Abstract
Exciton dynamics can be strongly affected by lattice vibrations through electronphonon coupling. This is rarely explored in twodimensional magnetic semiconductors. Focusing on bilayer CrI_{3}, we first show the presence of strong electronphonon coupling through temperaturedependent photoluminescence and absorption spectroscopy. We then report the observation of periodic broad modes up to the 8th order in Raman spectra, attributed to the polaronic character of excitons. We establish that this polaronic character is dominated by the coupling between the chargetransfer exciton at 1.96 eV and a longitudinal optical phonon at 120.6 cm^{−1}. We further show that the emergence of longrange magnetic order enhances the electronphonon coupling strength by ~50% and that the transition from layered antiferromagnetic to ferromagnetic order tunes the spectral intensity of the periodic broad modes, suggesting a strong coupling among the lattice, charge and spin in twodimensional CrI_{3}. Our study opens opportunities for tailoring lightmatter interactions in twodimensional magnetic semiconductors.
Introduction
The polaronic effect^{1}, which describes the strong coupling between charge and lattice vibrations, has a key role in a broad class of novel quantum phenomena ranging from colossal magnetoresistance^{2} to anomalous photovoltaic effect^{3}. In particular, the polaronic effect on excitons can profoundly modulate exciton dynamics upon photoexcitation and has been employed to describe intriguing optical and optoelectronic properties in materials such as hybrid organicinorganic perovskite solar cells^{4,5,6}. Compared with threedimensional (3D) bulk systems, twodimensional (2D) atomic crystals possess a couple of unique advantages in exploring the polaronic effect on exciton dynamics. First, the reduced dielectric screening in atomically thin samples enhances both the excitonic effect^{7} and the electron–phonon (eph) coupling^{8}, which is expected to promote the polaronic effect of excitons. Second, unlike bulk materials in which the eph coupling is largely determined by intrinsic electronic and phonon band structures with limited tunability, 2D materials provide greater flexibility for engineering eph coupling through a number of approaches including carrier doping^{9,10} and interfacial coupling^{11,12,13,14,15}, as well as dimensionality modulation^{8}, and therefore hold high promise for the future development of optoelectronic devices.
The realization of a longrange magnetic order in 2D semiconducting CrI_{3} paves the way to engineer optical and optoelectronic properties of 2D magnetic semiconductors^{16,17,18,19,20,21,22,23}. The large excitonic effect^{24} from the localized molecular orbitals, of neither Wanniertype in 2D TMDCs nor Frenkeltype in ionic crystals, can be considered as the microscopic origin of the giant magnetooptical Kerr effect^{25} and magnetic circular dichroism^{26} signals in 2D CrI_{3}. Meanwhile, the strong eph coupling is suggested to cause the large Stokes shift, profound broadness, and skewed lineshape in the photoluminescence (PL) spectra of 2D CrI_{3}^{26}. The coexistence of excitons and strong eph coupling in 2D CrI_{3} naturally leads to open experimental questions of whether polaronic character emerges in the exciton dynamics and whether they are affected by the longrange magnetic order.
One fingerprint for the polaronic effect is the development of phonondressed electronic bands that appear as satellite bands in proximity to the original undressed one. Such features manifest as multiple equally spaced replica bands in angleresolved photoemission spectroscopy (ARPES)^{9,14,27,28,29,30,31,32} or as discrete absorption and emission lines in linear optical spectroscopy^{33}. However, such signatures of the polaronic effect have not been revealed so far in 2D CrI_{3}, as the sizable bandgap (~1.1 eV)^{26} and extreme surface sensitivity^{34} of CrI_{3} make ARPES measurements challenging, whereas the potential inhomogeneous broadening could largely smear out individual lines for phonondressed satellite bands in linear optical spectroscopy.
