Coherent Phonon‐Induced Modulation of Charge Transfer in 2D Hybrid Perovskites

Electron–phonon interactions play an essential role in charge transport and transfer processes in semiconductors. For most structures, tailoring electron–phonon interactions for specific functionality remains elusive. Here, it is shown that, in hybrid perovskites, coherent phonon modes can be used to manipulate charge transfer. In the 2D double perovskite, (AE2T)2AgBiI8 (AE2T: 5,5“‐diylbis(amino‐ethyl)‐(2,2”‐(2)thiophene)), the valence band maximum derived from the [Ag0.5Bi0.5I4]2– framework lies in close proximity to the AE2T‐derived HOMO level, thereby forming a type‐II heterostructure. During transient absorption spectroscopy, pulsed excitation creates sustained coherent phonon modes, which periodically modulate the associated electronic levels. Thus, the energy offset at the organic–inorganic interface also oscillates periodically, providing a unique opportunity for modulation of interfacial charge transfer. Density‐functional theory corroborates the mechanism and identifies specific phonon modes as likely drivers of the coherent charge transfer. These observations are a striking example of how electron–phonon interactions can be used to manipulate fundamentally important charge and energy transfer processes in hybrid perovskites.

electronic states form bands that delocalize electrons, holes, and excitons across a significant spatial range. [1] As a result, these excitations experience band-like transport in which quasiparticles flow from high to low potential. On the other hand, in the weak-coupling limit, quasiparticles are localized in individual molecules or domains. They can still move to another domain or molecule if a neighboring domain with lower energy exists, but this transfer happens via a hoppinglike, i.e., random walk mechanism. [1] While the transport characteristics of most artificial optoelectronic systems are categorized into one of these two regimes, there exists a third regime that has gained significant attention over the past decades. In this intermediate regime, electronic states in neighboring sites are coupled with intermediate strength, enabling coherent wave-like motion of charges and excitons between several domains or molecules. [2][3][4] In its simplest picture, an optical excitation creates a superposition of two coupled states, which leads to a spatial oscillation of the carrier population from one molecule to the other. As long as the phase relationship in the superposed states is preserved, the coherent motion will spatially modulate exciton or charge populations in the complex structure. [5] This type of transport is rarely observed because coherences are difficult to sustain for longer periods at high temperatures. [2,6,7]

Introduction
Optoelectronic and electronic devices rely on manipulating charges and energy. Depending on the electronic coupling between the molecules or smallest structural units, the transport and transfer of these excitations across a semiconductor can follow two different mechanisms: band-like and hoppinglike. In the limit of strong coupling of molecular orbitals, In semiconductors, vibrational excitations can also exhibit coherent behavior. These vibrational coherences can be initiated when a short pulse with a large spectral bandwidth excites the material (see Supporting Information Section S1.1). [8][9][10][11][12] The resulting vibrational coherences lead to periodic lattice fluctuations (e.g., due to expansion and contraction of specific interatomic distances in the photoexcited region). In transient absorption spectroscopy, these coherent lattice dynamics lead to periodic modulations in the amplitude and energy of the electronic transitions. [9,13] Under rare conditions vibrational coherences can be related to the charge transport and transfer kinetics. [14] However, in most condensed matter, phonon modes are delocalized across a spatial extent much larger than the electronic delocalization, and modulating charge and energy transport using phonons proves to be a significant challenge. [15,16] Artificial systems can enable such transport provided that two critical challenges can be overcome: 1) The material system should exhibit persistent phonon coherences, and, 2) the energy landscape for carriers should be tailored so that the energy levels of the donor and acceptor domains can be tuned in and out of resonance via phonon modes.
