crystals is identical to the band gap in thin films: https://www.nature.com/articles/s41467-017-00567-8 This is in direct contradiction to the results in Fig. 1d. In the manuscript at hand, the problem arises most probably from using diffuse reflectance measurements to determine the band gap of the single crystals. Diffuse reflectance measurements depend on parameters such as grain diameter, surface roughness, and refractive index. Deriving the band gap of a material from diffuse reflectance measurements is therefore likely to be inaccurate, see e.g.: http://www.sciencedirect.com/science/article/pii/S0927024807001948 I note that several groups in the perovskite community have used diffuse reflectance spectroscopy for (doped) perovskite crystals and derived too small band gaps. In general, I want to point out the importance of carefully executed and properly interpreted optical spectroscopy. To obtain the optical properties of single crystal samples, it is advisable to use a speculiar reflection technique (such as ellipsometry). For thin films transmittance is often a good choice. Diffuse reflectance should only be used for very fine powders and relatively weak absorption.
With respect to the PL measurements, I am not convinced that the apparent peak shift is not due to self-absorption. A clear hint is the reported shift with increased precursor concentration (and hence higher film thickness)."

Response:
We thank the reviewer for raising the important questions. However, we believe there are possible some misunderstandings that obfuscate his/her evaluation on the manuscript.
Firstly, we did not report a difference in the optical band gaps of perovskites in thin film or single crystal form. Instead, we show that there are weak absorption tails below the typically measured band gap. Due to the weak-transition characteristics, the absorption is usually not obvious in thin film, leading to the difference in the measured band gap of single crystal and thin film. Nonetheless, the band gap of perovskite thin film and single crystal should be identical, but there was a lot of misinterpretation previously. Secondly, we agree with the reviewer that diffuse reflectance measurements can be sensitive to many parameters. In our manuscript, we also pointed out any sub-gap defects (corresponding to grain condition, surface roughness as the reviewer points out) that could also have weak absorption and may overlap with the indirect band gap absorption, leading to inaccurate estimation of the real band gap in lead halide perovskites. Hence, we did not attribute the weak absorption immediately to the indirect band gap of the perovskites. Instead, we carefully performed further complimentary studies to validate our claim of indirect band gap: (a) the appearance of a second PL peak at the claimed indirect band gap position; (b) the second PL peak have a 2 nd order fluence dependence, implying band edge recombination; and (c) a strong photo-current peak at similar energy point. These results clearly support the weak absorption and emission are from the indirect band gap of lead halide perovskites.
For accurate measurement of the weak absorption coefficients near the indirect band gap, other techniques have been employed in previous reports. For example, Wang et al have successfully fitted the weak absorption part of the photo-thermal diffraction spectroscopy (PDS) data of MAPbI 3 film with an indirect band gap (Energy Environ. Sci., 2017, 10, 509-515). The diffuse reflectance data of MAPbI 3 SC measured in our previous paper (Adv. Energy Mater. 2016, 1600551) is in good agreement with the PDS data. The only disadvantage of diffuse reflectance spectroscopy is it cannot tell the absorption coefficients of single crystals. However, in this manuscript, we are not quantifying these parameters. Hence, we believe that it is not necessary to further perform more delicate experiments on this part.
Thirdly, the reviewer pointed out: "A clear hint is the reported shift with increased precursor concentration (and hence higher film thickness)," We respectfully disagree with this comment. The thickness of the films has been confirmed for several batches of samples. The thickest films (1M, highest concentration) always have a thickness of around 200 nm; while the other films generally have a thickness between 150 nm -200 nm. There is not much difference in the thickness of the films with different precursor concentration. And with the known absorption coefficients of MAPbBr 3 , it is easy to calculate that there is negligible reabsorption in the thin films. Similar results were obtained from other literature (e.g., Energy Environ. Sci., 2017, 10, 509;Physical Review B 2017, 95, 075207). We, therefore, have solid evidence to exclude the reabsorption effect in the films, rather than by empirical intuitions.
To avoid ambiguities, we revised the manuscript accordingly: In Page 4, Line 2 from the bottom: "We had previously performed diffuse reflectance spectroscopy (DRS) to measure MAPbI 3 SC absorption edge and the results were consistent with that of the photo-thermal diffraction spectroscopy reported elsewhere. 18,23 Here DRS is used to measure the absorption properties of the lead bromide perovskites and the absorption edges…" In Page 5, Line 5: "Peak 2 is absent in TF due to its weak absorbing and emitting nature" is changed to "Peak 2 is not prominent in TF due to its weak absorbing and emitting nature" In addition to the response to the reviewers, we made a few small revisions: In Page 4, Line 6: "At low temperatures, non-spherical A-site cations and surface/defects induced lattice distortion lead to a static centro-symmetry breaking that mainly contributes to the Rashba effect." In Page 11, Line 10: "The temperature-independent term should arise from static centrosymmetry breaking by the non-spherical A-site organic cations (MA, FA), surface distortion or internal interface distortions (such as twinning of orthorhombic phase, inclusion of different phases)…" Fig. 1d and my previous report was oversimplifying, my apologies to the authors. However, I still have problems with the interpretation of their optical spectra. The authors state in the manuscript that "Peak 2 is not prominent in TF due to its weak absorbing and emitting nature." However, it does appear in PL when the film quality is sufficiently high (Fig.  2a). Following the authors' interpretation, peak 2 should also be prominent in the absorption of this higher quality film. Why is this simple measurement not presented?