In this work, we exploit temperature and magnetic fielddependent resonant microRaman spectroscopy, to show the direct observation of the polaronic character of excitons in bilayer CrI_{3}. The polaronic effect manifests in Raman spectra as a welldefined, periodic pattern of broad modes that is distinct from sharper phonon peaks. The profile of this periodic pattern and its temperature and magnetic field dependence further reveal essential information including the eph coupling strength and the tunability of polaronic effect by the magnetism in bilayer CrI_{3}. We mainly focus on bilayer CrI_{3} because it features a single magnetic phase transition from the layered antiferromagnetic (AFM) to ferromagnetic (FM) order and briefly compare to the results on thicker CrI_{3} flakes afterwards.
Results
Excitonic transitions and strong electron–phonon coupling
We start by identifying excitonic transitions and eph coupling in bilayer CrI_{3} using temperaturedependent PL and linear absorption spectroscopy. Bilayer CrI_{3} was fully encapsulated between fewlayer hexagonal BN (hBN) and placed on a sapphire substrate (for details, see “Methods”). Linear absorption spectroscopy measurements were then performed in a transmission geometry (see “Methods”). Figure 1 shows representative PL and absorbance spectra taken at 80 K, 40 K, and 10 K that correspond to well above, slightly below, and well below the magnetic critical temperature T_{C} = 45 K, respectively^{25,26,34}. A single PL mode at 1.11 eV and three prominent absorbance peaks at 1.51 eV, 1.96 eV, and 2.68 eV (denoted as A, B, and C, respectively) are observed across the entire temperature range. These three energies are in good agreement with the ligandfield electronic transitions assigned by differential reflectance measurements on monolayer CrI_{3}^{26} and bulk CrI_{3}^{35,36} and have been later revealed to be bright exciton states through sophisticated first principle GW and BetheSalpeter equation calculations^{24}. The large Stokes shift (~400 meV) between the PL and A exciton absorption peak is consistent with previous report^{6} and indicates strong electron–phonon coupling in 2D CrI_{3}. Although the absorbance spectra show little temperature dependence except for the appearance of a weak shoulder at 1.79 eV at 10 K (orange arrow), the PL spectra are clearly temperature dependent. In particular, the temperature dependence of the PL full width at half maximum, \({\Gamma}(T)\), is well fitted by the model functional form, \({\Gamma}\left( T \right) = {\Gamma}_0 + \frac{\gamma }{{\exp \left( {\frac{{\hbar \omega _{{\mathrm{LO}}}}}{{k_BT}}} \right)  1}}\), with the first term for temperatureindependent inhomogeneous broadening and the second term for homogeneous broadening from the exciton coupling with a longitudinal optical (LO) phonon at frequency \(\omega _{{\mathrm{LO}}}\). Taking \(\omega _{{\mathrm{LO}}} = 120.6\) cm^{−1} found later on in Fig. 2, we obtain \({\Gamma}_0 = 163.9 \pm 2.7\) meV and \(\gamma = 164.2 \pm 8.1\) meV, which suggests that the broadness of the exciton modes arises from both inhomogeneous broadening from disorders and homogeneous broadening from eph coupling. The large homogeneous broadening parameter (\(\gamma\)) indicates strong vibronic modes mixing in the PL spectra, which precludes the formation of wellresolved phonon sidebands^{6}.
