Selective enhancement of optical nonlinearity in two-dimensional organic-inorganic lead iodide perovskites

Reducing the dimensionality of three-dimensional hybrid metal halide perovskites can improve their optoelectronic properties. Here, we show that the third-order optical nonlinearity, n 2, of hybrid lead iodide perovskites is enhanced in the two-dimensional Ruddlesden-Popper series, (CH3(CH2)3NH3)2(CH3NH3)n-1PbnI3n+1 (n = 1–4), where the layer number (n) is engineered for bandgap tuning from E g = 1.60 eV (n = ∞; bulk) to 2.40 eV (n = 1). Despite the unfavorable relation, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n_2} \propto E_{\rm{g}}^{ - 4}$$\end{document}n2∝Eg-4, strong quantum confinement causes these two-dimensional perovskites to exhibit four times stronger third harmonic generation at mid-infrared when compared with the three-dimensional counterpart, (CH3NH3)PbI3. Surprisingly, however, the impact of dimensional reduction on two-photon absorption, which is the Kramers-Kronig conjugate of n 2, is rather insignificant as demonstrated by broadband two-photon spectroscopy. The concomitant increase of bandgap and optical nonlinearity is truly remarkable in these novel perovskites, where the former increases the laser-induced damage threshold for high-power nonlinear optical applications.


Supplementary Note 1: Bandgap estimation of (BA)2(MA)n-1PbnI3n+1 (n = 1-)
In our previous study 1 , bandgaps of the title perovskites were roughly determined by extrapolating their absorption edges to the energy axis, yielding 1.50 eV (n = ), 1.91 eV (n = 4), 2.03 eV (n = 3), 2.17 eV (n = 2), and 2.43 eV (n = 1), respectively, at room temperature. However, the presence of excitonic absorption slightly below the fundamental band edge caused some uncertainty in the bandgap estimation of each compound. This effect could be less clear for the bulk perovskite (n = ) because the exciton line is not well resolved from the band edge; while the stability of excitons at room temperature is still under debate [2][3][4] , the optical response of MAPbI3 is excitonic. To evaluate the accurate dependence of (3) on the bandgap, g , in this work we estimated g of our perovskites by eliminating the excitonic contribution that can be modelled with a Gaussian peak. The spectral location of the exciton peak was determined to match with the low-energy onset of the absorption edge while consistently keeping the width of the exciton peak ~52 meV for all the 2D perovskites and ~43 meV for MAPbI3. These peaks are shown in Supplementary Figs. 1a-1e as black curves for n = , n = 4, n = 3, n = 2, and n = 1, respectively, overlaid with the experimental absorption spectra (coloured traces).
Since the perovskites are direct-gap semiconductors 1 , we plot ( ) 2 2 as a function of photon energy, , in Supplementary Fig. 2a where ( ) is obtained by subtracting the exciton peak from the experimental absorption data of Supplementary Figs. 1a-1e. Note that the exciton peak is therefore absent, allowing us to unambiguously determine g , which are 1.60 eV (n = ), 1.89 eV (n = 4), 2.00 eV (n = 3), 2.14 eV (n = 2), and 2.40 eV (n = 1), respectively. For comparison, we also plot ( ) 2 2 for the bulk perovskite without spectral filtering (dashed trace), which indeed better reveals the presence of the exciton peak; therefore, we believe that it is reasonable to 2 assume a finite exciton binding energy for n = . The exciton binding energy, ex , for each perovskite was also determined ( Supplementary Fig. 2b). We note that the measured ex = 405 meV for n =  is indeed reasonable consistent with not only the measured values by optical absorption 4 but also a precision measurement based on magnetoabsorption 5 . Both spectroscopic methods are not directly affected by the choice of the dielectric constant between 0 and ∞ . Most of all, we confirmed that this issue of exciton binding energy 4 minimally affects the bandgap dependence of the third-order nonlinearity of the bulk perovskite (n = ); both 2 vs. g and vs. g plots for n =  in the main text are well explained by the two-band model even with ex = 0. As expected, ex increases as the thickness of the perovskite layer reduces due to enhanced quantum confinement. As discussed in the main text and below, this exciton level can be directly excited by resonant two-photon absorption (2PA) in the 2D perovskites (n = 1-4). This resonant 2PA cannot be explained by a conventional two-band model if the band dispersion parameter, = / g , is defined using the fundamental bandgap, g : Excitonic 2PA occurs for slightly below 0.5 due to a finite exciton binding energy, but is only defined for 0.5 < < 1 for typical bandto-band transition 6 .

