Room-Temperature Coherent Optical Phonon in 2D Electronic Spectra of CH3NH3PbI3 Perovskite as a Possible Cooling Bottleneck

Evidence of Surface-Mediated Carrier-Phonon Scattering in MXene

In a two-dimensional (2D) metallic nanostructure, when a sample's thickness is shorter than a carrier mean free path, the ultrathin thickness may influence carrier and energy transport, owing to surface scattering. However, to date, for metallic 2D transition-metal carbides (MXenes), experiments and calculations related to surface scattering have not been performed. The contribution of ultrathin structures to carrier surface scattering in MXene is yet to be explored. Herein, to reveal this effect, we design various models, including metal/MXene, dielectric/MXene, and bulk structure, and analyze their carrier dynamics via ultrafast spectroscopy. The results related to carrier dynamics indicate that the influence of the dielectric/MXene interface and the temperature is negligible. In contrast, the carrier dynamic lifetimes are prolonged owing to weakened surface scattering in metal/MXene, which is supported by ab initio calculations. These results suggest that the carrier-phonon scattering is dominated by surface scattering. These findings can help guide effective energy transport and enhance energy conversion and catalysis.

Charge carrier dynamics and transient spectral evolutions in lead halide perovskites

Lead halide perovskites (LHPs) have emerged as promising materials for solar cell applications due to their unique photophysical properties. Most of the crucial properties related to solar cell performance such as carrier mobility, diffusion length, recombination rates, etc. have been estimated using ultrafast spectroscopic methods. While various methods have been developed to prepare and fabricate high-quality perovskite films for photovoltaic applications, understanding the charge carrier dynamics is also crucial at each stage of the charge generation, cooling, and recombination processes. Using femtosecond (fs) transient absorption (TA) spectroscopy, various stages of charge carrier dynamics in perovskite materials could be monitored. In this article, we focus on some of the recent experimental developments related to charge carrier dynamics in perovskites and discuss the current understanding of (1) exciton dissociation, (2) charge carrier thermalization, (3) hot carrier cooling, and (4) electron-phonon coupling along with some of the crucial spectral emergence in the pump-probe experiments of LHP materials.

Sub-8-fs pulses in the visible to near-infrared by a degenerate optical parametric amplifier

This work presents a single-stage optical parametric amplifier (OPA) operating at degeneracy (DOPA) and pumped by the third harmonic of a Yb:KGW laser system. This DOPA exploits the broad amplification bandwidth that occurs with type-I phase-matching in β-barium borate (BBO) when signal and idler overlap in the spectrum. The output pulses span from 590 to 780 nm (1.59-2.10 eV) with 7.75-fs duration after compression. Ultrashort pulses with similar bandwidths in this spectral window complement the existing array of optical parametric amplifiers that cover either the visible or the near-IR spectral regions with sub-10-fs pulses. This source of ultrashort optical pulses will enable the application of sophisticated spectroscopy techniques to the study of electronic coherences and energy migration pathways in biological, chemical, and condensed matter systems.

Carriers, Quasi-particles, and Collective Excitations in Halide Perovskites

Halide perovskites (HPs) are potential game-changing materials for a broad spectrum of optoelectronic applications ranging from photovoltaics, light-emitting devices, lasers to radiation detectors, ferroelectrics, thermoelectrics, etc. Underpinning this spectacular expansion is their fascinating photophysics involving a complex interplay of carrier, lattice, and quasi-particle interactions spanning several temporal orders that give rise to their remarkable optical and electronic properties. Herein, we critically examine and distill their dynamical behavior, collective interactions, and underlying mechanisms in conjunction with the experimental approaches. This review aims to provide a unified photophysical picture fundamental to understanding the outstanding light-harvesting and light-emitting properties of HPs. The hotbed of carrier and quasi-particle interactions uncovered in HPs underscores the critical role of ultrafast spectroscopy and fundamental photophysics studies in advancing perovskite optoelectronics.

Confinement and Exciton Binding Energy Effects on Hot Carrier Cooling in Lead Halide Perovskite Nanomaterials

The relaxation of the above-gap ("hot") carriers in lead halide perovskites (LHPs) is important for applications in photovoltaics and offers insights into carrier-carrier and carrier-phonon interactions. However, the role of quantum confinement in the hot carrier dynamics of nanosystems is still disputed. Here, we devise a single approach, ultrafast pump-push-probe spectroscopy, to study carrier cooling in six different size-controlled LHP nanomaterials. In cuboidal nanocrystals, we observe only a weak size effect on the cooling dynamics. In contrast, two-dimensional systems show suppression of the hot phonon bottleneck effect common in bulk perovskites. The proposed kinetic model describes the intrinsic and density-dependent cooling times accurately in all studied perovskite systems using only carrier-carrier, carrier-phonon, and excitonic coupling constants. This highlights the impact of exciton formation on carrier cooling and promotes dimensional confinement as a tool for engineering carrier-phonon and carrier-carrier interactions in LHP optoelectronic materials.