Comment 1. I have indeed misinterpreted the intention of
Response 1: We thank the reviewer for his frank, open views and are very grateful for his sincere feedback to help us strengthen our manuscript. About the comment on the interpretation of the optical spectra, the indirect absorption is always not comparable to that of direct absorption, hence, we can not see any prominent difference in absorption for different films. However, absorption and emission are two different processes. For emission (photoluminescence), the photoexcited carriers tend to relax to the lower energy states (here E in < E d ), therefore, the indirect band edge is much higher populated than the direct band edge. The indirect PL intensity can be comparable to that of direct PL. A good example is germanium (Ge) which shows similar optical properties. Secondly, the photoexcited carriers can interact with the lattice, forming polaron or self-trapped exciton, which may also change the transition probability.
Comment 2: I would also like to note that peak 2 was not observed in these high quality MAPbBr3 films with high PLQEs: https://pubs.acs.org/doi/10.1021/acsenergylett.8b00509 Response: We thank the reviewer for the interesting question. After reading through the paper, we found the PL spectrum is from the control sample (MAPbBr 3 film). The PLQE is ~1%, which is not high as the reviewer had mentioned. Moreover, the effective carrier lifetime of the film used for PL is still not comparable to our best quality thin film (1M, ~ 40 ns). In the paper, as the authors claimed, the control sample shows initial fast decay within tens of ns, followed by a slow component of 47 ns. The effective lifetime (effective lifetime is defined as the time of the PL reaching 1/e of its initial intensity) shall then be less than 47 ns. After we digitize the data from the paper ( Figure R1a), we found the effective lifetime of the sample used for PL is only ~20 ns. This data/value does not account for the presence of even faster decays. This is because of the lower system resolution of the TCSPC system (than a Streak Camera system) and we would also like to highlight that we do not see the rise time of the PL data which was somehow left out by the authors. So it is possible that the real effective PL lifetime is much less than 20 ns. Instead, our streak camera system has a much higher time resolution and the lifetime measured is more accurate. The high quality films in our experiment has a lifetime of around 40 ns. We would also like to point out that the film in our manuscript prepared with 0.5 M precursor concentration has an effective lifetime of ~18 ns, which is more like the control film used in the ACS Energy Lett paper. As we see from our results (Figure 2a), the second peak has become much weaker for the film prepared with 0.5 M precursor concentration compared to that of 1 M, which is almost negligible for film with 0.25 M precursor concentration. It is possible that the quality of the films in the ACS Energy Lett paper is not as high as it is believed to be. Hence, the absence of the dual peak in their data.
Secondly, even the PL peak shown in the ACS Energy Lett paper does not show very symmetric single peak (the fitting of the digitized data using single Voigt function is presented in Figure R1b).
Last but not the least, the carrier lifetime and PLQE are relatively good metrics to evaluate whether a film is of high quality or not. But there are too many factors that may affect carrier lifetime and PLQE (e.g., grain size). Hence, there are no perfect methods to compare film quality prepared in different laboratories. Also, as we mentioned in our manuscript, the dual peak emission is sensitive to film preparing conditions, stochiometric ratio, local environment, etc.
Based on above points, we believe that our conclusion is still valid. Figure R1. (a) The effective lifetime of the MAPbBr 3 film in the ACS Energy Lett paper (PL decay is digitized from Figure 3b in the paper). (b) The PL spectrum digitized from Figure 3a in that paper and its fitting with a single Voigt function.
Comment 3: Furthermore, there is some inconsistency regarding film thicknesses. In the response to my previous report, the authors write:"The thickest films (1M, highest concentration) always have a thickness of around 200 nm; while the other films generally have a thickness between 150 nm -200 nm." From the caption of Fig. 2: "Temperature-dependent PL peak positions for the film prepared with 1 M precursor concentration. This concentration matches that used for single crystal growth. The film has a thickness of around 220 nm, which is thicker than the film presented in Figure 1e (~ 100 nm)." Response 3: We thank the reviewer for pointing out a potential ambiguity. The film prepared with 0.25 M concentration has a thickness of around 150 nm and that prepared with 1M concentration is around 220 nm ( Figure R2). The PL in Figure 1e is measured with film prepared using 0.25 M concentration. We apologize for the confusion caused in the caption of Figure 2.
We have changed the caption of Fig.2 to avoid any potential ambiguity: "The film has a thickness of around 220 nm, which is thicker than the film presented in Figure 1e (~ 100 nm)." In addition, a sentence was added in Figure 1e: "The TF was prepared using 0.25 M precursor

Reviewer #6
The manuscripts presents a comprehensive data set on lead-bromide-perovskite single crystals and thin films. While most of the data have been reported before in many previous publications by the authors and other groups, this work puts the information in context and resolves some apparent discrepancies in the literature. Therefore, I recommend publication in Nature Communications in agreement with some of the previous reviewers. For the change of the detection polarization, we had also performed the measurement previously, but had not shown the data. Indeed, the effect reverses as shown in Figure R3. We have incorporated Figure R3 in the revised SI ( Figure S7) and made changes in the main manuscript in Page 9, 2 nd line from the bottom: "…optically pumped valley polarization. The same conclusion can be obtained when the detection polarization is reversed ( Figure S7). …" For references showing circularly-polarized PL spectroscopy can be used to identify spin-polarized band structure, we have added a few references in the manuscript in Page 9, Paragraph 2: "The technique is widely used to selectively excite spin-valleys to achieve valley polarization, which provides a good indication of how well the valley identity of charge carriers is preserved before recombination. 36,50,51 " where reference 50, 51, 52 are:

50.
Zeng We also thank the reviewer for providing some more references which we had missed in our manuscript about reabsorption. We have incorporated them into the manuscript in Page 6, last line: "exciton-electron scattering (H emission) or biexciton emission; and (7)