Polaronic character in Raman spectra
We next proceed to perform resonant microRaman spectroscopy measurements with an incident wavelength of 633 nm matching the energy of the B exciton on an encapsulated bilayer CrI_{3} flake placed on a SiO_{2}/Si substrate (see “Methods”). Figure 2a displays a representative Raman spectrum acquired in the crossed linear polarization channel at 40 K (slightly below T_{C} = 45 K). Note that this spectrum covers a much wider frequency range than earlier Raman studies on CrI_{3}^{34,37,38,39,40,41,42,43,44}. The multiphonon scattering is visible up to the 3rd order, and their zoomin Raman spectra are shown in the inset of Fig. 2a. The 1storder singlephonon peaks appear in the relatively low frequency range of 50–150 cm^{−1}, and are assigned to be of either A_{g} or E_{g} symmetries under the C_{3i} point group (see Supplementary Note 1), which is consistent with earlier work^{34,37,38,39,40,41,42,43,44} and proves the high quality of our samples. The 2ndorder twophonon and the 3rdorder threephonon modes show up in slightly higher frequency ranges of 190–290 cm^{−1} and 310–410 cm^{−1}, respectively, and show decreasing mode intensities at higherorder processes, same as typical multiphonon overtones under harmonic approximation^{45} or cascade model^{46}. In addition to and distinct from these multiphonon features, we resolve a remarkable periodic modulation across a wide frequency range of 70–1100 cm^{−1} in the low intensity part of the Raman spectrum (highlighted by the orange shaded area in Fig. 2a). This low intensity periodic pattern consists of clean, individual Lorentzian profiles and survives up to the 8th order (Fig. 2b), well beyond the highest order (3rd order) of multiphonon overtones, and each order of it spans for ~50 cm^{−1} frequency range, much wider than the linewidth of any observed phonon modes (insets of Fig. 2a for phonons). Such a periodic pattern is also observed in the antiStoke’s side at higher temperatures in bilayer CrI_{3}, for example, up to the 2nd order at 290 K (see Supplementary Note 2), which clearly supports its Raman origin instead of luminescence.
We fit this low intensity periodic pattern using a summation of Lorentzian profiles of the form \(\mathop {\sum }\nolimits_N \frac{{A_N\left( {\frac{{{\Gamma}_N}}{2}} \right)^2}}{{\left( {\omega  \omega _N} \right)^2 + \left( {\frac{{{\Gamma}_N}}{2}} \right)^2}} + C\) with central frequency \(\omega _N\), linewidth \({\Gamma}_N\), and peak intensity \(A_N\) of the Nth period and a constant background \(C\) (see fitting procedure in “Methods”). Among all eight orders (\(N = 1,\,2,\, \ldots ,8.\)) in Fig. 2b, the presence of the 1storder broad mode is deliberately validated in Fig. 2c that fitting with this 1storder broad mode (orange shaded broad peak in the bottom panel) is visibly better than without it (top panel). This improved fitting by involving the 1storder broad mode is further rigorously confirmed by the bootstrap method^{47} (see Supplementary Note 3). Figure 2d shows a plot of the central frequency \({\upomega}_N\) as a function of the order N with data taken at 40 K (\(N = 1,\,2,\, \ldots ,\,8\)) and 290 K (\(N =  2,\,  1,\, \ldots ,\,3\)), from which a linear regression fit gives a periodicity of \(120.6 \pm 0.9\) cm^{−1} and an interception of 0 ± 0.2 cm^{−1}. To the best of our knowledge, such a periodic pattern made of individual Lorentzian profiles previously has only been seen in multiphonon Raman spectra of Cd, Yb, and Eu monochalcogenides described by configurationcoordinate model^{48,49,50,51,52,53,54,55}. However, the periodic pattern observed in bilayer CrI_{3} here differs from these monochalcogenide multiphonon modes, as the broad linewidth of 1storder mode contradicts with the sharp 1storder forbidden LO phonon in Cd and Yb monochalcogenides^{48,49,50,51} and the persistence (or even enhancement) of higherorder multiphonon below T_{C} = 45 K is in stark contrast to the disappearance of paramagnetic spin disorderinduced multiphonon below magnetic phase transitions in Eu monochalcogenides^{52,53,54,55}. Because no known multiphonon model can capture all characteristics of our observed periodic pattern as well as the broad linewidths of each mode, we are inspired to consider the electronic origin. Indeed, strikingly similar features have been seen in polaron systems through the energy dispersion curves (EDCs) of ARPES^{9,14,27,28,29,30,31,32} and linear absorption and PL spectroscopy^{5,33,56}. In those cases, the periodic patterns in their energy spectra arise from the phonondressed electronic state replicas, or sometimes also referred as phononFloquet states^{57}, and the periodicity is given by the frequency of the coupled phonon. Owing to the high resemblance between the lineshapes of our Raman spectrum and those polaron energy spectra^{5,14,27,28,29,30,31,32,56}, we propose that this periodic pattern in Raman spectra of 2D CrI_{3} stems from inelastic light scattering between the phonondressed electronic states caused by the polaronic character of B excitons in 2D CrI_{3}, whereby the B exciton at 1.96 eV, with the electron(hole) in the weakly dispersive conduction (highly dispersive valence) band of Cr 3d (I 5p) orbital character^{24,58}, couples strongly to a phonon at 120.6 cm^{−1}^{59}. It is worth noting that a recent theoretical work predicts magnetic polaronic states in 2D CrI_{3} because of chargemagnetism coupling^{60}, whereas our work suggests polaronic exciton states due to chargelattice coupling.
