How Lattice and Charge Fluctuations Control Carrier Dynamics in Halide Perovskites

Polaronic Mass Enhancement and Polaronic Excitons in Metal Halide Perovskites

In metal halide perovskites, the complex dielectric screening together with low energy of phonon modes leads to non-negligible Fröhlich coupling. While this feature of perovskites has already been used to explain some of the puzzling aspects of carrier transport in these materials, the possible impact of polaronic effects on the optical response, especially excitonic properties, is much less explored. Here, with the use of magneto-optical spectroscopy, we revealed the non-hydrogenic character of the excitons in metal halide perovskites, resulting from the pronounced Fröhlich coupling. Our results can be well described by the polaronic-exciton picture where electron and hole interactions are no longer described by a Coulomb potential. Furthermore, we show experimental evidence that the carrier-phonon interaction leads to the enhancement of the carrier's effective mass. Notably, our measurements reveal a pronounced temperature dependence of the carrier's effective mass, which we attribute to a band structure renormalization induced by the population of low-energy phonon modes. This interpretation finds support in our first-principles calculations.

Disentangling the effects of structure and lone-pair electrons in the lattice dynamics of halide perovskites

Halide perovskites show great optoelectronic performance, but their favorable properties are paired with unusually strong anharmonicity. It was proposed that this combination derives from the ns2 electron configuration of octahedral cations and associated pseudo-Jahn-Teller effect. We show that such cations are not a prerequisite for the strong anharmonicity and low-energy lattice dynamics encountered in these materials. We combine X-ray diffraction, infrared and Raman spectroscopies, and molecular dynamics to contrast the lattice dynamics of CsSrBr3 with those of CsPbBr3, two compounds that are structurally similar but with the former lacking ns2 cations with the propensity to form electron lone pairs. We exploit low-frequency diffusive Raman scattering, nominally symmetry-forbidden in the cubic phase, as a fingerprint of anharmonicity and reveal that low-frequency tilting occurs irrespective of octahedral cation electron configuration. This highlights the role of structure in perovskite lattice dynamics, providing design rules for the emerging class of soft perovskite semiconductors.

Exciton polaron formation and hot-carrier relaxation in rigid Dion-Jacobson-type two-dimensional perovskites

The efficiency of two-dimensional Dion-Jacobson-type materials relies on the complex interplay between electronic and lattice dynamics; however, questions remain about the functional role of exciton-phonon interactions. Here we establish the robust polaronic nature of the excitons in these materials at room temperature by combining ultrafast spectroscopy and electronic structure calculations. We show that polaronic distortion is associated with low-frequency (30-60 cm-1) lead iodide octahedral lattice motions. More importantly, we discover how targeted ligand modification of this two-dimensional perovskite structure manipulates exciton-phonon coupling, exciton polaron population and carrier cooling. At high excitation density, stronger exciton-phonon coupling increases the hot-carrier lifetime, forming a hot-phonon bottleneck. Our study provides detailed insight into the exciton-phonon coupling and its role in carrier cooling in two-dimensional perovskites relevant for developing emerging hybrid semiconductor materials with tailored properties.

2D Hybrid Perovskites: From Static and Dynamic Structures to Potential Applications

2D perovskites have received great attention recently due to their structural tunability and environmental stability, making them highly promising candidates for various applications by breaking property bottlenecks that affect established materials. However, in 2D perovskites, the complicated interplay between organic spacers and inorganic slabs makes structural analysis challenging to interpret. A deeper understanding of the structure-property relationship in these systems is urgently needed to enable high-performance tunable optoelectronic devices. Herein, this study examines how structural changes, from constant lattice distortion and variable structural evolution, modeled with both static and dynamic structural descriptors, affect macroscopic properties and ultimately device performance. The effect of chemical composition, crystallographic inhomogeneity, and mechanical-stress-induced static structural changes and corresponding electronic band variations is reported. In addition, the structure dynamics are described from the viewpoint of anharmonic vibrations, which impact electron-phonon coupling and the carriers' dynamic processes. Correlated carrier-matter interactions, known as polarons and acting on fine electronic structures, are then discussed. Finally, reliable guidelines to facilitate design to exploit structural features and rationally achieve breakthroughs in 2D perovskite applications are proposed. This review provides a global structural landscape of 2D perovskites, expected to promote the prosperity of these materials in emerging device applications.

Optically Triggered Emergent Mesostructures in Monolayer WS2

The ultrahigh surface area of two-dimensional materials can drive multimodal coupling between optical, electrical, and mechanical properties that leads to emergent dynamical responses not possible in three-dimensional systems. We observed that optical excitation of the WS2 monolayer above the exciton energy creates symmetrically patterned mechanical protrusions which can be controlled by laser intensity and wavelength. This observed photostrictive behavior is attributed to lattice expansion due to the formation of polarons, which are charge carriers dressed by lattice vibrations. Scanning Kelvin probe force microscopy measurements and density functional theory calculations reveal unconventional charge transport properties such as the spatially and optical intensity-dependent conversion in the WS2 monolayer from apparent n- to p-type and the subsequent formation of effective p-n junctions at the boundaries between regions with different defect densities. The strong opto-electrical-mechanical coupling in the WS2 monolayer reveals previously unexplored properties, which can lead to new applications in optically driven ultrathin microactuators.

