Efficient up-conversion in CsPbBr_3 nanocrystals via phonon-driven exciton-polaron formation

Domain: earth_science
Published: 2025-07-01
Editorial outcome: minor_revision

Abstract
Lead halide perovskite nanocrystals demonstrate efficient up-conversion, although the precise mechanism remains a subject of active research. This study utilizes steady-state and time-resolved spectroscopy methods to unravel the mechanism driving the up-conversion process in CsPbBr3 nanocrystals. Employing above- and below-gap photoluminescence measurements, we extract a distinct phonon mode with an energy of ~7 meV and identify the Pb-Br-Pb bending mode as the phonon involved in the up-conversion process. This result was corroborated by Raman spectroscopy. We confirm an up-conversion efficiency reaching up to 75%. Transient absorption measurements under conditions of sub-gap excitation also unexpectedly reveal coherent phonons for the subset of nanocrystals undergoing up-conversion. This coherence implies that the up-conversion and subsequent relaxation is accompanied by a synchronized and phased lattice motion. This study reveals that efficient up-conversion in CsPbBr3 nanocrystals is powered by a unique interplay between the soft lattice structure, phonons, and excited states dynamics.

Introduction
Laser cooling in solid-state semiconductors, first proposed by Pringsheim in 1929, has the potential to advance applications from high-power laser temperature control to quantum sensing and computing1–4. Attainment of laser cooling in semiconductors depends on two sequential processes: efficient up-conversion, where phonons, as thermal degree of freedom of the system, annihilate upon sub-bandgap light absorption to arrive at an excited state population; and anti-Stokes photoluminescence (ASPL), where the emitted photon energy is higher than that of the excitation electron, as illustrated in Supplementary Fig. 1. Once an electron undergoes up-conversion to arrive at the conduction band edge, competition between radiative and non-radiative decay pathways determines whether net cooling is observed in solid-state semiconductor materials5,6. Radiative emission without generation of a phonon leads to an overall reduction in phonon population, while non-radiative recombination results in phonon generation.

To achieve an efficient up-conversion process, which is a prerequisite for net laser cooling, a near-unity photoluminescence quantum yield (PLQY) of the semiconducting material is required2. Early efforts focused on improving laser cooling in bulk GaAs semiconductors. Refinements in growth techniques and surface chemical treatments to remove surface recombination sites led to an external quantum efficiency (EQE) of 99.5%6. However, the expected net cooling effect remained elusive in bulk materials, in part due to the substantial absorption coefficient and refractive index of bulk semiconductors, which lead to photon re-absorption. The shift in research focus towards nanomaterials is primarily driven by their superior ability to control photon re-absorption and their consistently high quality, which result in high PLQY compared to their optimized bulk and thin film counterparts7. Past studies using nanomaterials have reported showing photon up-conversion and even instances of net cooling which await further validation8–12. Nevertheless, these outcomes emphasize the potential within the semiconducting nanomaterials regime to lead to photon up-conversion and achieve net cooling.

Among promising semiconducting nanomaterials candidates for up-conversion2, cesium lead tribromide (CsPbBr3) perovskite nanocrystals exhibit substantial up-conversion efficiencies2,13,14, as well as a remarkably low trap density and high tolerance for shallow surface defects, which contribute to their near-unity PLQY15–17. On an ensemble and single-particle level, CsPbBr3 nanocrystals can up-convert photons with efficiencies up to 75% when the excitation source is detuned below the bandgap by 23 meV14. However, this phonon-assisted up-conversion process is particularly delicate and complex because more vibrational degrees of freedom create a larger hot thermal population to excite, but these same degrees of freedom tend to abrogate photoluminescence in favor of non-radiative relaxation. Additionally, coherent phonon oscillations have been directly observed in layered perovskites18,19, and a recent report on quasi-two-dimensional perovskites showed that the coherent oscillations are involved in the up-conversion process of carriers20.

Here, we deploy a combination of steady-state and excited-state measurements to resolve the specific phonons involved in the efficient up-conversion process within CsPbBr3 nanocrystals, determine up-conversion efficiency at different detuning energies, and investigate how electron-phonon coupling changes in nanocrystals undergoing up-conversion. Using a tunable laser, we leverage the exponential relationship between the excitation wavelengths and the ratio of laser intensity to ASPL intensity to extract the phonon energy related to the up-conversion process. We identify the Pb-Br-Pb bending mode, with energy ~7 meV21–24, as the phonon involved in up-conversion within CsPbBr3 nanocrystals. In excited-state measurements, the above-gap excitation results in the expected intraband cooling characteristics. However, with below-gap excitation, an unexpected coherent phonon oscillation emerges at early times as exciton-polarons form within the subset of nanocrystals undergoing up-conversion. These coherent lattice vibrations are synchronized to the frequency of the Pb-Br-Pb bending phonon mode, which implies that the up-conversion and subsequent relaxation is accompanied by a synchronized and phased lattice motion. In all, this work provides invaluable insight into how the intricate interplay between the soft lattice structure, phonons, and excited states dynamics contributes to efficient up-conversion in CsPbBr3 nanocrystals.