We then proceed to identify the source and the character of the phonon at 120.6 cm^{−1}. We first rule out the possibility of this phonon arising from either the hBN encapsulation layers or the SiO_{2}/Si substrate, as a similar periodic pattern in the Raman spectrum is also observed in bare bulk CrI_{3} crystals (see Supplementary Note 4). Compared with the calculated phonon band dispersion of monolayer CrI_{3}^{61}, we then propose the LO phonon calculated to be at ~115 cm^{−1} as a promising candidate, whose slight energy difference from the experimental value of 120.6 cm^{−1} could result from the omission of eph coupling in calculations. This LO phonon mode belongs to the parityodd E_{u} symmetry of the C_{3i} point group, and its atomic displacement field transforms like an inplane electronic field (E_{x}, E_{y}) (see inset of Fig. 2d)^{61}. Its odd parity makes it Ramaninactive and absent in the 1storder phonon spectra (Fig. 2a inset, top panel), whereas its polar displacement field allows for its strong coupling to electrons/holes and prompts the polaronic character of the chargetransfer B exciton (see Supplementary Note 5 for measurements with additional laser wavelengths). In addition, this LO phonon band is nearly dispersionless and has a large density of states, further increasing its potential for coupling with the B exciton in 2D CrI_{3}.
Temperature dependence of the polaronic effect
Given the coexistence of a 2D longrange ferromagnetic order and polaronic effect of excitons below T_{C} = 45 K in bilayer CrI_{3}, it is natural to explore the interplay between the two. For this, we have performed careful temperaturedependent Raman spectroscopy measurements and fitted the periodic pattern in every spectrum with a sum of Lorentzian profiles. Figure 3a displays the periodic pattern in Raman spectra taken at 70 K and 10 K, well above and below T_{C}, respectively. Comparing these spectra, not only do more highorder replica bands become visible at lower temperatures (i.e., from \(N = 6\) at 70 K to \(N = 8\) at 10 K), but also the spectral weight shifts toward the higherorder bands (i.e., from \(N = 1\) at 70 K for the strongest mode to between \(N =\) 3 and 4 at 10 K in Fig. 3b). The appearance of higherorder modes at lower temperatures possibly results from a combination of the narrow exciton linewidth (~50 cm^{−1}) and the dispersionless nature of coupled LO phonon. More importantly, the spectral weight distribution (A_{N} vs. N) quantifies the eph coupling strength, and its spectral shift across T_{C} confirms the interplay between the polaronic effect and the magnetic order in bilayer CrI_{3}. Theoretically, the polaron system consisting of dispersionless LO phonons and charges is one of the few exactly solvable models in manybody physics^{62}, and the calculated polaron spectra can be welldescribed by a Poisson distribution function, \(A_N = A_0\frac{{e^{  \alpha }\alpha ^N}}{{N!}}\)^{63,64}, where \(A_0\) is the peak intensity of the original electronic band, \(A_N\) is the peak intensity for the Nth replica band with \(N\) phonon(s) dressed, and \(\alpha\) is a constant related to the eph coupling in 3D (i.e., \(\alpha _{3{\mathrm{D}}}\)) that can be scaled by a factor of \(3{\uppi}/4\) for 2D (i.e., \(\alpha _{2{\mathrm{D}}}\))^{65}. By fitting the extracted Lorentzian peak intensity profile at every temperature to the Poisson distribution function (see fits of 10 K and 70 K data in Fig. 3b), we achieve a comparable fitting quality to that for ARPES EDCs in polaron systems^{9,31} at every temperature and eventually arrive at the temperature dependence of \(\alpha _{2{\mathrm{D}}}\), which remains nearly constant until the system is cooled to T_{C} and then increases by almost 50% at the lowest available temperature 10 K of our setup (Fig. 3c). In addition to the anomalous enhancement of \(\alpha _{2{\mathrm{D}}}\) across T_{C}, the value of \(\alpha _{2{\mathrm{D}}} = 1.5\) at 10 K is the highest among known 2D polaron systems including graphene/BN heterostructures (\(\alpha _{2{\mathrm{D}}} = 0.9\))^{14} and bare SrTiO_{3} surfaces (\(\alpha _{2{\mathrm{D}}} = 1.1\))^{29}.