Direct Observation of Ultrafast Lattice Distortions during Exciton-Polaron Formation in Lead Halide Perovskite Nanocrystals

The microscopic origin of slow hot-carrier cooling in lead halide perovskites remains debated and has direct implications for applications. Slow hot-carrier cooling of several picoseconds has been attributed to either polaron formation or a hot-phonon bottleneck effect at high excited carrier densities (>10¹⁸ cm^-3). These effects cannot be unambiguously disentangled with optical experiments alone. However, they can be distinguished by direct observations of ultrafast lattice dynamics, as these effects are expected to create qualitatively distinct fingerprints. To this end, we employ femtosecond electron diffraction and directly measure the sub-picosecond lattice dynamics of weakly confined CsPbBr₃ nanocrystals following above-gap photoexcitation. While we do not observe signatures of a hot-phonon bottleneck lasting several picoseconds, the data reveal a light-induced structural distortion appearing on a time scale varying between 380 and 1200 fs depending on the excitation fluence. We attribute these dynamics to the effect of exciton-polarons on the lattice and the slower dynamics at high fluences to slower sub-picosecond hot-carrier cooling, which slows down the establishment of the exciton-polaron population. Further analysis and simulations show that the distortion is consistent with motions of the [PbBr₃]^- octahedral ionic cage, and closest agreement with the data is obtained for Pb-Br bond lengthening. Our work demonstrates how direct studies of lattice dynamics on the sub-picosecond time scale can discriminate between competing scenarios proposed in the literature to explain the origin of slow hot-carrier cooling in lead halide perovskites.

Ultrafast Spectroscopy of Plasmons and Free Carriers in 2D MXenes

2D MXenes have diverse and chemically tunable optical properties that arise from an interplay between free carriers, interband transitions, and plasmon resonances. The nature of photoexcitations and their dynamics in three different members of the MXene family, Ti₃ C₂ , Mo₂ Ti₂ C₃ , and Nb₂ C, are investigated using two complementary pump-probe techniques, transient optical absorption, and time-resolved terahertz (THz) spectroscopy. Measurements reveal pronounced plasmonic effects in the visible and near-IR in all three. Optical excitation, with either 400 or 800 nm pulses, results in a rapid increase in lattice temperature, evidenced by a pronounced broadening of the plasmon mode that presents as a plasmon bleach in transient absorption measurements. Observed kinetics of plasmon bleach recovery provide a means to monitor lattice cooling. Remarkably slow cooling, proceeding over hundreds of picoseconds to nanoseconds time scales, implies MXenes have low thermal conductivities. The slowest recovery kinetics are observed in the MXene with the highest free carrier density, viz. Ti₃ C₂ , that supports phonon scattering by free carriers as a possible mechanism limiting thermal conductivity. These new insights into photoexcitation dynamics can facilitate their applications in photothermal solar energy conversion, plasmonic devices, and even photothermal therapy and drug delivery.

Phonon signatures for polaron formation in an anharmonic semiconductor

Mechanistic studies on lead halide perovskites (LHPs) in recent years have suggested charge carrier screening as partially responsible for long carrier diffusion lengths and lifetimes that are key to superior optoelectronic properties. These findings have led to the ferroelectric large polaron proposal, which attributes efficient charge carrier screening to the extended ordering of dipoles from symmetry-breaking unit cells that undergo local structural distortion and break inversion symmetry. It remains an open question whether this proposal applies in general to semiconductors with LHP-like anharmonic and dynamically disordered phonons. Here, we study electron-phonon coupling in Bi₂O₂Se, a semiconductor which bears resemblance to LHPs in ionic bonding, spin-orbit coupling, band transport with long carrier diffusion lengths and lifetimes, and phonon disorder as revealed by temperature-dependent Raman spectroscopy. Using coherent phonon spectroscopy, we show the strong coupling of an anharmonic phonon mode at 1.50 THz to photo-excited charge carriers, while the Raman excitation of this mode is symmetry-forbidden in the ground-state. Density functional theory calculations show that this mode, originating from the A_1g phonon of out-of-plane Bi/Se motion, gains oscillator strength from symmetry-lowering in polaron formation. Specifically, lattice distortion upon ultrafast charge localization results in extended ordering of symmetry-breaking unit cells and a planar polaron wavefunction, namely a two-dimensional polaron in a three-dimensional lattice. This study provides experimental and theoretical insights into charge interaction with anharmonic phonons in Bi₂O₂Se and suggests ferroelectric polaron formation may be a general principle for efficient charge carrier screening and for defect-tolerant semiconductors.

Transient Suppression of Carrier Mobility Due to Hot Optical Phonons in Lead Bromide Perovskites

In lead halide perovskites, owing to the strong Fröhlich coupling, carrier dynamics that governs the optoelectronic performance is greatly affected by the lattice vibrations. In this emerging class of materials, injected hot carriers quickly relax by emitting optical phonons, and if this process is sufficiently fast, hot optical phonons can be generated, which may in turn hamper the carrier transport. However, the transient interaction between hot phonons and carriers has not yet been investigated. Herein, we identified the transient absorption feature of hot phonons in lead bromide perovskites and then extracted the hot-phonon dynamics. The hot-phonon decay mechanism was uncovered by temperature-dependent measurements. The hot-phonon decay in lead bromide perovskites was an order of magnitude faster than that in GaAs, attributed to the large anharmonicity arising from the lattice softness and structural fluctuation. The carrier mobility was also transiently suppressed by hot phonons, and the mobility recovery was accompanied by the decay of hot phonons.