Hybrid perovskite materials combine organic and inorganic units into the same crystalline structure wherein the optical and electronic properties of the two components can be tailored with additional flexibility compared to all-organic or all-inorganic semiconductors. Here, we show that the energy level oscillations due to vibrational wave packet dynamics can periodically tune electronic donor state into resonance with an acceptor state and lead to modulations in local charge populations across a donor/acceptor interface. [17,18] Figure 1 shows the structural, electronic, and optical properties of the crystalline hybrid perovskite with the generalized chemical formula (AE2T) 2 AgBiI 8 , where AE2T 2+ represents the divalent organic cation (diprotonated 5,5′-diylbis(aminoethyl)- [2,2′-bithiophene]) and [Ag 0.5 Bi 0.5 I 4 ] 2− represents the corresponding inorganic stoichiometric unit. Figure 1a shows the computationally optimized atomic structure of the (AE2T) 2 AgBiI 8 compound as obtained in this work. All density functional theory (DFT) calculations were performed using the FHI-aims code [19][20][21][22] with technical details provided in the Supporting Information (Section S2). The structure shown in Figure 1a is derived from the (AE2T) 2 AgBiI 8 structure, which was published earlier based on single-crystal X-ray diffraction and the same DFT approach as in the present work. [23] Specifically, the Perdew-Burke-Ernzerhof (PBE) [24] density functional and the Tkatchenko-Scheffler (TS) dispersion correction [25] were used and validated for hybrid perovskite structure optimization in several previous works by our group. [17,18,[26][27][28][29] In the present work (Supporting Information Section S2.1), we further analyzed the DFT-PBE+TS optimized structure of ref. [23] (Figure S14a, Supporting Information) as a preparatory step for phonon calculations. Interestingly, this process led to a lower energy structure than the computational/XRD structure in ref. [23], with Ag atoms displaced from the center of the AgI 6 octahedra ( Figure S14b, Supporting Information), revealing that the structure with roughly centered Ag positions (Figure S14a, Supporting Information) is likely a metastable structure. A subsequent more detailed structure search identified a new Adv. Funct. Mater. 2023, 33, 2213021 Figure 1. a) Atomic structure of the hybrid perovskite (AE2T) 2 AgBiI 8 , fully relaxed using DFT-PBE+TS until the maximum energy gradient as a function of atomic positions and lattice vectors is 0.003 eV Å −1 . The initial (AE2T) 2 AgBiI 8 atomic structure is taken from Ref [23] . b) UV-vis absorption measurement results for (AE2T) 2 AgBiI 8 . The inset of (b) highlights the 2 eV bandgap of the material. c) DFT-HSE06+SOC energy band structure of (AE2T) 2 AgBiI 8 . d) Organic and inorganic frontier energy level alignments in (AE2T) 2 Figure 1a and also in Figure S14c (Supporting Information), the energy of which is lower by 0.28 eV per 312-atom supercell than the energy of the structure of Ref. [23] (Figure S14a, Supporting Information). This lowest-energy structure is used as the static (AE2T) 2 AgBiI 8 structure throughout this work. The rationale for this structure choice is that the actual atomic structure observed in XRD is expected to be a static average of a disordered structure with short-range order similar to Figure 1a. For example, a similar displacement of Ag + cation is observed in the bromide-based silver bismuth double perovskite BA 4 AgBiBr 8 (BA = butylammonium). [30,31] The electronic structure of the static (AE2T) 2 AgBiI 8 structure in Figure 1a was calculated by hybrid density functional theory, DFT-HSE06 [32][33][34] with an exchange mixing parameter of 0.25 and a screening parameter of 0.11 (Bohr radius) −1 , including second-variational spin-orbit coupling (SOC), [22] and is shown in Figure 1c. The valence band maximum (VBM) is set to be the energy zero for all band structures and densities of states (DOSs) shown in this paper. The band structure is color mapped according to the inorganic species' fractional contribution (determined by a Mulliken decomposition) to the corresponding states. The projected DOS as shown in Figure S19b (Supporting Information), indicates that the VBM frontier orbitals are derived from the organic component while the conduction band minimum (CBM) is mainly formed by the inorganic component (p orbitals of Bi and I). We finally plot the separate frontier orbital energies of the organic and inorganic components in Figure 1d, showing that (AE2T) 2 AgBiI 8 is a type IIb [26] heterostructure with an indirect band gap of 2.02 eV. The predicted gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for the organic component on its own is ≈3.23 eV. The inorganic VBM is found to be only 0.24 eV below the overall (organicderived) VBM. The bandgap between the overall VBM and CBM can be seen to be ≈2 eV, in agreement with both of our band structure calculations, absorption spectra (see Figure 1b), and with the previously reported value, 2.00(2) eV [23] .

Results and Discussion
In order to study the charge transfer kinetics expected from the type II band alignment, [23] we performed transient absorption spectroscopy (TAS) measurements. Figure S6a (Supporting Information) shows the evolution of the transient transmission spectra of (AE2T) 2 AgBiI 8 for the probe energy range of 1.6-2.6 eV and delay time range of 0-6 ps. The sample was excited using an 80-fs pulsed laser with 3.1 eV photon energy. An oscillatory beating signal can be seen on top of non-oscillatory dynamics. At this excitation energy, only the inorganic component of (AE2T) 2 AgBiI 8 is excited, as the optical gap of the AE2T component (i.e., LUMO-HOMO difference) is higher than 3.1 eV (see Figure 1b and neat organic absorption spectrum in ref. [17]). Figure 2a shows the contour plot of the oscillatory component (after the non-oscillatory background of carrier dynamics in Figure S6a, Supporting Information, is removed) of TAS data to highlight the observed beatings after photo-excitation (see Supporting Information Section S1.4 for details). The central hypothesis of this study is that the vibrational coherences created by the pulsed laser excitations periodically modulate the energy level alignment between the valence band of the inorganic and HOMO of the organic components, causing photo-excited holes initially excited in the inorganic perovskite to oscillate between the two components of the material. In other words, coherent phonons periodically   modulate the hole transfer process across the organic-inorganic interface. We show below that alternative explanations, such as pure transition dipole oscillator strength changes due to periodic compression and expansion of the material, cannot explain our observations when discussing the oscillations related to the organic component's signal.
In Figure 2b, we plot transient absorption spectra at time delays corresponding to the nodes and anti-nodes of the oscillations observed in Figure S6a (Supporting Information). These time delays are specifically chosen to highlight the oscillations of both the intensity and spectral positions of transient signals.