Magnetic field dependence of the polaronic effect
It has been shown that bilayer CrI_{3} transitions from a layered AFM to FM with increasing outofplane magnetic field (\(B_ \bot\)) above the critical value B_{C} of 0.7 T^{17,21,25,26}. We then finally explore the evolution of the polaronic effect across this magnetic phase transition by performing magnetic fielddependent Raman spectroscopy measurements. Here, we choose circularly polarized light to perform magnetic fielddependent measurements in order to eliminate any Faraday effect from the optical components that are situated in close proximity to the strong magnetic field. Figure 4a shows Raman spectra taken at \(B_ \bot\) = 0 T and \(\pm{\!}\)1 T, below and above B_{C}, respectively, in both RR and LL channels, where RR(LL) stands for the polarization channel selecting the righthanded (lefthanded) circular polarization for both incident and scattered light (see Supplementary Note 6). At 0 T, the spectra are identical in the RR and LL channels, consistent with zero net magnetization in the layered AFM state for bilayer CrI_{3} at \(\left {B_ \bot } \right {\,}< {\,}B_{\mathrm{C}}\). At \(\pm{\!}\)1 T, the spectra in the RR and LL channels show opposite relative intensities under opposite magnetic field directions, owing to the fact that the net magnetization in the FM state for bilayer CrI_{3} at \(\left {B_ \bot } \right {\,}> {\,}B_{\mathrm{C}}\) breaks the equivalence between the RR and LL channels. To better quantify the magnetic field dependence of the spectra, we measured Raman spectra in the RR and LL channels at \(B_ \bot\) from \(\)1.4 T to 1.4 T every 0.1 T. We fit the spectrum at every magnetic field to extract \(A_N\) first and then \(A_0\) and \(\alpha _{2{\mathrm{D}}}\). Figure 4b shows that \(A_0\) has abrupt changes at \(B_ \bot = \pm\)0.7 T in both RR and LL channels, consistent with the first order magnetic phase transition at B_{C}. Furthermore, the magnetic field dependence of \(A_0\) shows an opposite trend in the RR channel from that in the LL channel, whereas the sum of \(A_0\) from both channels remain nearly constant to the varying magnetic field. This observation can be understood by that, under a timereversal operation, the RR channel transforms into the LL channel and the direction of the net magnetization at \(\left {B_ \bot } \right {\,}> {\,}B_{\mathrm{C}}\) flips, resulting in that the Raman spectrum in the RR channel at \(B_ \bot {\,}> {\,}0.7\) T is equivalent to the spectrum in the LL channel at \(B_ \bot {\,}< {\!}0.7\) T. Figure 4c shows that \(\alpha _{2{\mathrm{D}}}\) is magnetic field independent, suggesting that the interlayer magnetic order barely affects the eph coupling strength and that the inplane longrange magnetic order is responsible for the strong enhancement of eph coupling at T_{C}. This finding corroborates with the fact that the 120.6 cm^{−1} phonon has inplane atomic displacement.