Phase Transitions and Dynamics in Mixed Three- and Low-Dimensional Lead Halide Perovskites

Lead halide perovskites are extensively investigated as efficient solution-processable materials for photovoltaic applications. The greatest stability and performance of these compounds are achieved by mixing different ions at all three sites of the APbX3 structure. Despite the extensive use of mixed lead halide perovskites in photovoltaic devices, a detailed and systematic understanding of the mixing-induced effects on the structural and dynamic aspects of these materials is still lacking. The goal of this review is to summarize the current state of knowledge on mixing effects on the structural phase transitions, crystal symmetry, cation and lattice dynamics, and phase diagrams of three- and low-dimensional lead halide perovskites. This review analyzes different mixing recipes and ingredients providing a comprehensive picture of mixing effects and their relation to the attractive properties of these materials.

Self-energy correction and numerical simulation for efficient lead-free double perovskite solar cells

Inorganic double perovskites have garnered significant attention due to their desirable characteristics, such as low-toxicity, stability and long charge-carrier lifetimes. However, most double perovskites, especially Cs2AgBiBr6, have wide bandgaps, which limits power conversion efficiencies. In this work, through the first principles method corrected by self-energy, we investigate the mechanical, electric and optical properties of Cs2B'B''Br6 (B' = Ag, Au, Cu; B'' = Bi, Al, Sb, In). Based on performance screening, three kinds of materials with good toughness, high carrier mobility and wide visible-light absorption (around 105 cm-1) are obtained, which are compared with Cs2AgBiBr6. Meanwhile, we use a SACPS-1D simulation to design lead-free double perovskites with excellent properties suitable for photovoltaic solar cell devices, which are made into a planar perovskite heterojunction. Ultimately, the optimal structure is determined to be FTO/WS2/Cs2CuBiBr6/spiro-OMeTAD/Ag, which achieves a power conversion efficiency of 14.08%, surpassing the conventional structure efficiency of 6.1%. It provides valuable guidance for the structure design of a lead-free double perovskite device and offers new insights into the development of optoelectronic devices for solar energy utilization.

Excitonic Polarons and Self-Trapped Excitons from First-Principles Exciton-Phonon Couplings

Excitons consist of electrons and holes held together by their attractive Coulomb interaction. Although excitons are neutral excitations, spatial fluctuations in their charge density couple with the ions of the crystal lattice. This coupling can lower the exciton energy and lead to the formation of a localized excitonic polaron or even a self-trapped exciton in the presence of strong exciton-phonon interactions. Here, we develop a theoretical and computational approach to compute excitonic polarons and self-trapped excitons from first principles. Our methodology combines the many-body Bethe-Salpeter approach with density-functional perturbation theory and does not require explicit supercell calculations. As a proof of concept, we demonstrate our method for a compound of the halide perovskite family.

Interlayer Charge Transport in 2D Lead Halide Perovskites from First Principles

We report on the implementation of a versatile projection-operator diabatization approach to calculate electronic coupling integrals in layered periodic systems. The approach is applied to model charge transport across the saturated organic spacers in two-dimensional (2D) lead halide perovskites. The calculations yield out-of-plane charge transfer rates that decay exponentially with the increasing length of the alkyl chain, range from a few nanoseconds to milliseconds, and are supportive of a hopping mechanism. Most importantly, we show that the charge carriers strongly couple to distortions of the Pb-I framework and that accounting for the associated nonlocal dynamic disorder increases the thermally averaged interlayer rates by a few orders of magnitude compared to the frozen-ion 0 K-optimized structure. Our formalism provides the first comprehensive insight into the role of the organic spacer cation on vertical transport in 2D lead halide perovskites and can be readily extended to functional π-conjugated spacers, where we expect the improved energy alignment with the inorganic layout to speed up the charge transfer between the semiconducting layers.

Influence of an Organic Salt-Based Stabilizing Additive on Charge Carrier Dynamics in Triple Cation Perovskite Solar Cells

Besides further improvement in the power conversion efficiency (PCE) of perovskite solar cells (PSC), their long-term stability must also be ensured. Additives such as organic cations with halide counter anions are considered promising candidates to address this challenge, conferring both higher performance and increased stability to perovskite-based devices. Here, a stabilizing additive (N,N-dimethylmethyleneiminium chloride, [Dmmim]Cl) is identified, and its effect on charge carrier mobility and lifetime under thermal stress in triple cation perovskite (Cs0.05 MA0.05 FA0.90 PbI3 ) thin films is investigated. To explore the fundamental mechanisms limiting charge carrier mobility, temperature-dependent microwave conductivity measurements are performed. Different mobility behaviors across two temperature regions are revealed, following the power law Tm , indicating two different dominant scattering mechanisms. The low-temperature region is assigned to charge carrier scattering with polar optical phonons, while a strong decrease in mobility at high temperatures is due to dynamic disorder. The results obtained rationalize the improved stability of the [Dmmim]Cl-doped films and devices compared to the undoped reference samples, by limiting temperature-activated mobile ions and retarding degradation of the perovskite film.