Results
Steady-state dynamics

We synthesized high-quality CsPbBr3 nanocrystals to avoid non-radiative pathways that might otherwise obscure the sub-bandgap dynamics involved in the up-conversion process25. CsPbBr3 nanocrystals were synthesized following a modified version of previous reports (details in the Method section)13,26. Figure 1a shows the steady-state absorption and photoluminescence (PL) spectra with band edge emission peak at ~2.43eV and a full width at half maximum (FWHM) of 81.38meV. The as-synthesized (no-post synthetic treatment) sample of CsPbBr3 nanocrystals exhibits a very high absolute PLQY, approaching ~100% unity within 2.0% uncertainty, as shown in Fig. 1b. This near-unity PLQY, an attribute of lead-halide perovskite nanocrystals27–29, highlights their suitability for our study. The nanocrystals are highly monodispersed, Fig. 1c, which is also indicated by the narrow linewidth in the PL spectrum.

We employed a tunable laser with a narrow bandwidth of 3 nm to photoexcite the high-quality nanocrystals below the band edge at different wavelengths. A long-pass filter with a wavelength of 515 nm was employed to prevent any unexpected broad bandwidth in the laser spectrum from exciting the sample, as depicted in Supplementary Fig. 2. Figure 2a (and inset) shows the ASPL as a result of excitation below the band edge at room temperature over a wavelength range of 515 to 550 nm. The ASPL in CsPbBr3 is expected14, and we find that with increasing excitation wavelengths, the ratio of laser peak intensity at a single wavelength to the ASPL peak intensity follows an exponential form (Fig. 2b, see also log plot in the inset). We fit the data to an Arrhenius equation to extract a characteristic energy (Ech) as follows:

Iexc / Iaspl = e(Eg - hν) / Ech (1)

where Eg is the bandgap energy, hν is the excitation energy, and Ech is a characteristic energy. This characteristic energy involves both κBT at room temperature (RT) and the phonon energy (Ep) responsible for the up-conversion process. Specifically, the phonon energy is determined by subtracting the thermal energy from the characteristic energy:

Ep = Ech - κBT (2)

From the fit shown in Fig. 2b, we retrieve Ep = 7.3 meV (59 cm-1) which corresponds to the Pb-Br-Pb bending mode in CsPbBr3 nanocrystals21,22. The presence of this low frequency is confirmed by Raman spectroscopy (peak 62.98 cm-1), as shown in Fig. 2c (see Supplementary Fig. 3 for raw data and background fit). The lowest observed frequency (25.42 cm-1) corresponds to the octahedral twist30,31. The 104.66 and 127.38 cm-1 frequencies are assigned to the longitudinal optical (LO) phonon modes associated with the stretching of the Pb-Br bonds in the [PbX6]4- sublattice, while the 309.88 and 317.62 cm-1 modes are assigned to higher order scattering based on previous reports21–24.

To quantify the up-conversion efficiency, the ASPL is compared to the Stokes PL which is the cap efficiency (i.e., all exciton excited above bandgap that reached the band edge). Following the work of Zhang et al.2 the relation between Stokes PL, ASPL, and up-conversion efficiency (η) is formulated as follows:

Ispl = Iexc As PLQY (3)

Iaspl = Ias Aas η PLQY (4)

where Ispl and Iaspl are the Stokes PL and ASPL intensities, Iexc and Ias are the Stokes and anti-Stokes excitation intensities, As and Aas are the Stokes and anti-Stokes absorptance, and η is the up-conversion efficiency. Measurement of the up-conversion efficiency (Fig. 2a) is performed such that Ispl and Iaspl are similar in value. This allows us to rearrange Eqs. (3) and (4) to solve for η as follows:

η ≈ (Ispl / Iaspl) * (As / Aas) (5)

Equation (5) requires Aas that be known for every excitation wavelength detuned into the CsPbBr3 nanocrystals energy gap. Due to the low sensitivity of a typical spectrophotometer at the absorption band tail, we relied on the fact that absorption is related to the Urbach energy through the absorption coefficient. We fit the slope of the absorption coefficient from the band edge, where a single representative energy is utilized32 (Fig. 2d, more details in SI), extracted the Urbach energy, 31 meV, and calculated the absorptance at the anti-Stokes position, Aas, at different excitation wavelengths. The Urbach energy of 31 meV falls within the lower range of typical Br vacancy levels, as theoretically calculated (within 100 meV), for Br-deficient CsPbBr3 nanocrystals28. This observation is also consistent with other experimental findings, which have reported Urbach energy values ranging from 40 to 48 meV33,34. This suggests that our nanocrystals exhibit significantly reduced defect states. The Urbach energy of nanocrystals in contrast to bulk is expected to vary, owing to factors such as different surface chemistry, reconstructions, and disorder32.