A positive photo-bleaching (PB) signal ≈2.20 eV corresponds to the photobleaching from the VBM to the CBM of the inorganic framework. The photoinduced absorption (PIA) feature at 2.5 eV (labeled as "PIA i ") is attributed to the excited state absorption also within the inorganic framework (mostly dominated by Bi-p, I-p to Bi-p, I-p, and Ag-d transitions of electron, see Figures S19, Supporting Information [18] ). We assign the second PIA feature ≈1.9 eV (labeled as "PIA o ") to the optical excited state absorption of the hole polarons in the organic framework (see Supplementary Section S1.2 for the details of these assignments). Observed PB and PIA features all exhibit periodic beating patterns that last for ≈2 ps after the pulsed excitation (see Figure S6a, Supporting Information).
These spectral features overlap with each other, requiring detailed analysis of the data. Both amplitude and frequency modulations (AM and FM) of the dynamic spectra can cause intensity oscillations in TAS. [9,13] To analyze these dynamics, we deconvolved the overlapping TAS spectral features by fitting the data with multiple Gaussian distribution functions (to model broadened optical transitions) and quantitatively analyzed the beating patterns and related electronic behavior of these resulting best-fit parameters (see Supporting Information Section S1.3 for details of this analysis). This also allows us to de-convolve the AM and FM contributions to the oscillations as peak intensity (see Figure 2c) and peak position (see Figure 2d) oscillations of Gaussian lines, respectively. It is apparent from Figure 2c that there are phase variations of the PIA i , PB, and PIA o intensity oscillations (see red dashed line as a guide). It is also interesting that the peak positions of the PIA i and PB features are also oscillating with time; however, the spectral position of PIA o is steady (Figure 2d). In fact, it was not possible to obtain a fit in which PIA o oscillates, even when the other peaks are forced to be steady, while it was possible to obtain an acceptable global fit when we completely fixed the peak position of PIA o at ≈2.06 eV. This indicates that, while the coherent phonon mode modulates the energy levels of the inorganic framework, it has only a minimal effect on the organic counterpart. This is also in-line with the fact that coherent phonons originate from the inorganic component of the hybrid material.
As discussed above, both AM and FM could cause oscillations in the transient intensity in 1D TAS experiment. [9,13] AM could arise from the oscillating transition dipole moment (TDM) due to the dynamic non-Condon effects. [13,35] In contrast, FM would result from the oscillating energy levels due to the Fröhlich interaction of longitudinal optical phonons and deformation potential interaction of longitudinal acoustic phonons with charge carriers. [36][37][38][39][40][41] In simpler terms, the oscillating lattice deformations associated with the phonons modulate the energy of carriers in the lattice. In hybrid materials, this causes the energy levels at the interface of the organic and inorganic to shift periodically relative to one another, which can cause the carrier population to oscillate between the organic and inorganic components. This oscillatory carrier population will also contribute to the AM of the transient absorption intensity signal due to the oscillatory changes in the occupied density of states.
Given the considerations above, we analyze the AM component of the TAS signal in detail. Since the energy level difference between the organic LUMO and inorganic CBM levels is large (>1 eV, see Figure 1d), the energy level oscillations cannot cause electron populations to oscillate between the organic and inorganic layers. Hence, it is safe to assume that AM of the PIA i is purely due to TDM modulation. On the other hand, because the HOMO level of the organic component and VBM level of the inorganic component are energetically close to one another (see Figure 1d), the AM of the PIA o could be due to both TDM modulation and the hole population alternating between the organic and inorganic. Our analysis below shows that the AM oscillations in PIA o show the behavior expected for the hole population modulation but not for the TDM.
We first modeled the oscillations in the amplitudes of the PIA features of (AE2T) 2 AgBiI 8 samples using a damped sinusoidal function and the non-oscillatory background: Here, S represents the PIA intensity traces, and the first term on the right-hand side of the equation "N non-osc ", is the monotonic decay component of the measured signal (see Supporting Information Section S1.4). The second term corresponds to the oscillatory component where ω is the angular frequency, ϕ is the initial phase and τ is the damping time of the oscillations. In our analysis, we first determined the frequency of oscillation in all features using a fast Fourier transform (FFT) (see Figure S12, Supporting Information). All of the features have beating frequencies centered at ≈111-117 cm −1 , suggesting that there is a common phonon mode modulating the amplitudes in these transitions.
It is important to note that, if there is a hole transfer manipulation as we suggest, the amplitude oscillations of the transitions that involve inorganic VBM and organic HOMO levels should be coupled. In other words, when the hole population oscillates between inorganic and organic, both the organicrelated PIA o and inorganic-related PB will be modulated at the same time. In addition to this, PB amplitude will also be modulated due to TDM oscillations. As discussed above, the PIA i feature is a transition in the conduction band manifold of the inorganic; it is solely due to TDM changes and hole transfer between the organic and inorganic will not impact it.
As a result, we should be able to reconstruct the amplitude oscillations in the PB from population oscillations obtained from PIA o and TDM oscillations obtained from PIA i features.