Double-quantum-zero-quantum 2D coherent spectroscopy reveals quantum coherence between collective states in an atomic vapor

We report a novel, to the best of our knowledge, double-quantum-zero-quantum two-dimensional coherent spectroscopy (2DCS) that allows direct detection of the quantum coherence between multiparticle collective states. Through correlating the double-quantum coherence and the zero-quantum coherence, signatures for coherence between collective states can be well isolated as side peaks and readily identified in the 2D spectrum. The experiment is implemented in a vapor of rubidium atoms in a collinear 2DCS setup. Good agreement with a theoretical simulation using density matrix confirms the essential role of the interatomic correlation effect in generating the side peak signals. This 2D spectrum technique paves a new avenue for studying the coherent coupling of highly excited states and many-body properties.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Mixed halide bulk perovskite triplet sensitizers: Interplay between band alignment, mid-gap traps, and phonons

Photon upconversion, particularly via triplet-triplet annihilation (TTA), could prove beneficial in expanding the efficiencies and overall impacts of optoelectronic devices across a multitude of technologies. The recent development of bulk metal halide perovskites as triplet sensitizers is one potential step toward the industrialization of upconversion-enabled devices. Here, we investigate the impact of varying additions of bromide into a lead iodide perovskite thin film on the TTA upconversion process in the annihilator molecule rubrene. We find an interplay between the bromide content and the overall device efficiency. In particular, a higher bromide content results in higher internal upconversion efficiencies enabled by more efficient charge extraction at the interface likely due to a more favorable band alignment. However, the external upconversion efficiency decreases as the absorption cross section in the near infrared is reduced. The highest upconversion performance is found in our study for a bromide content of 5%. This result can be traced back to a high absorption cross section in the near infrared and higher photoluminescence quantum yield in comparison to the iodide-only perovskite and an increased driving force for charge transfer.

Polarons and Charge Localization in Metal-Halide Semiconductors for Photovoltaic and Light-Emitting Devices

Metal-halide semiconductors have shown excellent performance in optoelectronic applications such as solar cells, light-emitting diodes, and detectors. In this review the role of charge-lattice interactions and polaron formation in a wide range of these promising materials, including perovskites, double perovskites, Ruddlesden-Popper layered perovskites, nanocrystals, vacancy-ordered, and other novel structures, is summarized. The formation of Fröhlich-type "large" polarons in archetypal bulk metal-halide ABX₃ perovskites and its dependence on A-cation, B-metal, and X-halide composition, which is now relatively well understood, are discussed. It is found that, for nanostructured and novel metal-halide materials, a larger variation in the strengths of polaronic effects is reported across the literature, potentially deriving from variations in potential barriers and the presence of interfaces at which lattice relaxation may be enhanced. Such findings are further discussed in the context of different experimental approaches used to explore polaronic effects, cautioning that firm conclusions are often hampered by the presence of alternate processes and interactions giving rise to similar experimental signatures. Overall, a complete understanding of polaronic effects will prove essential given their direct influence on optoelectronic properties such as charge-carrier mobilities and emission spectra, which are critical to the performance of energy and optoelectronic applications.

Accelerated Hot-Carrier Cooling in MAPbI3 Perovskite by Pressure-Induced Lattice Compression

Hot-carrier cooling (HCC) in metal halide perovskites above the Mott transition is significantly slower than in conventional semiconductors. This effect is commonly attributed to a hot-phonon bottleneck, but the influence of the lattice properties on the HCC behavior is poorly understood. Using pressure-dependent transient absorption spectroscopy, we find that at an excitation density below the Mott transition, pressure does not affect the HCC. On the contrary, above the Mott transition, HCC in methylammonium lead iodide is around 2-3 times faster at 0.3 GPa than at ambient pressure. Our electron-phonon coupling calculations reveal ∼2-fold stronger electron-phonon coupling for the inorganic cage mode at 0.3 GPa. However, our experiments reveal that pressure promotes faster HCC only above the Mott transition. Altogether, these findings suggest a change in the nature of excited carriers above the Mott transition threshold, providing insights into the electronic behavior of devices operating at such high charge-carrier densities.

Solvated Electrons in Solids-Ferroelectric Large Polarons in Lead Halide Perovskites

Solvation plays a pivotal role in chemistry and biology. A solid-state analogy of solvation is polaron formation, but the magnitude of Coulomb screening is typically an order of magnitude weaker than that of solvation in aqueous solutions. Here, we describe a new class of polarons, the ferroelectric large polaron, proposed initially by Miyata and Zhu in 2018 (Miyata, K.; Zhu, X.-Y. Ferroelectric Large Polarons. Nat. Mater. 2018, 17 (5), 379-381). This type of polaron allows efficient Coulomb screening of an electron or hole by extended ordering of dipoles from symmetry-broken unit cells. The local ordering is reflected in the ferroelectric-like THz dielectric responses of lead halide perovskites (LHPs) and may be partially responsible for their exceptional optoelectronic performances. Despite the likely absence of long-range ferroelectricity in LHPs, a charge carrier may be localized to and/or induce the formation of nanoscale domain boundaries of locally ordered dipoles. Based on the known planar nature of energetically favorable domain boundaries in ferroelectric materials, we propose that a ferroelectric polaron localizes to planar boundaries of transient polar nanodomains. This proposal is supported by dynamic simulations showing sheet-like transient electron or hole wave functions in LHPs. Thus, the Belgian-waffle-shaped ferroelectric polaron in the three-dimensional LHP crystal structure is a large polaron in two dimensions and a small polaron in the perpendicular direction. The ferroelectric large polaron may form in other crystalline solids characterized by dynamic symmetry breaking and polar fluctuations. We suggest that the ability to form ferroelectric large polarons can be a general principle for the efficient screening of charge carriers from scattering with other charge carriers, with charged defects and with longitudinal optical phonons, thus contributing to enhanced optoelectronic properties.