Using this Stokes and anti-Stokes data, we calculated the up-conversion efficiency for every excitation wavelength (Fig. 2e). These measurements yielded values for η from 62% down to 3.0% for λexc = 515 nm (ΔE=24 meV) and λexc = 550 nm (ΔE=177 meV), respectively. Our results are in good agreement with previously reported values for CsPbBr3 nanocrystals14.

To further assess the role of phonons in the up-conversion process, we conducted a comparative analysis of up-conversion efficiency under two different temperature conditions: RT and liquid nitrogen (LN) temperature (~77 K). This analysis was performed on a freshly prepared sample with a PL emission peak at 2.43 eV (as shown in Supplementary Fig. 4). In both cases, we observed that the ratio of laser intensity to ASPL intensity exhibited an exponential relationship. Based on this relationship, we determined the phonon energy associated with the up-conversion process as 9 meV (corresponding to 72 cm-1) at RT and 9.1 meV (corresponding to 73 cm-1) at LN temperature. Notably, these phonon energies fall within the range of the Pb-Br-Pb bending mode21–24.

We used the Urbach energy of the new sample, 30 meV, to calculate up-conversion efficiencies as above. As depicted in Supplementary Fig. 4f, our results clearly illustrate a significant reduction in up-conversion efficiency (~2.8-fold reduction on average) when the sample is cooled to cryogenic temperatures. Phonon population follows a Boltzmann distribution that is dependent on both energy and temperature factors. Therefore, we compared the ratio of the number of phonons (Np) at RT and LN as follows:

Np(RT) / Np(LN) ≈ e-Ep(RT)/κBT(RT) / e-Ep(LN)/κBT(LN) (6)

yielding a value of ~2.8. Remarkably, this value closely corresponds to the ratio of up-conversion efficiencies at the two temperature conditions (see Supplementary Fig. 4f inset). We also determined that room temperature falls within the optimal temperature range for maximizing up-conversion efficiency (depicted in Supplementary Fig. 5; detailed further in the SI).

To further confirm that the ASPL is coming from the band edge emission, we measured time-resolved PL at RT for above- and below-gap excitations. Figure 3 illustrates that the decays follow a mono-exponential form with similar lifetimes. This result suggests that, regardless of whether the electron is excited above the band edge or up-converted to the band edge, decay originates from the band edge.

Excited State Dynamics

To investigate how up-conversion affects electron-lattice vibration (electron-phonon coupling) in the nanocrystals, we next employed ultra-fast time-resolved spectroscopic measurements. We performed transient absorption spectroscopy (TA) to elucidate the initial dynamics of excited states within the colloidal CsPbBr3 nanocrystals with above- and below-gap excitation. Above-gap excitation was achieved by delivering 31.7 μJ/cm2 pumping pulse power with 35 fs pulses centered at 440 nm. Since intense pumping below the gap can electronically excite semiconductors via two-photon absorption, we first investigated the pump fluence dependence of our below-gap excitation (at 540 nm) and followed band edge bleach signals that corresponded to electron-hole pair excitation. As presented in Fig. 4, a linear dependence on pump fluence clearly exists at 2 ps and 10 ps pump-probe time delays (both subsequent to typical carrier cooling timescales). We discern a linear scaling of bleach amplitude with pump power up to ~300 μJ/cm2. This linear regime indicates that signals below this power originate from a one-photon process consistent with up-conversion, helps us to avoid higher intensity regimes that would convolve up-conversion and two-photon pumping, and also allows us to judiciously select a power level that provides an optimal signal-to-noise ratio. Consequently, we set the below-gap pump power at 217.3 μJ/cm2 for this investigation (notably, Supplementary Fig. 6 also demonstrates similar effects with 163 μJ/cm2).