Stacking Arrangement and Orientation of Aromatic Cations Tune Bandgap and Charge Transport of 2D Organic-Inorganic Hybrid Perovskites

Chemical modifications on aromatic spacers of 2D perovskites have been demonstrated to be an effective strategy to simultaneously improve optoelectronic properties and stability. However, its underlying mechanism is poorly understood. By using 2D phenyl-based perovskites ([C6 H5 (CH2 )m NH3 ]2 PbI4 ) as models, the authors have revealed how the chemical nature of aromatic cations tunes the bandgap and charge transport of 2D perovskites by utilizing sum-frequency generation vibrational spectroscopy to determine the stacking arrangement and orientation of aromatic cations. It is found that the antiparallel slip-stack arrangement of phenyl rings between adjacent layers induces an indirect band gap, resulting in anomalous carrier dynamics. Incorporation of the CH2 moiety causes stacking rearrangement of the phenyl ring and thus promotes an indirect to direct bandgap transition. In direct-bandgap perovskites, higher carrier mobility correlates with a larger orientation angle of the phenyl ring. Further optimizing the orientation angle by introducing a para-substituted element in a phenyl ring, higher carrier mobility is obtained. This work highlights the importance of leveraging stacking arrangement and orientation of the aromatic cations to tune the photophysical properties, which opens up an avenue for advancing high-performance 2D perovskites optoelectronics via molecular engineering.

Optically detected magnetic resonance spectroscopic analyses on the role of magnetic ions in colloidal nanocrystals

Incorporating magnetic ions into semiconductor nanocrystals has emerged as a prominent research field for manipulating spin-related properties. The magnetic ions within the host semiconductor experience spin-exchange interactions with photogenerated carriers and are often involved in the recombination routes, stimulating special magneto-optical effects. The current account presents a comparative study, emphasizing the impact of engineering nanostructures and selecting magnetic ions in shaping carrier-magnetic ion interactions. Various host materials, including the II-VI group, halide perovskites, and I-III-VI2 in diverse structural configurations such as core/shell quantum dots, seeded nanorods, and nanoplatelets, incorporated with magnetic ions such as Mn2+, Ni2+, and Cu1+/2+ are highlighted. These materials have recently been investigated by us using state-of-the-art steady-state and transient optically detected magnetic resonance (ODMR) spectroscopy to explore individual spin-dynamics between the photogenerated carriers and magnetic ions and their dependence on morphology, location, crystal composition, and type of the magnetic ion. The information extracted from the analyses of the ODMR spectra in those studies exposes fundamental physical parameters, such as g-factors, exchange coupling constants, and hyperfine interactions, together providing insights into the nature of the carrier (electron, hole, dopant), its local surroundings (isotropic/anisotropic), and spin dynamics. The findings illuminate the importance of ODMR spectroscopy in advancing our understanding of the role of magnetic ions in semiconductor nanocrystals and offer valuable knowledge for designing magnetic materials intended for various spin-related technologies.

Discovery of enhanced lattice dynamics in a single-layered hybrid perovskite

Layered hybrid perovskites exhibit emergent physical properties and exceptional functional performances, but the coexistence of lattice order and structural disorder severely hinders our understanding of these materials. One unsolved problem regards how the lattice dynamics are affected by the dimensional engineering of the inorganic frameworks and their interaction with the molecular moieties. Here, we address this question by using a combination of spontaneous Raman scattering, terahertz spectroscopy, and molecular dynamics simulations. This approach reveals the structural dynamics in and out of equilibrium and provides unexpected observables that differentiate single- and double-layered perovskites. While no distinct vibrational coherence is observed in double-layered perovskites, an off-resonant terahertz pulse can drive a long-lived coherent phonon mode in the single-layered system. This difference highlights the dramatic change in the lattice environment as the dimension is reduced, and the findings pave the way for ultrafast structural engineering and high-speed optical modulators based on layered perovskites.