Observation of Charge Generation via Photoinduced Stark Effect in Mixed-Cation Lead Bromide Perovskite Thin Films

Extensive transient absorption studies on hybrid organic-inorganic lead halide perovskites have elucidated many optical properties important for their device performance. Despite the enormous progress, the derivative shaped photoinduced absorption feature in transient spectra that is above the bandgap has many explanations, including the photoinduced Stark effect, where the bandgap is blue shifted due to a local electric field generated by charges. In this work, we employ broad band transient absorption and two-dimensional electronic spectroscopy (2DES) to examine the early transient events after photoexcitation of [CH(NH₂)₂]_0.83Cs_0.17PbBr₃ (FA_0.83Cs_0.17PbBr₃). 2DES resolves a photomodulation feature at the excitation energy of the exciton, suggesting the presence of a dipole field created by a polaron pair shifting the exciton transition to higher energies. As this polaron pair dissociates over 200 fs, the exciton transition shifts to higher energies over the same time scale, evidenced by the 2DES diagonal energy spectra. Given that the observations are well explained in terms of the Stark effect, our work provides extra grounds to support the Stark effect assignment of the above-gap photoinduced absorption. Furthermore, our study reports on the time scale of charge generation, contributing to the fundamental understanding of mixed-cation lead bromide perovskite photophysics.

Fast phase cycling in non-collinear optical two-dimensional coherent spectroscopy

As optical two-dimensional coherent spectroscopy (2DCS) is extended to a broader range of applications, it is critical to improve the detection sensitivity of optical 2DCS. We developed a fast phase-cycling scheme in a non-collinear optical 2DCS implementation by using liquid crystal phase retarders to modulate the phases of two excitation pulses. The background in the signal can be eliminated by combining either two or four interferograms measured with a proper phase configuration. The effectiveness of this method was validated in optical 2DCS measurements of an atomic vapor. This fast phase-cycling scheme will enable optical 2DCS in novel emerging applications that require enhanced detection sensitivity.

Protecting hot carriers by tuning hybrid perovskite structures with alkali cations

Successful implementation of hot carrier solar cells requires preserving high carrier temperature as carriers migrate through the active layer. Here, we demonstrated that addition of alkali cations in hybrid organic-inorganic lead halide perovskites led to substantially elevated carrier temperature, reduced threshold for phonon bottleneck, and enhanced hot carrier transport. The synergetic effects from the Rb, Cs, and K cations result in ~900 K increase in the effective carrier temperature at a carrier density around 10¹⁸ cm^-3 with an excitation 1.45 eV above the bandgap. In the doped thin films, the protected hot carriers migrate 100 s of nanometers longer than the undoped sample as imaged by ultrafast microscopy. We attributed these improvements to the relaxation of lattice strain and passivation of halide vacancies by alkali cations based on x-ray structural characterizations and first principles calculations.

Charge Carrier Relaxation in Colloidal FAPbI3 Nanostructures Using Global Analysis

We study the hot charge carrier relaxation process in weakly confined hybrid lead iodide perovskite colloidal nanostructures, FAPbI₃ (FA = formaminidium), using femtosecond transient absorption (TA). We compare the conventional analysis method based on the extraction of the carrier temperature (T_c) by fitting the high-energy tail of the band-edge bleach with a global analysis method modeling the continuous evolution of the spectral lineshape in time using a simple sequential kinetic model. This practical approach results in a more accurate way to determine the charge carrier relaxation dynamics. At high excitation fluence (density of charge carriers above 10¹⁸ cm⁻³), the cooling time increases up to almost 1 ps in thick nanoplates (NPs) and cubic nanocrystals (NCs), indicating the hot phonon bottleneck effect. Furthermore, Auger heating resulting from the multi-charge carrier recombination process slows down the relaxation even further to tens and hundreds of picoseconds. These two processes could only be well disentangled by analyzing simultaneously the spectral lineshape and amplitude evolution.

Photoinduced Vibrations Drive Ultrafast Structural Distortion in Lead Halide Perovskite

The success of organic–inorganic perovskites in optoelectronics is dictated by the complex interplay between various underlying microscopic phenomena. The structural dynamics of organic cations and the inorganic sublattice after photoexcitation are hypothesized to have a direct effect on the material properties, thereby affecting the overall device performance. Here, we use ultrafast heterodyne-detected two-dimensional (2D) electronic spectroscopy to reveal impulsively excited vibrational modes of methylammonium (MA) lead iodide perovskite, which drive the structural distortion after photoexcitation. Vibrational analysis of the measured data allows us to monitor the time-evolved librational motion of the MA cation along with the vibrational coherences of the inorganic sublattice. Wavelet analysis of the observed vibrational coherences reveals the coherent generation of the librational motion of the MA cation within ∼300 fs complemented with the coherent evolution of the inorganic skeletal motion. To rationalize this observation, we employed the configuration interaction singles (CIS), which support our experimental observations of the coherent generation of librational motions in the MA cation and highlight the importance of the anharmonic interaction between the MA cation and the inorganic sublattice. Moreover, our advanced theoretical calculations predict the transfer of the photoinduced vibrational coherence from the MA cation to the inorganic sublattice, leading to reorganization of the lattice to form a polaronic state with a long lifetime. Our study uncovers the interplay of the organic cation and inorganic sublattice during formation of the polaron, which may lead to novel design principles for the next generation of perovskite solar cell materials.