For above-gap excitation (440 nm), the TA spectral map exhibits several distinct characteristics. Immediately following excitation, a pronounced induced absorption is observed near 512 nm that decays within 1 ps (Fig. 5a, b). A band-edge bleach feature also appears and completes rising within this timeframe. The red-shifted induced absorption feature is conventionally linked to the presence and relaxation of a hot exciton state wherein intraband cooling of electrons and holes to band-edge states occurs upon phonon generation35,36. Within the first 1 ps, the measurements reveal a slight red shift (~1 nm) in the exciton transition, consistent with exciton-exciton Coulomb interactions35,37. It is worth noting that the cooling of a hot exciton sometimes results in the generation of coherent phonons if cooling is fast compared to the phonon period, which can induce oscillatory behavior in the TA signal. Under this excitation condition, the composition does not exhibit such a phenomenon. Upon integrating the area under the TA curve versus pump-probe time delay (Fig. 5b inset), a distinct plateau in the values becomes evident after 0.7 ps. This timescale aligns with polaron formation in CsPbBr3 nanocrystals23, which can also lead to induced absorption near 486 nm with a similar timescale38 (Fig. 5c).

For below-gap excitation (540 nm) conducted in the linear regime, distinct features appear in the TA spectra. Notwithstanding the coherent signal near time zero, a photoinduced absorption signal again emerges near 512 nm upon excitation (Fig. 5d, e) and decays on a similar timescale to the above-gap condition. Note, however, that the 512 nm induced absorption signal nominally should not appear owing to an absence of hot excitons, and band-edge bleach formation should approach the instrument response function, as intraband relaxation does not occur under this condition. Time-resolved spectra also appear appreciably distinct, which we elaborate on below. Remarkably, we also observe oscillatory spectral signals emerging below the band edge in the TA spectrum in Fig. 5d (along the border of ground-state bleach and the photoinduced absorption), where the oscillation frequency can be quantified by performing fast Fourier transform (FFT) along the time axis. We obtained a characteristic frequency value of approximately 50 cm-1 (illustrated in Fig. 6a), which corresponds to the frequency of the Pb-Br-Pb bending phonon mode. The observation of coherent phonons in this scenario implies that phonons are involved in the ultrafast up-conversion and relaxation processes, which may seem counterintuitive since below-gap excitation conditions generate neither a hot electron nor a hot hole and presumably remove phonons from any excited nanocrystal. Thus, nanocrystals undergoing up-conversion contain a quantum of the specific phonon that impulsively gets removed upon absorption, and the observed oscillation reveals a dominant relaxation mechanism on the path to polaron formation. This outcome reinforces the assertion that the efficient up-conversion in CsPbBr3 nanocrystals is associated with the Pb-Br-Pb bending mode, as visually represented in Fig. 6b.

The distinctive lineshapes observed in the below-gap excitation TA spectra (Fig. 5d) are also worth discussing. During the initial period (<1 ps), the TA spectra exhibit characteristics of a second derivative, which subsequently transform into a symmetric above-gap-excitation-like pattern. It is important to highlight that, unlike typical above-gap excitation scenarios, the integrated area of the TA curves crosses zero as time advances. This intriguing observation suggests that the polaron generated during the early stages plays a crucial role in facilitating electron-phonon coupling for up-conversion by inducing charge redistribution and lattice distortion due to the soft lattice of CsPbBr323,39. The charge redistribution is marked by the noticeable red-shift (~3 nm) in the TA spectra, which can be attributed to the intricate interplay of many-body Coulomb interactions23. This transition in line shape occurs within a short interval of 0.7 ps, which serves as additional confirmation of the critical involvement of polarons in the up-conversion process23. We also observe a noticeable delay in the rise and decay of the time traces when monitoring below the band edge, as opposed to above the gap, for both above- and below-gap excitations (Fig. 5c, f).

Methods
Chemicals
Lead (II) acetate trihydrate (PbOAc2·3H2O, 99.999%), oleylamine (OAm, 70%), 1-octadecene (ODE, 90%), and benzoyl bromide (BzBr, 97%) were purchased from Sigma-Aldrich. Cesium carbonate (Cs2CO3, 99.9%, Metal basis) and oleic acid (OA, 90%) were purchased from Thermo Scientific Chemicals. Other chemicals used include anhydrous toluene (99.8%) and hexane.

Synthesis
CsPbBr3 nanocrystals were synthesized following a slightly modified version of previously published procedures13,26. Briefly, ODE (10 ml), oleic acid (0.6 ml), oleylamine (2 ml), PbOAc2 (0.4 mmol) and Cs2CO3 (0.06 mmol) were loaded in a 50 ml round-bottom flask, degassed, and heated at 120 oC for 1 h. Then, under nitrogen, the temperature was raised to 140 oC for 15 min followed by degassing at 120 oC for 10 min. The injection temperature was then set at 200 oC, under nitrogen, and BzBr (1.7 mmol) solution was injected swiftly. CsPbBr3 nanocrystals formed almost instantly but were allowed to grow for 30-40 seconds before quenching in an ice-water bath. The nanocrystals were cleaned in an inert environment via successive precipitation at 10 k rpm without antisolvents and dissolution using toluene. Nanocrystals were stored in 5 ml toluene.