In order to test these arguments, we fit the oscillations using Equation 1 (see Table 1; Sec. S1.4, Table S1 and Figure S13, Supporting Information). Table 1 summarizes the parameters  obtained for an oscillatory component of the fit and Table S1 www.afm-journal.de www.advancedsciencenews.com 2213021 (5 of 12) © 2023 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH (Supporting Information) shows details for the non-oscillatory component. Full details of these analyses are discussed in Supplementary Section S1.4. In order to obtain these fits, we first used Equation (1) to determine the best-fit parameters (initial phase ϕ, dephasing time constant τ, and the amplitudes A osc ) for both of the PIA i and PIA o features (see Table 1 for parameters and Figure S13a,b, Supporting Information, for fits).
Using these values, we modeled the PB as a linear superposition of the PIA i and PIA o signals ( Figure S13c, Supporting Information). Figure S13d (Supporting Information) shows the final fit results using both oscillatory and non-oscillatory components. Remarkably, the superposition accurately fits the PB oscillations only when the contribution of the PIA o feature is phase-shifted by 0.81п (see Table 1, highlighted in bold). This phase difference is very close to п and consistent with the fact that the hole population oscillates between the organic and inorganic moieties (i.e., when the hole population on the organic moiety increases, the hole population on the inorganic moiety decreases).
In past work it was shown that the HOMO-LUMO gap of the organic component decreases with an increasing number of thiophene rings n for (AEnT)PbX 4 [17] (where n stands for the number of thiophene rings and X stands for halide component). This reduction in gap provides an interesting opportunity to study the charge sloshing dynamics when the energy difference between organic HOMO and inorganic VBM is altered. To explore this idea, we performed similar measurements on (AE3T) 2 AgBiI 8 and (AE4T) 2 AgBiI 8 films as well. A comparison of absorption spectra of these samples in Figure S5 (Supporting Information) shows that the lower energy regions of the spectra and band gap remain similar in all three samples, whereas the higher energy spectral features exhibit significant variations and can be attributed to the organic HOMO-LUMO gap change. [17] Thus, the offset between organic HOMO and inorganic VBM is also expected to change between these samples, and charge transfer oscillation might cease to exist if the proximity is lifted. Details of the material processing and XRD characterization of these samples can be found in the Experimental Section and Supporting Information Section S3.
TAS measurements for (AE3T) 2 AgBiI 8 and (AE4T) 2 AgBiI 8 samples are shown in Figure S6 Figure S6,Supporting Information). See Supporting Information Section S1.2 for details of the assignments. The dynamics of the assigned features are summarized in Figure 3. Features are deconvolved using multiple Gaussian lines as described above (also described in Supporting Information Section S1.3). Figure 3a,c shows the de-convolved dynamics of the organic PIA o and inorganic PB features, respectively, for all three samples. Coherent phonons lead to oscillations in the PB (Figure 3a) and PIA i (all green plots in Figure S10, Supporting Information) peak amplitudes for all three compounds for ≈2 ps. Background subtracted oscillatory components of PB and PIA o signals are shown in Figure S10g,h (Supporting Information), respectively. FFT of these oscillatory components of PB and PIA o are shown in Figure 3b,d, respectively (see Supporting Information Section S1.4 for details of non-oscillatory dynamics removal). For (AE3T) 2 AgBiI 8 and (AE4T) 2 AgBiI 8 , the energy of oscillations is red-shifted and has higher intensity compared to (AE2T) 2 AgBiI 8 (see Figure 3a,b). In contrast, the intensity of the oscillations of PIA o in (AE3T) 2 AgBiI 8 is reduced, and in (AE4T) 2 AgBiI 8 , the oscillations cease to exist completely (see Figure 3c,d). In the (AE4T) 2 AgBiI 8 sample, the organic HOMO and inorganic VBM are presumably further removed from one another than in (AE3T) 2 AgBiI 8 and (AE2T) 2 AgBiI 8 , in analogy to the Pb-based compounds (AEnT)PbI 4 , for which the band offsets were analyzed in detail in Figure S1 of Ref. [17]. We therefore attribute the absence of the oscillatory feature in PIA o of (AE4T) 2 AgBiI 8 to a presumed larger inorganic VBM/organic HOMO offset and, thus, to the absence of the periodically modulated charge transfer in the AE4T-based compound. Figure S10b,d,f (Supporting Information) shows the dynamics of spectral peak positions of the (AE2T) 2 AgBiI 8 , (AE3T) 2 AgBiI 8 , and (AE4T) 2 AgBiI 8 , respectively. For all compounds, the peak positions for the presumed inorganic-derived PB oscillate (blue plots in Figure S10b,d,f, Supporting Information) while the organic-derived PIA o feature retains a constant peak energy (magenta and orange plots in Figure S10b,d,f, Supporting Information), similar to the (AE2T) 2 AgBiI 8 compound.