Global Analysis for Time and Spectrally Resolved Multidimensional Microscopy: Application to CH3NH3PbI3 Perovskite Thin Films

The advancement of improved photoactive materials, such as those proposed for next-generation solar cells, low-power lighting, and lasing applications, requires a deep understanding of their correlated spatial, spectral, and temporal properties. In principle, correlated time-resolved microscopy techniques are capable of capturing such information. However, the large data sets that encapsulate temporal, spectral, and spatial information create the prodigious challenge of analyzing gigabytes of correlated data, which typically takes enormous computational resources. These challenges motivate the development of robust and efficient data analysis tools to realize fast spatial and spectral decomposition and to gain physical insights that arise from statistical analysis. Herein, we propose a reliable and fast global analysis method based on variable projection and subsampling methods, which exhibits exceptionally high sensitivity to buried spatial and spectral information in large and multidimensional microscopy data sets as compared to traditional methods. The reliability and robustness of this new method is tested on transient absorption and impulsive vibrational microscopy data sets acquired on polycrystalline CH₃NH₃PbI₃ perovskite films.

First-principles calculations of electronic structure and optical and elastic properties of the novel ABX3-type LaWN3 perovskite structure

The development of ABX₃-type advanced perovskite materials has become a focus for both scientific researchers and the material genome initiative (MGI). In addition to the traditional perovskite ABO₃ and halide perovskite ABX₃, LaWN₃ is discovered as a new ABX₃-type advanced perovskite structure. The elastic and optical properties of this novel LaWN₃ structure are systematically studied via DFT. Based on the calculated elastic constants, the bulk modulus, shear modulus, Young's modulus and Pugh modulus ratio are precisely obtained. Results show that (1) LaWN₃ is an indirect bandgap semiconductor with a hybrid occuring near the Fermi level and the main contributions are La-d, W-d and N-p. (2) LaWN₃ has a certain ductility. The optical constants, such as absorption spectrum, energy-loss spectrum, conductivity, dielectric function, reflectivity and refractive index, are analyzed and the static dielectric constant is 10.98 and the refractivity index is 3.31. (3) The optical constants of LaWN₃ are higher than those of other existing ABX₃-type materials, showing very promising application as a functional perovskite in the future. The existence of this stable LaWN₃ structure might widen the perovskite material's application, such as in photodetectors, light-emitting diodes, perovskite solar cells, fuel cells and so on.

Using first-principles calculation, the stable R3c LaWN₃ as a new ABX₃-type advanced perovskite structure is designed in the plan of the material genome initiative (MGI), which helps to widen the nowadays nitride perovskite material's application.

Dark Subgap States in Metal-Halide Perovskites Revealed by Coherent Multidimensional Spectroscopy

Metal-halide perovskites show excellent properties for photovoltaic and optoelectronic applications, with power conversion efficiencies of solar cell and LEDs exceeding 20%. Being solution processed, these polycrystalline materials likely contain a large density of defects compared to melt-grown semiconductors. Surprisingly, typical effects from defects (absorption below the bandgap, low fill factor and open circuit voltage in devices, strong nonradiative recombination) are not observed. In this work, we study thin films of metal-halide perovskites CH₃NH₃PbX₃ (X = Br, I) with ultrafast multidimensional optical spectroscopy to resolve the dynamics of band and defect states. We observe a shared ground state between the band-edge transitions and a continuum of sub-bandgap states, which extends at least 350 meV below the band edge). We explain the comparatively large bleaching of the dark sub-bandgap states with oscillator strength borrowing from the band-edge transition. Our results show that upon valence to conduction band excitation, such subgap states are instantaneously bleached for large parts of the carrier lifetime and conversely that most dark sub-bandgap states can be populated by light excitation. This observation helps to unravel the photophysical origin of the unexpected optoelectronic properties of these materials.

Dynamic Screening and Slow Cooling of Hot Carriers in Lead Halide Perovskites

Among the exceptional properties of lead halide perovskites (LHPs) is the ultraslow cooling of hot carriers. Carrier densities below the Mott density for large polarons (≤ ≈10¹⁸ cm^-3 ) are focused on here. As in other semiconductors, a nascent hot electron distribution initially cools down via emission of longitudinal optical (LO) phonons on the 10^-14 -10^-13 s timescale. What distinguishes LHPs from conventional semiconductors is the exceptionally efficient screening in the former. The dielectric screening in LHPs on the 10^-13 s timescale results in an order-of-magnitude reduction in the Coulomb potential upon the formation of a large polaron, likely with ferroelectric-like local ordering. Further LO-phonon emission is inhibited, and this leads to partial retention of hot electron energy on the 10^-12 s timescale, more so in hybrid LHPs than in their all-inorganic counterparts. Further cooling of hot polarons occurs on the 10^-10 s timescale, and this can be attributed to the slow diffusion of heat out of the large polaron volume due to the low thermal conductivity of LHPs. Like other carrier properties, slow hot carrier cooling in LHPs can be intimately related to efficient screening in a soft, anharmonic, and dynamically disordered lattice.