Optical spectroscopy
Absorption spectra were collected using a Shimadzu UV-3600 spectrophotometer. Photoluminescence spectra were acquired on a Horiba Jobin Yvon Fluorolog-3 spectrophotometer equipped with a Synapse OE-CCD detector. Time-resolved photoluminescence as well as sub-bandgap photoexcitation were collected on a Picoquant Fluotime 300 equipped with PMA 175 and an LDH-P-C-405 diode laser with an excitation wavelength of 408 nm and a Solea supercontinuum laser with bandwidth of 3 nm. Absolute quantum yield measurements were collected using an integrating sphere coupled with an Ocean Optics QE Pro spectrometer and a 415-nm fiber-coupled LED excitation source (M415F3, Thorlabs, 14.4 mW).

Raman spectroscopy
Low-frequency Raman spectra were measured at room temperature using a confocal Raman microsystem in backscattering geometry at GSECARS, Advanced Photon Source, Argonne National Laboratory. The laser excitation source was 946 nm with 50 mW power, in conjunction with a spectrometer (Acton SpectraPro SP-2500, 1200 grooves/mm grating) and a PIXIS 100 back-illuminated deep depletion CCD camera. Three-notch filters were used to suppress the Rayleigh scattering. Detailed acquisition setup can be found elsewhere40. Data were collected within the range of -450 cm-1 to 450 cm-1 with an average exposure of 30 s. The samples remained stable throughout the spectral acquisition process. For post-processing, the background was subtracted by a background fit with 5th-order asymmetric truncated quadratic function.

TEM
TEM and HRTEM images were acquired on a FEI Tecnai T20 S-TWIN TEM operating at 200 kV with a LaB6 filament and equipped with a Gatan Rio 16 IS camera with 4k resolution.