Given the periodically modulated charge transfer observed in TAS, a key question that arises is: Can we identify the phonon mode or phonon modes that are responsible for the observed charge transfer? To answer this question, we pursued DFT calculations of phonons, an analysis of electron-phonon coupling based on changes of electronic eigenstates in Kohn-Sham DFT, and Raman intensity calculations. [42] The answer is complicated by the fact that a structure of the size of (AE2T) 2 AgBiI 8 has an abundance of phonon modes in the relevant frequency range. Additionally, the oscillations in question involve electronically excited states (i.e., carrier populations). However, a phonon mode that is as pronounced as that seen in TAS might be robust enough to emerge, at least qualitatively, also in (electronic) ground-state phonon calculations. Phonon modes were therefore calculated at the level of DFT-PBE+TS for the lowest-energy structure of Figure 1a, since this structure is expected to reflect most closely the instantaneous atomic positions of (AE2T) 2  Specifically, we focus on identifying phonon modes that have a similar energy to the experimentally extracted phonon energy (≈115 cm −1 ) and study their impact on the energy offset between the inorganic VBM and the organic HOMO. Because the intensity of the change in the transmission is proportional to the Raman tensor (regardless of the mechanism), only the Raman active modes can be detected with TAS measurements. [10,43,44] Thus, we further filtered out phonon modes by calculating their Raman intensity (see below). We hypothesize that a particular phonon mode exists that i) modulates the inorganic-organic VBM-HOMO offset, ii) does not modulate the peak position of the PIA o feature (Figure 2d), and iii) is Raman active.
To obtain the phonon vibration modes, we performed phonon calculations of (AE2T) 2 AgBiI 8 using the finite displacement method (FDM). [45] We used the "2×(2×2)" supercell model (see Ref. [46] for the notation) of the structure shown in Figure 1a, which contains 312 atoms and is thus rather computationally demanding. The full phonon density of states (DOS) is shown in Figure S15 (Supporting Information) and the associated phonon band structure is shown in Figure S16 (Supporting Information). Interestingly, this phonon DOS still shows some imaginary frequency modes, concentrated on the Brillouin zone boundary away from the Gamma point and indicating that an even larger supercell ( Figure S17a, Supporting Information) would be needed to obtain a dynamically stable structure. We performed a geometry optimization for the larger supercell of Figure S17a (Supporting Information) (624 atoms) and found it to be lower in energy by 3 meV (per 624 atoms) than the original 2×(2×2) supercell of Figure 1a. However, the computational cost of a full analysis (including phonon modes, Raman spectra, and electron-phonon couplings) for this larger structure would be excessive. Given that the imaginary frequencies in Figure S16 (Supporting Information) do not exceed 30 cm −1 in magnitude, i.e., significantly below the TAS oscillation frequency of 114 cm −1 , we therefore base the remainder of the analysis on the computationally more feasible 2×(2×2) supercell with 312 atoms.
As discussed above, a Raman active phonon mode can cause the oscillations observed in TAS. Raman spectra of (AE2T) 2 AgBiI 8 measured from the single crystal sample are shown together with FFT spectra of PIA o oscillations in Figure 4a. For comparison, the theoretical Raman spectra calculated using density-functional perturbation theory (DFPT) [42] and FFT spectra of PIA o are shown in Figure 4b. We converted the theoretical Raman intensities computed for each individual phonon mode into a continuous spectrum by applying a Gaussian broadening function with a broadening parameter of 20 cm −1 , chosen to provide a qualitative visual match to the experimental spectra in Figure 4a. It can clearly be seen that in all of these, peak positions match well. Clearly, the experiment and theory are consistent under these assumptions, with the experimental peak occurring at ≈116.7 cm −1 , the FFT peak at ≈117.9 cm −1 , and the computational peak at ≈119.7 cm −1 . The computational spectra are dominated by a single phonon mode  The electron-phonon coupling effect of 48 zone-center (Γ point) phonon modes between 95 and 125 cm −1 (shaded yellow area in Figure S16a, Supporting Information) was further investigated using the frozen phonon method, i.e., by calculating the change of Kohn-Sham electronic levels along fixed geometry snapshots created by adding or subtracting the displacement associated with each phonon to/from the minimum-energy geometry. The computational details are given in Sec. S2.5 in the Supplementary Notes. As an example, Figure 5a shows the phonon vibration pattern of the phonon mode at 115.6 cm −1 , where the breathing mode of AgI 6 octahedra and the flipping/folding mode of the rings of AE2T molecules are highlighted because these AgI 6 octahedra and AE2T molecules are found to be the major contributor to the organic HOMO and inorganic VBM and thus are drawn separately from the complete structure for the clarity. The complete phonon mode at 115.6 cm −1 is shown in Figure S22a, Supporting Information, and the location of the structure shown in Figure 5a in the complete unit cell can be found in Figure S22a (Supporting Information). The phonon vibration animation is shown in the GIF file attached in the Supplementary Files). Using the phonon vibration vector (shown in Figure S22a, Supporting Information) as a unit displacement vector D, we can construct structure snapshots along the phonon oscillation by adding a displacement vector (ξ · D), given by a dimensionless phonon amplitude ξ multiplied by the unit displacement vector D, to the equilibrium (AE2T) 2 AgBiI 8 atomic coordinates. Each snapshot structure's electronic structure is then calculated with DFT-PBE+SOC, revealing the change in individual energy levels and their character along the phonon path. We define the organic HOMO (Org. HOMO) and inorganic VBM (Inorg. VBM) band states of the static structure as the highest occupied energy states whose organic species contribution is larger than 70% and less than 30%, respectively, among all the reciprocal space k grid points, as shown in Figure S20  ε ξ band levels for all the snapshot structures with phonon amplitude ξ changing from -2 to +2. We here use DFT-PBE+SOC instead of the computationally much more expensive DFT-HSE06+SOC method because we expect the shifts associated with individual bands due to local structure changes to be correctly resolved already in DFT-PBE+SOC. Note that this is in contrast to the overall band gap and the absolute alignments of the organic and inorganic bands with respect to one another. For a comparison of the overall band structure features, we also show the band structures and PDOS of the un-displaced (static) structure calculated with DFT-HSE06+SOC and DFT-PBE+SOC in Figure S19 (Supporting Information). As can be seen there, the features of the projected DOS as well as the individual levels are still qualitatively comparable between both functionals, although their overall energies are shifted. We will next focus on the changes in energy level differences (i.e., the quantities that we expect to be reproduced already in DFT-PBE+SOC) as a function of geometry corresponding to individual phonon modes.
