Organic and inorganic sublattice coupling in two-dimensional lead halide perovskites

Two-dimensional layered organic-inorganic halide perovskites have successfully spread to diverse optoelectronic applications. Nevertheless, there remain gaps in our understanding of the interactions between organic and inorganic sublattices that form the foundation of their remarkable properties. Here, we examine these interactions using pump-probe spectroscopy and ab initio molecular dynamics simulations. Unlike off-resonant pumping, resonant excitation of the organic sublattice alters both the electronic and lattice degrees of freedom within the inorganic sublattice, indicating the existence of electronic coupling. Theoretical simulations verify that the reduced bandgap is likely due to the enhanced distortion index of the inorganic octahedra. Further evidence of the mechanical coupling between these two sublattices is revealed through the slow heat transfer process, where the resultant lattice tensile strain launches coherent longitudinal acoustic phonons. Our findings explicate the intimate electronic and mechanical couplings between the organic and inorganic sublattices, crucial for tailoring the optoelectronic properties of two-dimensional halide perovskites.

As reported in previous works 1,2 , the low-frequency phonon modes (< ~150 cm -1 ) are dominated by the vibrational motion of the PbI6 octahedra with mode located at ~135 cm -1 exhibiting mixed contributions from PEA cations and PbI6 octahedra whereas the high-frequency phonon modes (> 200 cm -1 ) are governed by the vibrational motion of PEA cations.The vibrational coupling between these two sublattices is thus relatively weak.
Note that in Supplementary Fig. 5a, the phonon down-conversion process involves two successive processes: intramolecular energy redistribution within the PEA cation followed by the heat transfer from organic PEA cation to inorganic PbI6 octahedra through anharmonic coupling. 3,4For the former, it involves sequential energy down-conversion through all the intermediate phonon modes starting from the excited high-energy phonon mode (i.e., N-H stretching motion) to the lowest-lying phonon modes.The duration of this process is in general longer than the lifetime of activated phonon modes.
For the latter, it involves the heat transfer from the phonon modes of organic cation to those of inorganic octahedra which is governed by the overlapping vibrational density of states and the coupling between the organic and inorganic sublattices. 3,5Nevertheless, the large mass difference which results in a large energy difference of the phonon modes as well as their relatively weak coupling though hydrogen bonding and electrostatic interaction between these two sublattice lead to a significant weak mechanical coupling, thereby slow heat transfer.This inefficient mechanical coupling results in slow heat transfer which is evident from the increase of duration time of regime ③ with pump fluence.Supplementary Fig. 9 shows a comparison of the distinct TA spectra generated by resonant pump of PEA cations using a MIR laser pulse versus that by off-resonant pump using an IR laser pulse at 1.5 µm.Apart from the same COPs-induced oscillation component, the former features a positive Δ (peak P1) due to reduction of exciton energy and is followed by a negative Δ at longer times because of the increase of exciton energy arising from thermal lattice expansion.Conversely, the latter is characterized by a negative Δ due to band-filling of the ground-state absorption owing to multiphoton absorption.The temperature dependence of the bandgap under quasi-harmonic approximation consists of contributions from thermal expansion and electron-phonon interactions: 6 where  , ⃗ is the number of phonons at  branch with wave vector  ,  is the volume.Normally,  g  is determined by the bonding feature of the atomic orbitals and is thus a constant that is weakly dependent on temperature in a single phase.The second term of Eq. (1) refers to the phonon contribution that varies with temperature because of the different phonon occupation number.By assuming that the lattice constant shows a linear temperature dependence, Eq. ( 1) is usually simplified as: 7  g () =  g (0 where  refers to the  th phonon contribution with occupation number   and contribution factor   . We first determine the (PEA)2PbI4 film's optical bandgap (free exciton) which is the low-energy peak position in the absorption spectrum.This peak position corresponds to the crossing point in the / spectrum, as shown in Supplementary Fig. 16b.The extracted optical bandgap as a function of temperature is displayed in Supplementary Fig. 16c.The optical bandgap exhibits a linear dependence on the temperature, indicating that the electron-phonon coupling only plays a negligible role.Linear fitting of the optical bandgap with temperature yields the value of  = 0.17 meV/K.
where  1 and  2 are prefactors,  BG =  0 −log(1 −  4 ), where  is a constant and  is a constant of proportionality.

Supplementary
Fig. 5| Observation of slow phonon-down conversion.a Raman spectrum of (PEA)2PbI4 at 77 K. Inset shows a zoom-in of the Raman spectrum that is dominated by the vibrational motion of PEA cation.b Fluence-dependent TA kinetics of (PEA)2PbI4 films monitored at P1 with pump at 3.3µm.c Duration of regime ③ as a function of pump fluence (scatters) and the corresponding curve-fit (red curve) using  =  0 +  exp (−   0), where ,  0 and  0 are constants.
Supplementary Fig. 6| TA kinetics in the first ~15 ps. a Fluence-dependent TA kinetics in the first ~15 ps of (PEA)2PbI4 films monitored at P1 with pump at 3.3µm.b Normalized fluence-dependent TA kinetics monitored at P1. Supplementary Fig. 7| TA kinetics and curve fittings.TA kinetics (black curve), the curve-fit (red curve) and the fitting residual (blue curve) monitored at P1 of (PEA)2PbI4 films pumped with a MIR laser pulse of 3.3 µm with a fluence of 2 mJ cm -2 at 77 K. Supplementary Fig. 9| TA features for resonant and off-resonant excitations.comparison of 2D contourplot of TA spectrum, representative TA spectrum at different delay times and TA kinetics monitored at P1 of (PEA)2PbI4 films obtained with resonant pump using a MIR laser pulse at 3.3 µm (a, b, and c) and with offresonant pump using an IR laser pulse at 1.5 µm (d, e, and f).Note that a, b and c are replots of Figure 1 of the main text.

Supplementary
Fig. 16| Temperature-dependent optical bandgap.a Temperature-dependent linear absorption spectrum of (PEA)2PbI4 films.b / as a function of wavelength for (PEA)2PbI4 films at 77 K.The crossing point indicated by the arrow corresponds to the optical bandgap.c Extracted optical bandgap (filled scatters) as a function of temperature and the linear fit (red line).