Synergy of 3D and 2D Perovskites for Durable, Efficient Solar Cells and Beyond

Three-dimensional (3D) organic-inorganic lead halide perovskites have emerged in the past few years as a promising material for low-cost, high-efficiency optoelectronic devices. Spurred by this recent interest, several subclasses of halide perovskites such as two-dimensional (2D) halide perovskites have begun to play a significant role in advancing the fundamental understanding of the structural, chemical, and physical properties of halide perovskites, which are technologically relevant. While the chemistry of these 2D materials is similar to that of the 3D halide perovskites, their layered structure with a hybrid organic-inorganic interface induces new emergent properties that can significantly or sometimes subtly be important. Synergistic properties can be realized in systems that combine different materials exhibiting different dimensionalities by exploiting their intrinsic compatibility. In many cases, the weaknesses of each material can be alleviated in heteroarchitectures. For example, 3D-2D halide perovskites can demonstrate novel behavior that neither material would be capable of separately. This review describes how the structural differences between 3D halide perovskites and 2D halide perovskites give rise to their disparate materials properties, discusses strategies for realizing mixed-dimensional systems of various architectures through solution-processing techniques, and presents a comprehensive outlook for the use of 3D-2D systems in solar cells. Finally, we investigate applications of 3D-2D systems beyond photovoltaics and offer our perspective on mixed-dimensional perovskite systems as semiconductor materials with unrivaled tunability, efficiency, and technologically relevant durability.

Ultrafast imaging of polariton propagation and interactions

Semiconductor excitations can hybridize with cavity photons to form exciton-polaritons (EPs) with remarkable properties, including light-like energy flow combined with matter-like interactions. To fully harness these properties, EPs must retain ballistic, coherent transport despite matter-mediated interactions with lattice phonons. Here we develop a nonlinear momentum-resolved optical approach that directly images EPs in real space on femtosecond scales in a range of polaritonic architectures. We focus our analysis on EP propagation in layered halide perovskite microcavities. We reveal that EP-phonon interactions lead to a large renormalization of EP velocities at high excitonic fractions at room temperature. Despite these strong EP-phonon interactions, ballistic transport is maintained for up to half-exciton EPs, in agreement with quantum simulations of dynamic disorder shielding through light-matter hybridization. Above 50% excitonic character, rapid decoherence leads to diffusive transport. Our work provides a general framework to precisely balance EP coherence, velocity, and nonlinear interactions.

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.

Size-Dependent Lattice Symmetry Breaking Determines the Exciton Fine Structure of Perovskite Nanocrystals

The order of bright and dark excitonic states in lead-halide perovskite nanocrystals is debated. It has been proposed that the Rashba effect, driven by lattice-induced symmetry breaking, causes a bright excitonic ground state. Direct measurements of excitonic spectra, however, show the signatures of a dark ground state, bringing the role of the Rashba effect into question. We use an atomistic theory to model the exciton fine structure of perovskite nanocrystals, accounting for realistic lattice distortions. We calculate optical gaps and excitonic features that compare favorably with experimental works. The exciton fine structure splittings show a nonmonotonic size dependence due to a structural transition between cubic and orthorhombic phases. Additionally, the excitonic ground state is found to be dark with spin triplet character, exhibiting a small Rashba coupling. We additionally explore the effects of nanocrystal shape on the fine structure, clarifying observations on polydisperse nanocrystals.

Lattice disorder influences the photocarrier dynamics in lead halide perovskites

Revealing the structural impact of lead halide perovskites on photocarrier dynamics is essential for the associated solar cells but deficient in experimental visualization. In this study, with femtosecond spectroscopy, we for the first time explored the contribution of the disorder of the distorted PbX₆ octahedrons and A-site cations on the carrier behaviours. It was found that photoinduced carriers recombine almost twice slower and diffuse 20% faster in the disordered, β-phased samples than in the ordered, γ-phased ones. Yet within the same phase, with a similar PbX₆ orientation but various A-site mobility, the carrier diffusion and recombination have no apparent difference. Thus we firmly conclude that lattice disorder effectively influences the carrier dynamics and therein the Pb-X sublattice is worth more than A-site cations, which should inspire future lead halide perovskite design and applications.

Light-Induced Structural Dynamics and Charge Transport in Layered Halide Perovskite Thin Films

The dynamic nature of the metal halide perovskite lattice upon photoexcitation plays a vital role in their properties. Here we report an observation of light-induced structure dynamics in quasi-2D Ruddlesden-Popper phase perovskite thin films and its impact on the carrier transport properties. By a time-resolved X-ray scattering technique, we observe a rapid lattice expansion upon photoexcitation, followed by a slow relaxation over the course of 100 ns in the dark. Theoretical modeling suggests that the expansion originates from the lattice's thermal fluctuations caused by photon energy deposition. Power dependent optical spectroscopy and photoconductivity indicate that high laser powers triggered a strong local structural disorder, which increased the charge dissociation activation energy that results in localized transport. Our study investigates the impact of laser energy deposition on the lattices and the subsequent carrier transport properties, that are relevant to device operations.