In Figure 5, we analyze a particular phonon mode at 115.6 cm −1 , i.e., close to the oscillation frequency of interest seen in TAS. As can be seen from the directions and magnitude of the atomic displacements (partial image of the most important motion in Figure 5a; see Figure S22, Supporting Information for the full phonon mode), this is a non-trivial, delocalized mode that distorts both the organic and inorganic components. The inorganic part displays a clear AgI 6 octahedral and BiI 6 octahedral breathing pattern. The organic part exhibits a complex flipping/folding pattern of AE2T molecules. The Mulliken decomposition shows that ≈50% of the Org. HOMO is contributed by the rings of the two AE2T molecules shown in Figure 5a while the rest of the contribution is smeared among the other 14 AE2T molecules, and ≈80% of the Inorg. VBM is contributed by the two AgI 6 octahedra shown in Figure 5a. Along the atomic vibration coordinate of the phonon mode at 115.6 cm −1 , Figure 4. a) Raman spectrum (gray curve) of (AE2T) 2 AgBiI 8 single crystal samples and two-Gaussian curve fit (black curve). The FFT spectrum of the PIA o signal is also plotted in magenta hollow circles and the corresponding Lorentzian fit is shown as the magenta dashed curve. b) DFPT-computed Raman intensities for individual phonon modes (dark red vertical bars) and Gaussian-broadened spectrum (solid black line) with a Gaussian broadening parameter of 20 cm −1 . The FFT spectrum of PIA o signal is also plotted in magenta hollow circles and the corresponding Lorentzian fit is shown as the magenta dashed curve. The phonon modes are calculated using FHI-aims' "really tight" numerical settings and DFT-PBE+TS. Based on the eigenmodes, the electric-field response in DFPT was subsequently calculated with PBE as exchange-correlation (xc) kernel, "light" numerical settings, and dense radial integration grids (radial_multiplier2 [49] in FHI-aims for all the species).
the breathing AgI 6 octahedra and flipping/folding AE2T molecules impact the Org. HOMO and Inorg. VBM energy levels, as shown in Figure 5b,c, respectively. The amplitude value is denoted in dimensionless units from −2 to 2, within which the total energy landscape along the phonon mode is practically exactly harmonic, as shown in Figure S18 (Supporting Information). The energy change in this range is ≈0.1 eV, ≈4 times the thermal energy at room temperature of 0.025 eV; note that the TAS pump laser could actually excite more than a single phonon. The key point is that both the character of and the energy difference between the electronic levels change along this phonon mode. The color-coded symbols in Figure 5c show that the energy level identified as the Inorg. VBM ( ) VBM Inorg.
ε ξ actually hybridizes considerably with the organic-derived states and even becomes predominantly organic in character toward one end of the phonon displacement (phonon amplitude ξ = 2), indicating that charges would in fact be shifted if the associated energy level were to follow the nuclear displacements adiabatically. Likewise, the energy difference Δ (ξ) between Org. HOMO shown in Figure 5d, decreases significantly from one end of this phonon mode to the other as the phonon amplitude ξ changes from −2 to +2, creating a statistical driving force for coherent charge oscillations as observed in TAS. The slope of Δ (ξ) is a suitable qualitative measure for the electron-phonon coupling strength that is relevant to our TAS observations. Therefore, we define this slope, approximated between amplitude values ξ = −1 and ξ = +1, as a measure of the electron-phonon coupling strength as follows This measure of the electron-phonon coupling strength, C e −p , is plotted in Figure 5e for all phonon modes in the range between 95 and 125 cm −1 . The highest electron-phonon coupling strength C e −p is observed at ≈115 cm −1 . Specifically, the largest electron-phonon coupling effect occurs for the phonon modes 115.2 and 115.6 cm −1 , precisely where we observe the strongest population oscillations in TAS. Remarkably, these modes are also Raman active (Figure 4b). Although the mode with the highest Raman activity is found just above 120 cm −1 , taking the product of predicted Raman intensity and qualitative electron-phonon coupling strength as one measure for the likelihood of inducing the observed population oscillations clearly reveals the calculated phonon modes at 115.2 and 115.6 cm −1 as the most relevant phonon modes, as seen in Figure 5f. In Figure S23 (Supporting Information), we show the phonon modes of 115.2 cm −1 and the corresponding Org. HOMO and Inorg. VBM band level changes during phonon vibration. For phonon mode 115.2 cm −1 , the two AgI 6 octahedra exhibit breathing modes in which one AgI 6 octahedron is expanding while the other is contracting. This is different from phonon mode 115.6 cm −1 , where the two AgI 6 octahedra expand and contract at the same time. The AE2T molecules' vibration pattern is slightly different but both display complex flipping and folding patterns. The electron-phonon coupling strength for the phonon mode at 115.2 cm −1 as defined above is the highest among the phonons in the range between 95 and 125 cm −1 .