Time-resolved transient absorption
TA measurements were performed with a homebuilt setup at the Center for Nanoscale Materials on colloidal samples dispersed in hexane and sealed in 2 mm path length quartz sample cells. An amplified Ti:sapphire laser operating at 800 nm with a pulse width of 35 fs and repetition rate of 2 kHz was used to generate pump and probe beams. Pump pulses at 440 nm and 540 nm were each produced using an optical parametric amplifier and sum frequency generation and blocked in an alternating manner to produce a 1 kHz repetition rate. The probe beam was produced by focusing a portion of the 800 nm light, after a mechanical time delay, on a sapphire plate to create time-delayed white light probe pulses. Data shown implements background subtraction and temporal chirp correction.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors studied the up-conversion process in CsPbBr3 nanocrystals using steady-state\nphotoluminescence (PL) and transient absorption (TA) spectroscopy under below and above bandgap excitations. There\nhave been some demonstrations of efficient up-conversion in lead halide perovskites, but the detailed mechanism remains\nunclear. The authors successfully determined the dominant phonon mode (Pb-Br-Pb bending phonon mode) involved in the\nup-conversion process, and their results can advance our understanding of the up-conversion process in lead halide\nperovskites. Therefore, I think this manuscript is acceptable for publication in Nature Communication after minor revisions.\nSome comments are shown below.\n1. In perovskite materials, there are some reports for demonstrating laser cooling [Nat. Photonics 10, 115–121 (2016), Nano\nLett. 20, 8874–8879 (2020), Nano Lett. 24, 11255–11261 (2024)]. In this manuscript, the authors reported the value of the PL\nquantum yields (PLQYs) of their samples to be 100.0±2.0%. The samples with such high PLQYs have a great potential for\nachieving higher net optical cooling. I think that the paper could become stronger and attract more readers' attention if the\nauthors could add results and discussion on laser cooling experiment.\n2. It is not clear for me how to determine the up-conversion efficiency at liquid nitrogen (LN) temperature because the Urbach\nenergy at LN temperature is unclear (Does the value of 29.53 meV correspond to the value at LN temperature?). In general,\nthe Urbach energy depends on the temperature [e.g. Phys. Rev. Lett. 47, 1480 (1981)]. If we consider the unity PLQY (i.e. no\nstructural defects) and the dominant phonon mode to be ~7 meV, the Urbach energy should be almost linearly depending on\nthe temperature between room temperature (RT) to LN temperature. Therefore, according to the value at RT (30.95 meV),\nthe Urbach energy at LN temperature should be ≈8 meV, which is quite different from 29.53 meV.\nThe following are minor comments:\n3. I think “2.43 meV” in line 193 should be “2.43 eV”.", "reviewer_2": "The manuscript presents a comprehensive study on the up-conversion mechanism in CsPbBr3 nanocrystals, identifying the\nPb-Br-Pb bending mode as the key phonon involved. The authors employ steady-state and time-resolved spectroscopy to\ndemonstrate an up-conversion efficiency of up to 75% and reveal coherent phonon oscillations during the process.\nThe manuscript is well-written, and the experimental design is robust. The findings contribute valuable insights into the up-\nconversion mechanisms in perovskite nanocrystals and is suitable for publication in Nature Communications.\nI note only one inaccuracy in the section describing the time-resolved photoluminescence: line 212 “… we measured steady-\nstate time-resolved PL at RT…” and line 218 “Figure 3: Steady-state time-resolved PL…”. The PL measurements are time-\nresolved, but the photoexcitations are not in a “steady-state”. The correct term is therefore “time-resolved PL” and not\n“steady-state time-resolved PL”", "reviewer_3": "The authors present a detailed mechanistic study of photoluminescence up-conversion of CsPbBr3 nanocrystals via below band gap excitation. The insights gained are interesting and shed further light on the importance of the soft lattice in this family of materials, and more broadly, how specific vibrational modes impact both up conversion and polaron formation. The measurements are carefully and thoughtfully conducted with clear purpose that is well explained and described. While the phenomenon has been previously reported (ref 15), this report was observational and the thorough mechanistic presentation is of sufficient interest to a broad audience to be appropriate for publication in Nature Communications. There are some small organizational and presentation details which should be clarified before final publication.\n1) The authors mention a similar mechanism motivated for 2D perovskite up-conversion (ref 21) in the introduction. The\nmanuscript would be greatly improved by circling back to this similar observation in the conclusion to discuss how the two\nsystems may be similar or different in the lattice relaxation and how that contributes to up-conversion efficiency of\nmechanism.\n2) The authors utilize the intensity of excitation and ASPL to extract the phonon energy. The authors should clarify what\nmetric is used for intensity (single wavelength value, integrated area, etc).\n3) The authors state they extract Ephonon from Ech in their Arrhenius fits, but do not show the relationship between the two.\nThe authors should include that relation (even just in the SI).\n4) Figures 2d and 2e are discussed in opposite order in the main text. The flow of the discussion makes sense, so the\nauthors should swap the order of the panels in the figure for added clarity.\n5) Similar to point 2, the authors use the Urbach tail intensity to calculate the absorption of the different excitation spectra.\nThe authors should clarify if a single point was used, or the spectrum weighted absorption based on both the Urbach energy\nand the spectral width. If just a single wavelength was used, it would greatly enhance the manuscript to demonstrate or\njustify why this is a valid approximation.\n6) The discussion of expected energies for the Br vacancy is fairly vague in confirming consistency with previously reported\nvalues. For example, being within 100 meV of a value which is only 30.95 meV does not sound particularly consistent.