Structural Disorder in Higher-Temperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites

Solar cells and optoelectronic devices are exposed to heat that degrades performance. Therefore, elucidating temperature-dependent charge carrier dynamics is essential for device optimization. Charge carrier lifetimes decrease with temperature in conventional semiconductors. The opposite, anomalous trend is observed in some experiments performed with MAPbI₃ (MA = CH₃NH₃⁺) and other metal halide perovskites. Using ab initio quantum dynamics simulation, we establish the atomic mechanisms responsible for nonradiative electron-hole recombination in orthorhombic-, tetragonal-, and cubic MAPbI₃. We demonstrate that structural disorder arising from the phase transitions is as important as the disorder due to heating in the same phase. The carrier lifetimes grow both with increasing temperature in the same phase and upon transition to the higher-temperature phases. The increased lifetime is rationalized by structural disorder that induces partial charge localization, decreases nonadiabatic coupling, and shortens quantum coherence. Inelastic and elastic electron-vibrational interactions exhibit opposite dependence on temperature and phase. The partial disorder and localization arise from thermal motions of both the inorganic lattice and the organic cations and depend significantly on the phase. The structural deformations induced by thermal fluctuations and phase transitions are on the same order as deformations induced by defects, and hence, thermal disorder plays a very important role. Since charge localization increases carrier lifetimes but inhibits transport, an optimal regime maximizing carrier diffusion can be designed, depending on phase, temperature, material morphology, and device architecture. The atomistic mechanisms responsible for the enhanced carrier lifetimes at elevated temperatures provide guidelines for the design of improved solar energy and optoelectronic materials.

Intrinsic Carrier Diffusion in Perovskite Thin Films Uncovered by Transient Reflectance Spectroscopy

Carrier diffusion and surface recombination are key processes influencing the performance of conventional semiconductor devices. However, the interplay of photon recycling together with these processes in halide perovskites obfuscates our understanding. Herein, we discern these inherent processes in a thin FAPbBr₃ perovskite single crystal (PSC) utilizing a unique transient reflectance technique that allows accurate diffusion modeling with clear boundary conditions. Temperature-dependent measurements reveal the coexistence of shallow and deep traps at the surface. The inverse quadratic dependence of temperature on carrier mobility μ suggests an underlying scattering mechanism arising from the anharmonic deformation of the PbBr₆ cage. Our findings ascertain the fundamental limits of the intrinsic surface recombination velocity (S) and carrier diffusion coefficient (D) in PSC samples. Importantly, these insights will help resolve the ongoing debate and clarify the ambiguity surrounding the contributions of photon recycling and carrier diffusion in perovskite optoelectronics.

Renormalization of excitonic properties by polar phonons

We employ quasiparticle path integral molecular dynamics to study how theexcitonic properties of model semiconductors are altered by electron-phononcoupling. We describe ways within a path integral representation of the systemto evaluate the renormalized mass, binding energy, and radiative recombinationrate of excitons in the presence of a fluctuating lattice. To illustrate thisapproach, we consider Fr\"ohlich-type electron-phonon interactions and employan imaginary time influence functional to incorporate phonon-induced effectswithout approximation. The effective mass and binding energies are comparedwith perturbative and variational approaches, which provide qualitativelyconsistent trends. We evaluate electron-hole recombination rates as mediatedthrough both trap-assisted and bimolecular processes, developing a consistentstatistical mechanical approach valid in the reaction limited regime. Thesecalculations demonstrate how phonons screen electron-hole interactions,generically reducing exciton binding energies and increasing their radiativelifetimes.

Transversal Halide Motion Intensifies Band-To-Band Transitions in Halide Perovskites

Despite their puzzling vibrational characteristics that include strong signatures of anharmonicity and thermal disorder already around room temperature, halide perovskites (HaPs) exhibit favorable optoelectronic properties for applications in photovoltaics and beyond. Whether these vibrational properties are advantageous or detrimental to their optoelectronic properties remains, however, an important open question. Here, this issue is addressed by investigation of the finite-temperature optoelectronic properties in the prototypical cubic CsPbBr₃ , using first-principles molecular dynamics based on density-functional theory. It is shown that the dynamic flexibility associated with HaPs enables the so-called transversality, which manifests as a preference for large halide displacements perpendicular to the Pb-Br-Pb bonding axis. The authors find that transversality is concurrent with vibrational anharmonicity and leads to a rapid rise in the joint density of states, which is favorable for photovoltaics since this implies sharp optical absorption profiles. These findings are contrasted to the case of PbTe, a material that shares several key properties with CsPbBr₃ but cannot exhibit any transversality and, hence, is found to exhibit much wider band-edge distributions. The authors conclude that the dynamic structural flexibility in HaPs and their unusual vibrational characteristics might not just be a mere coincidence, but play active roles in establishing their favorable optoelectronic properties.

Probing the Disorder Inside the Cubic Unit Cell of Halide Perovskites from First-Principles

Strong deviations in the finite temperature atomic structure of halide perovskites from their average geometry can have profound impacts on optoelectronic and other device-relevant properties. Detailed mechanistic understandings of these structural fluctuations and their consequences remain, however, limited by the experimental and theoretical challenges involved in characterizing strongly anharmonic vibrational characteristics and their impact on other properties. We overcome some of these challenges by a theoretical characterization of the vibrational interactions that occur among the atoms in the prototypical cubic CsPbBr3. Our investigation based on first-principles molecular dynamics calculations finds that the motions of neighboring Cs-Br atoms interlock, which appears as the most likely Cs-Br distance being significantly shorter than what is inferred from an ideal cubic structure. This form of dynamic Cs-Br coupling coincides with very shallow dynamic potential wells for Br motions that occur across a locally and dynamically disordered energy landscape. We reveal an interesting dynamic coupling mechanism among the atoms within the nominal unit cell of cubic CsPbBr3 and quantify the important local structural fluctuations on an atomic scale.