As a result, the two phonon modes observed at 115.2 and 115.6 cm −1 present features that are remarkably consistent with the observed coherent hole-population oscillations that we surmised to be the cause of the PIA o feature oscillations in Figure 2. This leaves the question of the identity of the PIA o transition, which we tentatively attribute to filling hole states in the organic HOMO by electrons from energy levels situated ≈2 eV below the organic HOMO ( Figure S20, Supporting Information) in the TAS measurement. As shown in Figure S20c (Supporting Information), our DFT-PBE+SOC based energy band structure contains a set of organic-related energy levels ≈2 eV below the organic HOMO. However, while the PIA o feature shows a population oscillation, it does not show an energy oscillation, i.e., there should be zero electron-phonon coupling in the respective excitation. For the computed transition (DFT-PBE) ≈2 eV, we could not identify a phonon with zero electron-phonon coupling strength for the simple energy difference between the organic HOMO and one of the organicderived states ≈2 eV below in DFT-PBE. This is, in principle, not surprising, since there is no strong reason to expect the DFT-PBE energy level difference to accurately reflect the actual excitation energy of an excitation situated exclusively on the organic component, where we expect high exciton binding energies and high polaronic corrections to the energy difference in addition to the inherent uncertainty of DFT-PBE. We tentatively attribute the energetically relatively rigid nature of the PIA o feature to the fact that this feature fills a hole in the organic component, which would be highly localized and where the features of excitation energies would likely be distorted severely away from the molecular geometry encountered in equilibrium and in absence of the localized hole.
The schematic illustration in Figure 6 summarizes the observed charge oscillation arising within (AE2T) 2 AgBiI 8 . Figure 6a shows the time evolution of the polaron population of organic (PIA o ) during the first 3 ps. When the material is excited, electron-hole pairs are created at the inorganic sites. Owing to the proximity of inorganic VBM and organic HOMO levels, an initial ultrafast hole transfer to the organic component can take place (Figure 6b). Due to the coherent phonon motion, the energy difference between inorganic VBM and organic HOMO is modulated, which in turn leads to charge transfer back to the inorganic component (Figure 6c,d,e) until the coherent Figure 6. Summary schematics interpreting the TAS observations in this work. a) Early delay oscillatory dynamics of PIA o from 0 to 3 ps. b-d) Schematic depiction of atomic positions associated with the 115.6 cm −1 phonon mode but for exaggerated phonon vibration amplitude factors ξ of b) −50, c) 0 (static structure), d) +50 as defined in Equation (4) in the SI. Energy level alignments of the Org. HOMO and Inorg. VBM along the phonon mode (calculated for ξ = −2, 0, +2, respectively, using DFT-PBE+SOC) are shown below each structure. As indicated in Figure 6, the Org. HOMO is mostly contributed by the rings of the two AE2T molecules shown (pink shaded area), and the Inorg. VBM is mostly contributed by the two AgI 6 octahedra (green shaded area). As the AgI 6 octahedra shrink and the AE2T molecules fold (motion in (b)), the energy gap between the Org. HOMO and Inorg. HOMO increases from 0.177 to 0.192 eV. In contrast, as the AgI 6 octahedra expand and the AE2T molecules fold in the opposite direction (motion in (d)), the energy gap between the Org. HOMO and Inorg. HOMO decreases from 0.177 to 0.168 eV. This electron-phonon coupling of the (Org. HOMO -Inorg. VBM) energy difference will influence the charge transfer and thus the electron and hole populations of the Org. HOMO and Inorg. VBM, as indicated by the dark and light circles (dark circles represent transferred holes and light circles represent where the holes transferred from). This charge population change will then be picked up by the TAS measurements. The oscillation trend of PIA o , shown by the red, blue, and yellow stars in (a) can be related to the structural change and the corresponding energy level alignment changes from (b) to (d).