\nFurthermore, the high numerical precision to which this value is reported seems inconsistent with the range of values that\nare referenced. Either including reported error on the defect energy, or placing the variation in more context of why it would\nbe expected would strengthen the argument.\n7) The temperature dependence shown in figure S3f seems more central to the author’s argument while figure 4 seems more\nlike control measurements. Given limited main text figures, I would recommend swapping the two to focus the narrative more\nstrongly on the core scientific result.\n8) Given the (likely) variability in some of the measurements, many of the fits and scatter plots would be much improved by\nrigorous error analysis and inclusion. This will help the reader understand whether deviations from the expected behavior\nare well within expected statistical fluctuations, or if there are real deviations from predicted behavior occurring.\nAll in all, the manuscript is detailed, thorough, and presents a crucial insight into understanding an important process which\nis a highly promising application for perovskite nanocrystals and thus warrants publication in Nature Communications once\nthe above improvements have been addressed."}, "author_response": "Response to Reviewers\n\nReviewer #1 (Remarks to the Author):\nIn this manuscript, the authors studied the up-conversion process in CsPbBr3 nanocrystals using\nsteady-state photoluminescence (PL) and transient absorption (TA) spectroscopy under below and\nabove bandgap excitations. There have been some demonstrations of efficient up-conversion in\nlead halide perovskites, but the detailed mechanism remains unclear. The authors successfully\ndetermined the dominant phonon mode (Pb-Br-Pb bending phonon mode) involved in the up-\nconversion process, and their results can advance our understanding of the up-conversion process\nin lead halide perovskites. Therefore, I think this manuscript is acceptable for publication in Nature\nCommunication after minor revisions. Some comments are shown below.\n1. In perovskite materials, there are some reports for demonstrating laser cooling [Nat. Photonics\n10, 115–121 (2016), Nano Lett. 20, 8874–8879 (2020), Nano Lett. 24, 11255–11261 (2024)]. In\nthis manuscript, the authors reported the value of the PL quantum yields (PLQYs) of their samples\nto be 100.0±2.0%. The samples with such high PLQYs have a great potential for achieving higher\nnet optical cooling. I think that the paper could become stronger and attract more readers' attention\nif the authors could add results and discussion on laser cooling experiment.\nResponse: We thank the Reviewer for their helpful suggestion. We acknowledge the above-\nmentioned papers on their contributions to solid-state laser cooling and have included these\nreferences in the main text. We are actively pursuing laser cooling experiments with our samples.\nOur near-unity photoluminescence quantum yield (PLQY) samples are in solutions, and we are\ndeveloping and optimizing procedures to preserve the PLQY in solid form to demonstrate a solid-\nstate laser cooling., which will be prepared as a future publication. For this current work, the focus\nof this paper is to provide a fundamental mechanistic understanding on the up-conversion\nphenomenon in CsPbBr NCs.\n“14. Yamada, Y. et al. Optical Cooling of Dot-in-Crystal Halide Perovskites: Challenges of\nNonlinear Exciton Recombination. Nano Lett. 24, 11255–11261 (2024).\n”\n2. It is not clear for me how to determine the up-conversion efficiency at liquid nitrogen (LN)\ntemperature because the Urbach energy at LN temperature is unclear (Does the value of 29.53\nmeV correspond to the value at LN temperature?). In general, the Urbach energy depends on the\ntemperature [e.g. Phys. Rev. Lett. 47, 1480 (1981)]. If we consider the unity PLQY (i.e. no\nstructural defects) and the dominant phonon mode to be ~7 meV, the Urbach energy should be\nalmost linearly depending on the temperature between room temperature (RT) to LN temperature.\nTherefore, according to the value at RT (30.95 meV), the Urbach energy at LN temperature should\nbe ≈8 meV, which is quite different from 29.53 meV.\nResponse: The Urbach energy of 29.53 meV corresponds to the intrinsic disorder and electron-\nphonon interactions present in perovskite materials at ambient conditions. Even with near-unity\nphotoluminescence quantum yield (PLQY), perovskites, especially bromine (Br) or Iodine (I)\nbased [J. Am. Chem. Soc. 2018, 140, 50, 17760–17772], do not exhibit a perfect Urbach tail due\nto subtle surface imperfections. While Urbach energy typically decreases at lower temperatures,\nthe intrinsic disorder and surface imperfection in perovskites contribute significantly to the Urbach\ntail. Thus we don’t expect the reduction in Urbach energy to be proportional with temperature in\nperovskites solely on their near-unity photoluminescent quantum yield. Additionally, we opted for\nensemble measurements of Urbach energy, which contribute to the disorder, aligning with our\napproach of measuring Stokes and anti-Stokes photoluminescence at an ensemble level so that we\naccount for any scattering or size inhomogeneity when calculating the up-conversion efficiencies.\nThe following are minor comments:\n3. I think “2.43 meV” in line 193 should be “2.43 eV”.\nResponse: Thank you for identifying the error, we have corrected it.\nReviewer #2 (Remarks to the Author):\nThe manuscript presents a comprehensive study on the up-conversion mechanism in CsPbBr3\nnanocrystals, identifying the Pb-Br-Pb bending mode as the key phonon involved. The authors\nemploy steady-state and time-resolved spectroscopy to demonstrate an up-conversion efficiency\nof up to 75% and reveal coherent phonon oscillations during the process.\nThe manuscript is well-written, and the experimental design is robust. The findings contribute\nvaluable insights into the up-conversion mechanisms in perovskite nanocrystals and is suitable for\npublication in Nature Communications.\nI note only one inaccuracy in the section describing the time-resolved photoluminescence: line 212\n“… we measured steady-state time-resolved PL at RT…” and line 218 “Figure 3: Steady-state time-\nresolved PL…”. The PL measurements are time-resolved, but the photoexcitations are not in\na “steady-state”. The correct term is therefore “time-resolved PL” and not “steady-state time-\nresolved PL”\nResponse: We thank the Reviewer for identifying the error, we have removed the “Steady-state”.