Supplementary Note 2: Crystal symmetry of (BA)2(MA)n-1PbnI3n+1 (n = 1-4)
If crystallographic restrictions that demand an inversion centre are set aside, we can see that the layers with an even number of n are polar when viewed individually. This is illustrated by the shape of perovskite cavities which undergo a combination of in-phase and out-of-phase distortion. These distortions force the cavities to adopt either a distorted rhombus or regular square shape when viewed along the crystallographic axis ( Fig. 1b in the main text). This representation is a good intuitive measure of the polarity in the 2D perovskites and indicates that polarization is cancelled out along the plane (equal number of squares and rhombi). However, along the axis, polarization is nonzero (different number of squares and rhombi). Thus, overall polarization can be cancelled only if each layer completely cancels with its neighboring layer that exactly coincides with the crystallographic description; the layers are related through glide planes. This picture suggests that even the presence of minor defects, such as the ones listed below, may break the inversion symmetry, leading to a local polarization.
In fact, we have previously reported that the present set of compounds can crystallize in the corresponding polar space groups 1 although a margin of ambiguity of this assignment still remains. Structural defects arising from the flexible nature of the nanoscopically thin perovskite layers can thermally activate dynamic disorder of the perovskite lattice and most importantly twinning, a hallmark property of the perovskite crystal structure, which may easily smear out any long-range polarization effect. In light of the results presented here, however, we will follow the centrosymmetric assignment since it better justifies the experimental data as confirmed by very weak second harmonic radiation, i.e., (2) = 0. The notation in the main text is given in nonstandard crystallographic space groups so that the lattice parameters follow the < < sequence for all the compounds. The polar vs. nonpolar assignment of the crystal structure of the halide perovskites, in general, is still under serious debate and the assignment given in the main text is not necessarily a conclusive one. Our experiments were performed in the ambient condition on densely packed powders of size, = 90-125 μm, which is much larger than the optical wavelengths associated with input as well as third harmonic generation (THG) and/or photoluminescence (PL) from the sample. In this case, Mie scattering is dominant and the maximum scattering direction is highly oriented along 7 the input-beam direction 9 . In order to minimize this scattering effect, we therefore employed reflection geometry in which the mean free path for backward scattering is comparable to the powder particle size 9 ; this essentially corresponds to a single scattering event of the incident beam by only one layer of powders and multiple scattering is only significant along the forward direction.
Since our size of a capillary tube containing powders is also much larger than the particle size, the PL and THG are only generated from the front surface of the tube, which can be effectively captured under our reflection geometry. This condition ensures minimal effects by scattering on the estimation of NLO coefficients of our samples. As a clear evidence, we found that the measured 2PA coefficient, , of the reference powder is consistent with that determined from a bulk single crystal within a factor of two as described in the main text. We also confirmed that the measured optical signals from the sample powder are fairly consistent when the illumination spot was scanned over the various portions of the capillary tube.
We emphasis that our powder method yields more reliable NLO coefficients, compared with a typical Z-scan method using polycrystalline thin films. While thin-film measurement may reduce minor scattering effects, it can lead to an inaccurate estimation of optical nonlinearity because of submicron-size grains typically present in perovskite films. It is well known that such fine grains in a thin film causes significant enhancement in the nonlinear optical response due to extra charges accumulated on the grain boundaries 10 . For example, recent experiments using thin perovskite films also yielded very large optical nonlinearity [11][12][13] , which is far beyond the theoretical prediction of the two-band model 6 . Although such a large effect is desirable for actual NLO applications, it is clearly not the intrinsic property of the perovskites.  Fig. 1). is also slightly adjusted to fit the overall wavelength dependence. We found that the experimental 2PA dispersion is better explained when using the optical gap for the 2D perovskites with = 3500-4000see also Fig. 4c in the main text. 2PA of defect-induced transition for n = 3 and n = 4 is evident even with > 1400 nm up to 1700 nm.