oscillations de-phase in ≈1.5 ps. The phonon vibration-induced charge transfer between inorganic VBM and organic HOMO can also be corroborated by the frontier orbitals of inorganic HOMO plots for the phonon mode at ω = 115.6 cm −1 at vibration amplitude −2, 0, and 2, as shown in Figure S21 (Supporting Information). As shown in Figure S21 (Supporting Information), the electron density is concentrated around the inorganic part at phonon amplitude ξ = −2, but transfers gradually to the organic part as the amplitude increases to ξ = 2, with the ratio of inorganic to organic contributions to this orbital varying from 0.18/0.82 to 0.76/0.24. The phase shift close to p between the PIA o oscillation and its contribution to PB further shows that these two features are interrelated to each other as discussed in the above paragraphs. When the proximity is lifted between the inorganic VBM and organic HOMO of the material (i.e., when AE4T is used), charge transfer ceases to exist, as expected, and oscillations of the organic-related features dampen. It is a very interesting question whether these population oscillations are or can be excited in the form of electronically coherent wave packets across the crystal but answering that question requires further research using a 2D electronic spectroscopy. [47]

Conclusion
In conclusion, we show that the electron-phonon coupling in hybrid perovskites enables the engineering of complex structures that can utilize coherent processes to drive and manipulate charge transfer kinetics. In this particular system, the oscillation in the energy levels of the inorganic framework causes the hole population to controllably shift between the organic and inorganic components. Theoretical results support the charge transfer manipulation scheme and, remarkably, allow us to identify two specific phonon modes out of the many possible ones, which are coupled to the electronic excitations and which have all the characteristics necessary to explain the observed hole population oscillation features in TAS. The calculations suggest that Raman active phonon modes with large electron-phonon coupling strength at just above (computed) 115 cm −1 are likely responsible for the TAS oscillation observed at similar energy. This further indicates that the electronphonon coupling effect can be used as a new way to manipulate the charge transfer between organic and inorganic components in the 2D hybrid organic-inorganic perovskites. Thus, the mechanism introduced in this study may function as a new degree of freedom to consider when designing semiconductor devices based on rapid, optically controllable charge movement, e.g., for switching applications.

Experimental Section
Thin-Film Deposition: Polycrystalline powders and thin films of [AE2T] 2 AgBiI 8 were prepared using the methods described in the supplementary information of the authors' earlier work. [23] Briefly, 0.2 m dimethyl formamide (DMF) solution of [AE2T] 2 AgBiI 8 powders (≈40 µL) was spin-coated on glass substrates at a spin speed of 2000 rpm for 30 s and annealing at 150 °C for 10 min in an N 2 -filled glove box. Dark-red powders of [AE3T] 2 AgBiI 8 and [AE4T] 2 AgBiI 8 were obtained similarly [23] using stoichiometric amounts of [AE3T]-2HI or [AE4T]-2HI (0.024 mmoles), BiI 3 (0.012 mmoles) and AgI (0.012 mmoles). Thin films of [AE3T] 2 AgBiI 8 and [AE4T] 2 AgBiI 8 were prepared using 0.2 m solutions in DMF and 2:1 DMF: DMSO (DMSO = dimethyl sulfoxide), respectively, at a spin speed of 2000 rpm for 30 s and annealing at 150 °C for 10 min in an N 2 -filled glove box. For powder X-ray diffraction patterns, refer to [23] for [AE2T] 2 AgBiI 8 thin film, and Supporting Information Section S3 for [AE3T] 2 AgBiI 8 and [AE4T] 2 AgBiI 8 thin films . Details of [AEnT]-2HI (where n = 2, 3, and 4) synthesis can be found in Supporting Information Section S4. The visualization of the atomic structures were performed using Vesta. [48] Optical Characterization and Analysis: Steady-state absorption spectra of thin films were taken using an Agilent 8453 UV-vis spectrophotometer. Transient absorption experiments were performed at the NCSU Imaging and Kinetic Spectroscopy (IMAKS) Laboratory using a mode-locked Ti:sapphire laser (Coherent Libra). Sub picosecond absorption transients were detected using a Helios transient absorption spectrometer from Ultrafast Systems. A portion of the output from a 1 kHz Ti:sapphire Coherent Libra regenerative amplifier (4 mJ, 100 fs (fwhm) at 800 nm) was split into the pump and probe beams. The probe beam was sent to an optical delay stage to control pump-probe delay, while the pump beam was directed into an optical parametric amplifier (Coherent OPerA Solo) to generate the second harmonic generation of 400 nm. The pump beam was focused into a ≈800 µm spot on the sample and overlapped with the probe (≈200 µm). The relative polarizations of the pump and probe were set to 54.7°. Data analysis (modelling and fitting) was performed using Graphxyz: a Python-based open-source software. [50] De-convolution and FFT analysis were performed using the built-in functions of the MATLAB software platform (the resolution of FFT spectra was 2 cm −1 ). Raman spectra were collected at room temperature on a Horiba T64000 Raman spectrometer in the triple spectrometer operation mode with an Olympus MPLN100X Plan Achromat microscope objective. A 532 nm Nd:YAG laser (≈865 µW at sample position) was used to excite the sample with a 1% filter. The Raman spectrum was collected by an accumulation of three measurements, which each lasted 60 s.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.