Ultrafast Charge Carrier Relaxation in Inorganic Halide Perovskite Single Crystals Probed by Two-Dimensional Electronic Spectroscopy

Halide perovskites are promising optoelectronic materials. Despite impressive device performance, especially in photovoltaics, the femtosecond dynamics of elementary optical excitations and their interactions are still debated. Here we combine ultrafast two-dimensional electronic spectroscopy (2DES) and semiconductor Bloch equations (SBEs) to probe the room-temperature dynamics of nonequilibrium excitations in CsPbBr₃ crystals. Experimentally, we distinguish between excitonic and free-carrier transitions, extracting a ∼30 meV exciton binding energy, in agreement with our SBE calculations and with recent experimental studies. The 2DES dynamics indicate remarkably short, <30 fs carrier relaxation at a ∼3 meV/fs rate, much faster than previously anticipated for this material, but similar to that in direct band gap semiconductors such as GaAs. Dynamic screening of excitons by free carriers also develops on a similarly fast <30 fs time scale, emphasizing the role of carrier-carrier interactions for this material's optical properties. Our results suggest that strong electron-phonon couplings lead to ultrafast relaxation of charge carriers, which, in turn may limit halide perovskites' carrier mobilities.

Ultrafast Carrier Dynamics of Dual Emissions from the Orthorhombic Phase in Methylammonium Lead Iodide Perovskites Revealed by Two-Dimensional Coherent Spectroscopy

The fundamental understanding of photoexcitation landscape and dynamics in hybrid organic-inorganic perovskites is essential for improving their performance in solar cells and other applications. The dual emission features from the orthorhombic phase in perovskites have been the focus of numerous recent studies, and yet their underlying molecular origin remains elusive. We use optical two-dimensional coherent spectroscopy to study the carrier dynamics and coupling of the dual emissions in a methylammonium lead iodide film at 115 K. The two-dimensional spectra reveal an ultrafast redistribution of the photoexcited carriers into the two emission resonances within 250 fs. The high-energy resonance is a short-lived transient state, and the low-energy emission state interacts with coherent phonons. The observed carrier dynamics provide important experimental evidence that can be compared with potential theoretical models and contribute to the understanding of the dual emissions as well as the overall energy level structure in hybrid organic-inorganic perovskites.

Correction of spectral distortion in two-dimensional electronic spectroscopy arising from the wedge-based delay line

Unlike the probe wavelength, which is spectrally resolved by monochromator, the excitation wavelength in two-dimensional electronic spectroscopy is retrieved by means of Fourier transform of the interference signal introduced by the coherence delay time between the first and second excitation laser pulses. Hence, the calibration of delay lines would determine its accuracy. In this work, we showed that an inaccurate calibration factor of wedge-based delay line would result in a global peak shift and asymmetric spectral twists along the excitation axis. Both theoretical analysis and experiments have shown that such spectral distortions can be corrected by an accurately predetermined calibration factor. The relative accuracy of calibration factor reaches 3 × 10^-5 in our setup. The dispersion effect of wedges also has been considered for the broadband excitation.

Ultrafast correlated charge and lattice motion in a hybrid metal halide perovskite

Hybrid organic-inorganic halide perovskites have shown remarkable optoelectronic properties, exhibiting an impressive tolerance to defects believed to originate from correlated motion of charge carriers and the polar lattice forming large polarons. Few experimental techniques are capable of directly probing these correlations, requiring simultaneous sub-millielectron volt energy and femtosecond temporal resolution after absorption of a photon. Here, we use time-resolved multi-THz spectroscopy, sensitive to the internal excitations of the polaron, to temporally and energetically resolve the coherent coupling of charges to longitudinal optical phonons in single-crystal CH₃NH₃PbI₃ (MAPI). We observe room temperature intraband quantum beats arising from the coherent displacement of charge from the coupled phonon cloud. Our measurements provide strong evidence for the existence of polarons in MAPI at room temperature, suggesting that electron/hole-phonon coupling is a defining aspect of the hybrid metal-halide perovskites contributing to the protection from scattering and enhanced carrier lifetimes that define their usefulness in devices.

Optical Gain from Biexcitons in CsPbBr3 Nanocrystals Revealed by Two-dimensional Electronic Spectroscopy

Perovskite semiconductor nanocrystals (NCs) exhibit highly efficient optical gain, which is promising for laser applications. However, the intrinsic mechanism of optical gain in perovskite NCs, particularly whether more than one exciton per NCs is required, remains poorly understood. Here, we use two-dimensional electronic spectroscopy to resonantly probe the interplay between near-band-edge transitions during the buildup of optical gain in CsPbBr₃ NCs. We find compelling evidence to conclude that optical gain in CsPbBr₃ NCs is generated through stimulated emission from strongly interacting biexcitons. The threshold is largely determined by the competition between stimulated emission from biexcitons and excited-state absorption from single exciton to biexciton states. The findings in this work may guide future explorations of NC materials with low-threshold optical gain.

Intrinsic anion diffusivity in lead halide perovskites is facilitated by a soft lattice

Facile ionic transport in lead halide perovskites plays a critical role in device performance. Understanding the microscopic origins of high ionic conductivities has been complicated by indirect measurements and sample microstructural heterogeneities. Here, we report the direct visualization of halide anion interdiffusion in CsPbCl₃-CsPbBr₃ single crystalline perovskite nanowire heterojunctions using wide-field and confocal photoluminescence measurements. The combination of nanoscale imaging techniques with these single crystalline materials allows us to measure intrinsic anionic lattice diffusivities, free from complications of microscale inhomogeneity. Halide diffusivities were found to be between 10^-13 and ∼10^-12 cm²/second at about 100 °C, which are several orders of magnitudes lower than those reported in polycrystalline thin films. Spatially resolved photoluminescence lifetimes and surface potential measurements provide evidence of the central role of halide vacancies in facilitating ionic diffusion. Vacancy formation free energies computed from molecular simulation are small due to the easily deformable perovskite lattice, accounting for the high equilibrium vacancy concentration. Furthermore, molecular simulations suggest that ionic motion is facilitated by low-frequency lattice modes, resulting in low activation barriers for vacancy-mediated transport. This work elucidates the intrinsic solid-state ion diffusion mechanisms in this class of semisoft materials and offers guidelines for engineering materials with long-term stability in functional devices.