\nReviewer #3 (Remarks to the Author):\nThe authors present a detailed mechanistic study of photoluminescence up-conversion of CsPbBr3\nnanocrystals via below band gap excitation. The insights gained are interesting and shed further\nlight on the importance of the soft lattice in this family of materials, and more broadly, how specific\nvibrational modes impact both up conversion and polaron formation. The measurements are\ncarefully and thoughtfully conducted with clear purpose that is well explained and described.\nWhile the phenomenon has been previously reported (ref 15), this report was observational and\nthe thorough mechanistic presentation is of sufficient interest to a broad audience to be appropriate\nfor publication in Nature Communications. There are some small organizational and presentation\ndetails which should be clarified before final publication.\n1) The authors mention a similar mechanism motivated for 2D perovskite up-conversion (ref 21)\nin the introduction. The manuscript would be greatly improved by circling back to this similar\nobservation in the conclusion to discuss how the two systems may be similar or different in the\nlattice relaxation and how that contributes to up-conversion efficiency of mechanism.\nResponse: We thank the Reviewer for their suggestion. While we recognize the relevance of the\nmechanism in ref 21, our study focuses on lattice relaxation driven by Pb-Br-Pb bending mode, in\ncontract to the organic molecule motions highlighted in ref 21. Expanding the comparison in the\nconclusion could divert attention from our primary findings.\n2) The authors utilize the intensity of excitation and ASPL to extract the phonon energy. The\nauthors should clarify what metric is used for intensity (single wavelength value, integrated area,\netc).\nResponse: In our analysis, the peak intensity at a single wavelength was measured and used, as\ndetailed in the main text.\n3) The authors state they extract Ephonon from Ech in their Arrhenius fits, but do not show the\nrelationship between the two. The authors should include that relation (even just in the SI).\nResponse: To address the Reviewer’s comment, we included the following:\n“Specifically, the phonon energy is determined by subtracting the thermal energy from the\ncharacteristic energy:\n𝐸 = 𝐸 − 𝜅 𝑇\n! \"# $\n”\n4) Figures 2d and 2e are discussed in opposite order in the main text. The flow of the discussion\nmakes sense, so the authors should swap the order of the panels in the figure for added clarity.\nResponse: We thank the Reviewer for the helpful suggestion, we have reordered the two panels\nof the figure.\n5) Similar to point 2, the authors use the Urbach tail intensity to calculate the absorption of the\ndifferent excitation spectra. The authors should clarify if a single point was used, or the spectrum\nweighted absorption based on both the Urbach energy and the spectral width. If just a single\nwavelength was used, it would greatly enhance the manuscript to demonstrate or justify why this\nis a valid approximation.\nResponse: We used a single point fitting approach for the Urbach tail. To address the Reviewer’s\ncomment, we added the following to the main text:\n“…where a single representative energy is utilized…” and added the following citation:\n“Jean, J. et al. Radiative Efficiency Limit with Band Tailing Exceeds 30% for Quantum Dot Solar\nCells. ACS Energy Lett. 2, 2616–2624 (2017).”\n6) The discussion of expected energies for the Br vacancy is fairly vague in confirming consistency\nwith previously reported values. For example, being within 100 meV of a value which is only\n30.95 meV does not sound particularly consistent. Furthermore, the high numerical precision to\nwhich this value is reported seems inconsistent with the range of values that are referenced. Either\nincluding reported error on the defect energy, or placing the variation in more context of why it\nwould be expected would strengthen the argument.\nResponse: We appreciate the Reviewer’s feedback. We would like to clarify that the 100 meV\ndifference refers to theoretical Br vacancy energies in CsPbBr nanocrystals. This is to highlight\n3\nthe calculated Urbach energy from this work is on the same order of magnitude as pervious theory\nstudy, which validates our methodology on extracting the Urbach energy. We acknowledge the\nReviewer concern and have omitted including high precision from the fitted values of the Urbach\nenergy throughout the manuscript.\n7) The temperature dependence shown in figure S3f seems more central to the author’s argument\nwhile figure 4 seems more like control measurements. Given limited main text figures, I would\nrecommend swapping the two to focus the narrative more strongly on the core scientific result.\nResponse: Although temperature dependent up-conversion study is critical, our primary focus is\nto demonstrate the up-conversion under ambient conditions, which is critical for practical\napplications like solid-state laser cooling.\n8) Given the (likely) variability in some of the measurements, many of the fits and scatter plots\nwould be much improved by rigorous error analysis and inclusion. This will help the reader\nunderstand whether deviations from the expected behavior are well within expected statistical\nfluctuations, or if there are real deviations from predicted behavior occurring.\nResponse: Due to the variability and complexity of the synthesis, performing detailed error\nanalysis for each dataset was challenging. For example, Figure 2 and Figure S3 are different\nsamples with different up-conversion behaviors. Instead, we have included goodness-of-fit for the\nrelevant fits.\nAll in all, the manuscript is detailed, thorough, and presents a crucial insight into understanding\nan important process which is a highly promising application for perovskite nanocrystals and thus\nwarrants publication in Nature Communications once the above improvements have been\naddressed."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I confirmed the replies from the authors and the revised manuscript. I appreciate the efforts of the authors to answer\nquestions and comments by three referees. The authors have properly addressed all concerns. Therefore, I can recommend\npublication of the manuscript for Nature Communications."}, "author_response": ""}]

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