Discussions
Our further Raman spectroscopy studies on trilayer, fourlayer, and fivelayer CrI_{3} show qualitatively same findings as those in bilayer CrI_{3} (see Supplementary Note 7) and again echoes with the inplane nature of the 120.6 cm^{−1} E_{u} phonon and the intralayer chargetransfer B exciton. Our data and analysis reveal the phonondressed electronic states and suggest the polaronic character of excitons in 2D CrI_{3}, which arises from the strong coupling between the lattice and charge degrees of freedom and is dramatically modified by the spin degree of freedom of CrI_{3}. The exceptionally high number of phonondressed electronic state replicas (up to \(N = 8\)) further suggests 2D CrI_{3} as an outstanding platform to explore nontrivial phases out of phononFloquet engineering, whereas the significant coupling to the spin degree of freedom adds an extra flavor whose impact on the phononFloquet states has not been studied. For example, one can imagine creating topological states through the band inversion between the phonondressed replicas of CrI_{3} and the electronic state of a material in close proximity.
Methods
Sample fabrication
CrI_{3} single crystals were grown by the chemical vapor transport method, as detailed in ref. ^{40}. Bilayer CrI_{3} samples were exfoliated in a nitrogenfilled glove box. Using a polymerstamping transfer technique inside the glove box, bilayer and fewlayer CrI_{3} flakes were sandwiched between two fewlayer hBN flakes and transferred onto SiO_{2}/Si substrates and sapphire substrates for Raman spectroscopy and PL/linear absorption spectroscopy measurements, respectively.
Linear absorption spectroscopy
A bilayer CrI_{3} sample on a sapphire substrate was mounted in a closedcycle cryostat for the temperaturedependent absorption spectroscopy measurements. A broadband tungsten lamp was focused onto the sample via a 50× long working distance objective. The transmitted light was collected by another objective and coupled to a spectrometer with a spectral resolution of 0.2 nm. The absorption spectra were determined by \(1  \frac{{I_{{\mathrm{sample}}}(\lambda )}}{{I_{{\mathrm{substrate}}}(\lambda )}}\), where \(I_{{\mathrm{sample}}}(\lambda )\) and \(I_{{\mathrm{substrate}}}(\lambda )\) were the transmitted intensity through the combination of sample and substrate and through the bare substrate, respectively.
PL spectroscopy
PL spectra were acquired from the same bilayer CrI_{3} sample where we carried out linear absorption measurements. The sample was excited by a linearly polarized 633 nm laser focused to a ~2 μm spot. A power of 30 μW was used, which corresponds to a similar fluence reported in the literature^{26} (10 µW over a 1 μmdiameter spot). Transmitted righthanded circularly polarized PL signal was dispersed by a 600 grooves/mm, 750 nm blaze grating, and detected by an InGaAs camera.
Raman spectroscopy
Resonant microRaman spectroscopy measurements were carried out using a 633 nm excitation laser for the data in the main text and 473 nm, 532 nm, and 785 nm excitation lasers for data in Supplementary Note 5. The incident beam was focused by a 40× objective down to ~3 μm in diameter at the sample site, and the power was kept at ~ 80 μW. The scattered light was collected by the objective in a backscattering geometry, then dispersed by a Horiba LabRAM HR Evolution Raman spectrometer, and finally detected by a thermoelectric cooled CCD camera. A closedcycle helium cryostat is interfaced with the microRaman system for the temperaturedependent measurements. All thermal cycles were performed at a base pressure lower than 7 × 10^{−7} mbar. In addition, a cryogenfree magnet is integrated with the low temperature cryostat for the magnetic fielddependent measurements. In this experiment, the magnetic field was applied along the outofplane direction and covered a range of \( 1.4\) to \(+\)1.4 Tesla. In order to avoid the Faraday rotation of linearly polarized light as it transmits through the objective under the stray magnetic field, we used circularly polarized light to perform the magnetic fielddependent Raman measurements.