Diverging Expressions of Anharmonicity in Halide Perovskites

Lead-based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs₂ AgBiBr₆ , has been recently studied as a lead-free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead-based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead-based halide perovskites, the structural dynamics of Cs₂ AgBiBr₆ are investigated and are compared to its lead-based analog, CsPbBr₃ . Using temperature-dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs₂ AgBiBr₆ has well-defined normal modes throughout the measured temperature range, while CsPbBr₃ exhibits a complete breakdown of the normal-mode picture above 200 K. It is suggested that the breakdown of the normal-mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs₂ AgBiBr₆ is also discovered below ≈37 K.

Nonlocal Screening Dictates the Radiative Lifetimes of Excitations in Lead Halide Perovskites

We use path integral molecular dynamics simulations and theory to elucidate the interactions between charge carriers, as mediated by a lead halide perovskite lattice. We find that the charge-lattice coupling of MAPbI₃ results in a repulsive interaction between electrons and holes at intermediate distances. The effective interaction is understood using a Gaussian field theory, whereby the underlying soft, polar lattice contributes a nonlocal screening between quasiparticles. Path integral calculations of this nonlocal screening model are used to rationalize the small exciton binding energy and low radiative recombination rate observed experimentally and are compared to traditional Wannier-Mott and Fröhlich models, which fail to do so. These results clarify the origin of the high power conversion efficiencies in lead halide perovskites. Emergent repulsive electron-hole interactions provide a design principle for optimizing soft, polar semiconductors.

Photo-induced enhancement of lattice fluctuations in metal-halide perovskites

The optoelectronic properties of metal-halide perovskites (MHPs) are affected by lattice fluctuations. Using ultrafast pump-probe spectroscopy, we demonstrate that in state-of-the-art mixed-cation MHPs ultrafast photo-induced bandgap narrowing occurs with a linear to super-linear dependence on the excited carrier density ranging from 10¹⁷ cm^-3 to above 10¹⁸ cm^-3. Time-domain terahertz spectroscopy reveals carrier localization increases with carrier density. Both observations, the anomalous dependence of the bandgap narrowing and the increased carrier localization can be rationalized by photo-induced lattice fluctuations. The magnitude of the photo-induced lattice fluctuations depends on the intrinsic instability of the MHP lattice. Our findings provide insight into ultrafast processes in MHPs following photoexcitation and thus help to develop a concise picture of the ultrafast photophysics of this important class of emerging semiconductors.

Peculiar anharmonicity of Ruddlesden Popper metal halides: temperature-dependent phonon dephasing

The anharmonicity of the Ruddlesden Popper metal-halide lattice, and its consequences for their electronic and optical properties, are paramount in their basic semiconductor physics. It is thus critical to identify specific anharmonic optical phonons that govern their photophysics. Here, we address the nature of phonon-phonon scattering probabilities of the resonantly excited optical phonons that dress the electronic transitions in these materials. Based on the temperature dependence of the coherent phonon lifetimes, we isolate the dominant anharmonic phonon and quantify its phonon-phonon interaction strength. Intriguingly, we also observe that the anharmonicity is distinct for different phonons, with a few select modes exhibiting temperature-independent coherence lifetimes, indicating their predominantly harmonic nature. However, the population and dephasing dynamics of excitons are dominated by the anharmonic phonon.

Two-dimensional overdamped fluctuations of the soft perovskite lattice in CsPbBr3

Lead halide perovskites exhibit structural instabilities and large atomic fluctuations thought to impact their optical and thermal properties, yet detailed structural and temporal correlations of their atomic motions remain poorly understood. Here, these correlations are resolved in CsPbBr₃ crystals using momentum-resolved neutron and X-ray scattering measurements as a function of temperature, complemented with first-principles simulations. We uncover a striking network of diffuse scattering rods, arising from the liquid-like damping of low-energy Br-dominated phonons, reproduced in our simulations of the anharmonic phonon self-energy. These overdamped modes cover a continuum of wave vectors along the edges of the cubic Brillouin zone, corresponding to two-dimensional sheets of correlated rotations in real space, and could represent precursors to proposed two-dimensional polarons. Further, these motions directly impact the electronic gap edge states, linking soft anharmonic lattice dynamics and optoelectronic properties. These results provide insights into the highly unusual atomic dynamics of halide perovskites, relevant to further optimization of their optical and thermal properties.