Rotational Cation Dynamics in Metal Halide Perovskites: Effect on Phonons and Material Properties

The dynamics of organic cations in metal halide hybrid perovskites (MHPs) have been investigated using numerous experimental and computational techniques because of their suspected effects on the properties of MHPs. In this Perspective, we summarize and reconcile key findings and present new data to synthesize a unified understanding of the dynamics of the cations. We conclude that theory and experiment collectively paint a relatively complete picture of rotational dynamics within MHPs. This picture is then used to discuss the consequences of structural dynamics for electron-phonon interactions and their effect on material properties by providing a brief account of key studies that correlate cation dynamics with the dynamics of the inorganic sublattice and overall device properties.

High Magnetic Field Detunes Vibronic Resonances in Photosynthetic Light Harvesting

The origin and role of oscillatory features detected in recent femtosecond spectroscopy experiments of photosynthetic complexes remain elusive. A key hypothesis underneath of these observations relies on electronic-vibrational resonance, where vibrational levels of an acceptor chromophore match the donor-acceptor electronic gap, accelerating the downhill energy transfer. Here we identify and detune such vibronic resonances using a high magnetic field that exclusively shifts molecular exciton states. We implemented ultrafast pump-probe spectroscopy into a specialized 25 T magnetic field facility and studied the light-harvesting complex PC645 from a cryptophyte algae where strongly coupled chromophores form molecular exciton states. We detected a change in high-frequency coherent oscillations when the field was engaged. Quantum chemical calculations coupled with a vibronic model explain the experiment as a magnetic field-induced shift of the exciton states, which in turn affects the electronic-vibrational resonance between pigments within the protein. Our results demonstrate the delicate sensitivity of interpigment coherent oscillations of vibronic origin to electronic-vibrational resonance interactions in light-harvesting complexes.

Ultrafast Intraband Spectroscopy of Hot-Carrier Cooling in Lead-Halide Perovskites

The rapid relaxation of above-band-gap "hot" carriers (HCs) imposes the key efficiency limit in lead-halide perovskite (LHP) solar cells. Recent studies have indicated that HC cooling in these systems may be sensitive to materials composition, as well as the energy and density of excited states. However, the key parameters underpinning the cooling mechanism are currently under debate. Here we use a sequence of ultrafast optical pulses (visible pump-infrared push-infrared probe) to directly compare the intraband cooling dynamics in five common LHPs: FAPbI₃, FAPbBr₃, MAPbI₃, MAPbBr₃, and CsPbBr₃. We observe ∼100-900 fs cooling times, with slower cooling at higher HC densities. This effect is strongest in the all-inorganic Cs-based system, compared to the hybrid analogues with organic cations. These observations, together with band structure calculations, allow us to quantify the origin of the "hot-phonon bottleneck" in LHPs and assert the thermodynamic contribution of a symmetry-breaking organic cation toward rapid HC cooling.

Structural fluctuations cause spin-split states in tetragonal (CH3NH3)PbI3 as evidenced by the circular photogalvanic effect

Lead halide perovskites are used in thin-film solar cells, which owe their high efficiency to the long lifetimes of photocarriers. Various calculations find that a dynamical Rashba effect could significantly contribute to these long lifetimes. This effect is predicted to cause a spin splitting of the electronic bands of inversion-symmetric crystalline materials at finite temperatures, resulting in a slightly indirect band gap. Direct experimental evidence of the existence or the strength of the spin splitting is lacking. Here, we resonantly excite photocurrents in single crystalline ([Formula: see text])[Formula: see text] with circularly polarized light to clarify the existence of spin splittings in the band structure. We observe a circular photogalvanic effect, i.e., the photocurrent depends on the light helicity, in both orthorhombic and tetragonal ([Formula: see text])[Formula: see text] At room temperature, the effect peaks for excitation photon energies [Formula: see text] meV below the direct optical band gap. Temperature-dependent measurements reveal a sign change of the effect at the orthorhombic-tetragonal phase transition, indicating different microscopic origins in the two phases. Within the tetragonal phase, both [Formula: see text] and the amplitude of the circular photogalvanic effect increase with temperature. Our findings support a dynamical Rashba effect in this phase, i.e., a spin splitting caused by thermally induced structural fluctuations which break inversion symmetry.

Quantifying Polaron Formation and Charge Carrier Cooling in Lead-Iodide Perovskites

Notwithstanding the success of lead-halide perovskites in emerging solar energy conversion technologies, many of the fundamental photophysical phenomena in this material remain debated. Here, the initial steps following photogeneration of free charge carriers in lead-iodide perovskites are studied, and timescales of charge carrier cooling and polaron formation, as a function of temperature and charge carrier excess energy, are quantified. It is found, using terahertz time-domain spectroscopy (THz-TDS), that the observed femtosecond rise in the photoconductivity can be described very well using a simple model of sequential charge carrier cooling and polaron formation. For excitation above the bandgap, the carrier cooling time depends on the charge carrier excess energy and lattice temperature, with cooling rates varying between 1 and 6 meV fs-1 , depending on the cation. While carrier cooling depends on the cation, polaron formation occurs within ≈400 fs in CH3 NH3 PbI3 (MAPbI3 ), CH(NH2 )2 PbI3 (FAPbI3 ), and CsPbI3 . Its formation time is independent of temperature between 160 and 295 K. The very similar polaron formation dynamics observed for the three perovskites points to the critical role of the inorganic lattice, rather than the cations, for polaron formation.