Fitting procedure
For every sample, we have taken temperature and magnetic fielddependent Raman spectra on the hBN/SiO_{2}/Si substrate with the same experimental conditions as that on the CrI_{3} flakes. The Raman spectra from the substrate, an extremely gradual background with a Si phonon peak at ~525 cm^{−1}, shows no dependence on temperature (over the range of 10–70 K) and magnetic field (0–2.2 T). To fit the periodic oscillations in Raman spectra of CrI_{3} flakes, we follow the procedure described below. (I) we fit the Si phonon peak at ~525 cm^{−1} in both spectra taken on the CrI_{3} thin flake and the bare substrate to extract the Si peak intensity, \(I_{{\mathrm{Si}}}^{{\mathrm{sample}}}\) and \(I_{{\mathrm{Si}}}^{{\mathrm{substrate}}}\). (II) we multiply the background spectrum by a factor of \(\frac{{I_{{\mathrm{Si}}}^{{\mathrm{sample}}}}}{{I_{{\mathrm{Si}}}^{{\mathrm{substrate}}}}}\), which is ~1, and then subtract off the factored background from the raw Raman spectrum of sample. This process leads to the pure Raman signal for CrI_{3} whose baselines are nearly identical over the temperature range of interest (10–70 K). (III) we fit the sharp CrI_{3} phonon peaks with Lorentzian functions and subtract their fitted functions from the background free Raman spectrum from step (II). This leads to a clean spectrum with only periodic broad modes for a global fitting. (IV) we fit the clean spectrum from step (III) with a sum of multiple Lorentzian functions, \(\mathop {\sum }\nolimits_N \frac{{A_N\left( {\frac{{{\Gamma}_N}}{2}} \right)^2}}{{\left( {\omega  \omega _N} \right)^2 + \left( {\frac{{{\Gamma}_N}}{2}} \right)^2}} + C\). For the neatness of the data presentation in Figs. 2 and 3, we only show the fitted line from step IV in the plots.
Data availability
The data sets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
We thank X. Xu, M. Kira, R. Merlin, X. Qian, and H. Wang for useful discussions. L. Zhao acknowledges support by NSF CAREER grant no. DMR1749774. R. He acknowledges support by NSF CAREER grant no. DMR1760668 and NSF MRI grant no. DMR1337207. K. Sun acknowledges support through NSF grant no. NSFEFMA1741618. A. W. Tsen acknowledges support from the US Army Research Office (W911NF1910267), Ontario Early Researcher Award (ER1713199), and the National Science and Engineering Research Council of Canada (RGPIN201703815). This research was undertaken, thanks in part to funding from the Canada First Research Excellence Fund. H. Lei acknowledges support by the National Key R&D Program of China (grant no. 2016YFA0300504), the National Natural Science Foundation of China (no. 11574394, 11774423, and 11822412), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (15XNLQ07, 18XNLG14, and 19XNLG17). H. Deng and J. Horng acknowledge support by the Army Research Office under Awards W911NF1710312.
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W.J., R.H., and L.Z. conceived this project and designed the experiment; S.T., Y.F., and H.L. synthesized and characterized the bulk CrI_{3} single crystals; H.H.K., B.Y., F.Y., and A.W.T. fabricated and characterized the fewlayer samples; Z.Y., G.Y., and L.R. performed the Raman measurements under the guidance of R.H. and L.Z.; J.H., W.J., and H.D. performed the linear absorption and PL spectroscopy measurements; W.J., X.L., R.H., and L.Z. analyzed the data with discussions with K.S.; G.X. provided statistical modeling in data analysis; W.J., X.L., R.H., and L.Z. wrote the paper and all authors participated in the discussions of the results.
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Jin, W., Kim, H.H., Ye, Z. et al. Observation of the polaronic character of excitons in a twodimensional semiconducting magnet CrI_{3}. Nat Commun 11, 4780 (2020). https://doi.org/10.1038/s4146702018627x
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DOI: https://doi.org/10.1038/s4146702018627x
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