Strongly Anharmonic Octahedral Tilting in Two-Dimensional Hybrid Halide Perovskites

Recent investigations of two-dimensional (2D) hybrid organic-inorganic halide perovskites (HHPs) indicate that their optical and electronic properties are dominated by strong coupling to thermal fluctuations. While the optical properties of 2D-HHPs have been extensively studied, a comprehensive understanding of electron-phonon interactions is limited because little is known about their structural dynamics. This is partially because the unit cells of 2D-HHPs contain many atoms. Therefore, the thermal fluctuations are complex and difficult to elucidate in detail. To overcome this challenge, we use polarization-orientation Raman spectroscopy and ab initio calculations to compare the structural dynamics of the prototypical 2D-HHPs [(BA)2PbI4 and (PhE)2PbI4] to their three-dimensional (3D) counterpart, MAPbI3. Comparison to the simpler, 3D MAPbI3 crystal shows clear similarities with the structural dynamics of (BA)2PbI4 and (PhE)2PbI4 across a wide temperature range. The analogy between the 3D and 2D crystals allows us to isolate the effect of the organic cation on the structural dynamics of the inorganic scaffold of the 2D-HHPs. Furthermore, using this approach, we uncover the mechanism of the order-disorder phase transition of (BA)2PbI4 (274 K) and show that it involves relaxation of octahedral tilting coupled to anharmonic thermal fluctuations. These anharmonic fluctuations are important because they induce charge carrier localization and affect the optoelectronic performance of these materials.

Ab initio nonadiabatic molecular dynamics of charge carriers in metal halide perovskites

Photoinduced nonequilibrium processes in nanoscale materials play key roles in photovoltaic and photocatalytic applications. This review summarizes recent theoretical investigations of excited state dynamics in metal halide perovskites (MHPs), carried out using a state-of-the-art methodology combining nonadiabatic molecular dynamics with real-time time-dependent density functional theory. The simulations allow one to study evolution of charge carriers at the ab initio level and in the time-domain, in direct connection with time-resolved spectroscopy experiments. Eliminating the need for the common approximations, such as harmonic phonons, a choice of the reaction coordinate, weak electron-phonon coupling, a particular kinetic mechanism, and perturbative calculation of rate constants, we model full-dimensional quantum dynamics of electrons coupled to semiclassical vibrations. We study realistic aspects of material composition and structure and their influence on various nonequilibrium processes, including nonradiative trapping and relaxation of charge carriers, hot carrier cooling and luminescence, Auger-type charge-charge scattering, multiple excitons generation and recombination, charge and energy transfer between donor and acceptor materials, and charge recombination inside individual materials and across donor/acceptor interfaces. These phenomena are illustrated with representative materials and interfaces. Focus is placed on response to external perturbations, formation of point defects and their passivation, mixed stoichiometries, dopants, grain boundaries, and interfaces of MHPs with charge transport layers, and quantum confinement. In addition to bulk materials, perovskite quantum dots and 2D perovskites with different layer and spacer cation structures, edge passivation, and dielectric screening are discussed. The atomistic insights into excited state dynamics under realistic conditions provide the fundamental understanding needed for design of advanced solar energy and optoelectronic devices.

Vibrational relaxation dynamics in layered perovskite quantum wells

Organic-inorganic layered perovskites, or Ruddlesden-Popper perovskites, are two-dimensional quantum wells with layers of lead-halide octahedra stacked between organic ligand barriers. The combination of their dielectric confinement and ionic sublattice results in excitonic excitations with substantial binding energies that are strongly coupled to the surrounding soft, polar lattice. However, the ligand environment in layered perovskites can significantly alter their optical properties due to the complex dynamic disorder of the soft perovskite lattice. Here, we infer dynamic disorder through phonon dephasing lifetimes initiated by resonant impulsive stimulated Raman photoexcitation followed by transient absorption probing for a variety of ligand substitutions. We demonstrate that vibrational relaxation in layered perovskite formed from flexible alkyl-amines as organic barriers is fast and relatively independent of the lattice temperature. Relaxation in layered perovskites spaced by aromatic amines is slower, although still fast relative to bulk inorganic lead bromide lattices, with a rate that is temperature dependent. Using molecular dynamics simulations, we explain the fast rates of relaxation by quantifying the large anharmonic coupling of the optical modes with the ligand layers and rationalize the temperature independence due to their amorphous packing. This work provides a molecular and time-domain depiction of the relaxation of nascent optical excitations and opens opportunities to understand how they couple to the complex layered perovskite lattice, elucidating design principles for optoelectronic devices.

A reciprocal-space formulation of mixed quantum-classical dynamics

We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.

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.