Probing femtosecond lattice displacement upon photo-carrier generation in lead halide perovskite

Electronic properties and lattice vibrations are expected to be strongly correlated in metal-halide perovskites, due to the soft fluctuating nature of their crystal lattice. Thus, unveiling electron-phonon coupling dynamics upon ultrafast photoexcitation is necessary for understanding the optoelectronic behavior of the semiconductor. Here, we use impulsive vibrational spectroscopy to reveal vibrational modes of methylammonium lead-bromide perovskite under electronically resonant and non-resonant conditions. We identify two excited state coherent phonons at 89 and 106 cm^-1, whose phases reveal a shift of the potential energy minimum upon ultrafast photocarrier generation. This indicates the transition to a new geometry, reached after approximately 90 fs, and fully equilibrated within the phonons lifetime of about 1 ps. Our results unambiguously prove that these modes drive the crystalline distortion occurring upon photo-excitation, demonstrating the presence of polaronic effects.

Terahertz Emission from Hybrid Perovskites Driven by Ultrafast Charge Separation and Strong Electron-Phonon Coupling

Unusual photophysical properties of organic-inorganic hybrid perovskites have not only enabled exceptional performance in optoelectronic devices, but also led to debates on the nature of charge carriers in these materials. This study makes the first observation of intense terahertz (THz) emission from the hybrid perovskite methylammonium lead iodide (CH₃ NH₃ PbI₃ ) following photoexcitation, enabling an ultrafast probe of charge separation, hot-carrier transport, and carrier-lattice coupling under 1-sun-equivalent illumination conditions. Using this approach, the initial charge separation/transport in the hybrid perovskites is shown to be driven by diffusion and not by surface fields or intrinsic ferroelectricity. Diffusivities of the hot and band-edge carriers along the surface normal direction are calculated by analyzing the emitted THz transients, with direct implications for hot-carrier device applications. Furthermore, photogenerated carriers are found to drive coherent terahertz-frequency lattice distortions, associated with reorganizations of the lead-iodide octahedra as well as coupled vibrations of the organic and inorganic sublattices. This strong and coherent carrier-lattice coupling is resolved on femtosecond timescales and found to be important both for resonant and far-above-gap photoexcitation. This study indicates that ultrafast lattice distortions play a key role in the initial processes associated with charge transport.

Lead halide perovskites: Crystal-liquid duality, phonon glass electron crystals, and large polaron formation

Lead halide perovskites have been demonstrated as high performance materials in solar cells and light-emitting devices. These materials are characterized by coherent band transport expected from crystalline semiconductors, but dielectric responses and phonon dynamics typical of liquids. This "crystal-liquid" duality implies that lead halide perovskites belong to phonon glass electron crystals, a class of materials believed to make the most efficient thermoelectrics. We show that the crystal-liquid duality and the resulting dielectric response are responsible for large polaron formation and screening of charge carriers, leading to defect tolerance, moderate charge carrier mobility, and radiative recombination properties. Large polaron formation, along with the phonon glass character, may also explain the marked reduction in hot carrier cooling rates in these materials.

Cation Effect on Hot Carrier Cooling in Halide Perovskite Materials

Organic-inorganic lead-halide perovskites have received a revival of interest in the past few years as a promising class of materials for photovoltaic applications. Despite recent extensive research, the role of cations in defining the high photovoltaic performance of these materials is not fully understood. Here, we conduct nonadiabatic molecular dynamics simulations to study and compare nonradiative hot carrier relaxation in three lead-halide perovskite materials: CH₃NH₃PbI₃, HC(NH₂)₂PbI₃, and CsPbI₃. It is found that the relaxation of hot carriers to the band edges occurs on the ultrafast time scale and displays a strong quantitative dependence on the nature of the cations. The obtained results are explained in terms of electron-phonon couplings, which are strongly affected by the atomic displacements in the Pb-I framework triggered by the cation dynamics.

Large polarons in lead halide perovskites

Lead halide perovskites show marked defect tolerance responsible for their excellent optoelectronic properties. These properties might be explained by the formation of large polarons, but how they are formed and whether organic cations are essential remain open questions. We provide a direct time domain view of large polaron formation in single-crystal lead bromide perovskites CH₃NH₃PbBr₃ and CsPbBr₃. We found that large polaron forms predominantly from the deformation of the PbBr₃^- frameworks, irrespective of the cation type. The difference lies in the polaron formation time, which, in CH₃NH₃PbBr₃ (0.3 ps), is less than half of that in CsPbBr₃ (0.7 ps). First-principles calculations confirm large polaron formation, identify the Pb-Br-Pb deformation modes as responsible, and explain quantitatively the rate difference between CH₃NH₃PbBr₃ and CsPbBr₃. The findings reveal the general advantage of the soft [PbX₃]^- sublattice in charge carrier protection and suggest that there is likely no mechanistic limitations in using all-inorganic or mixed-cation lead halide perovskites to overcome instability problems and to tune the balance between charge carrier protection and mobility.