Simulations of Trions and Biexcitons in Layered Hybrid Organic-Inorganic Lead Halide Perovskites

Behaving like atomically precise two-dimensional quantum wells with non-negligible dielectric contrast, the layered hybrid organic-inorganic lead halide perovskites (HOIPs) have strong electronic interactions leading to tightly bound excitons with binding energies on the order of 500 meV. These strong interactions suggest the possibility of larger excitonic complexes like trions and biexcitons, which are hard to study numerically due to the complexity of the layered HOIPs. Here, we propose and parametrize a model Hamiltonian for excitonic complexes in layered HOIPs and we study the correlated eigenfunctions of trions and biexcitons using a combination of diffusion Monte Carlo and very large variational calculations with explicitly correlated Gaussian basis functions. Binding energies and spatial structures of these complexes are presented as a function of the layer thickness. The trion and biexciton of the thinnest layered HOIP have binding energies of 35 and 44 meV, respectively, whereas a single exfoliated layer is predicted to have trions and biexcitons with equal binding energies of 48 meV. We compare our findings to available experimental data and to that of other quasi-two-dimensional materials.

Charge-Carrier Mobility and Localization in Semiconducting Cu2AgBiI6 for Photovoltaic Applications

Lead-free silver-bismuth semiconductors have become increasingly popular materials for optoelectronic applications, building upon the success of lead halide perovskites. In these materials, charge-lattice couplings fundamentally determine charge transport, critically affecting device performance. In this study, we investigate the optoelectronic properties of the recently discovered lead-free semiconductor Cu₂AgBiI₆ using temperature-dependent photoluminescence, absorption, and optical-pump terahertz-probe spectroscopy. We report ultrafast charge-carrier localization effects, evident from sharp THz photoconductivity decays occurring within a few picoseconds after excitation and a rise in intensity with decreasing temperature of long-lived, highly Stokes-shifted photoluminescence. We conclude that charge carriers in Cu₂AgBiI₆ are subject to strong charge-lattice coupling. However, such small polarons still exhibit mobilities in excess of 1 cm² V^-1 s^-1 at room temperature because of low energetic barriers to formation and transport. Together with a low exciton binding energy of ∼29 meV and a direct band gap near 2.1 eV, these findings highlight Cu₂AgBiI₆ as an attractive lead-free material for photovoltaic applications.

Limits to Electrical Mobility in Lead-Halide Perovskite Semiconductors

Semiconducting polycrystalline thin films are cheap to produce and can be deposited on flexible substrates, yet high-performance electronic devices usually utilize single-crystal semiconductors, owing to their superior charge-carrier mobilities and longer diffusion lengths. Here we show that the electrical performance of polycrystalline films of metal-halide perovskites (MHPs) approaches that of single crystals at room temperature. Combining temperature-dependent terahertz conductivity measurements and ab initio calculations we uncover a complete picture of the origins of charge-carrier scattering in single crystals and polycrystalline films of CH₃NH₃PbI₃. We show that Fröhlich scattering of charge carriers with multiple phonon modes is the dominant mechanism limiting mobility, with grain-boundary scattering further reducing mobility in polycrystalline films. We reconcile the large discrepancy in charge-carrier diffusion lengths between single crystals and films by considering photon reabsorption. Thus, polycrystalline films of MHPs offer great promise for devices beyond solar cells, including light-emitting diodes and modulators.

Fast and Anomalous Exciton Diffusion in Two-Dimensional Hybrid Perovskites

Two-dimensional hybrid perovskites are currently in the spotlight of condensed matter and nanotechnology research due to their intriguing optoelectronic and vibrational properties with emerging potential for light-harvesting and light-emitting applications. While it is known that these natural quantum wells host tightly bound excitons, the mobilities of these fundamental optical excitations at the heart of the optoelectronic applications are barely explored. Here, we directly monitor the diffusion of excitons through ultrafast emission microscopy from liquid helium to room temperature in hBN-encapsulated two-dimensional hybrid perovskites. We find very fast diffusion with characteristic hallmarks of free exciton propagation for all temperatures above 50 K. In the cryogenic regime, we observe nonlinear, anomalous behavior with an exceptionally rapid expansion of the exciton cloud followed by a very slow and even negative effective diffusion. We discuss our findings in view of efficient exciton-phonon coupling, highlighting two-dimensional hybrids as promising platforms for basic research and optoelectronic applications.

Structurally Tunable Two-Dimensional Layered Perovskites: From Confinement and Enhanced Charge Transport to Prolonged Hot Carrier Cooling Dynamics

Two-dimensional (2D) layered metal halide perovskites are potential alternatives to three-dimensional perovskites in optoelectronic applications owing to their improved photostabilities and chemical stabilities. Recent investigations of 2D metal halide perovskites have demonstrated interesting optical and electronic properties of various structures that are controlled by their elemental composition and organic spacers. However, photovoltaic devices that utilize 2D perovskites suffer from poor device efficiency due to inefficient charge carrier separation and extraction. In this Perspective, we shed light on confinement control and structural variation strategies that provide better parameters for the efficient collection of charges. The influence of these strategies on the exciton binding energies, charge-carrier mobilities, hot-carrier dynamics, and electron-phonon coupling in 2D perovskites is thoroughly discussed; these parameters highlight unique opportunities for further system optimization. Beyond the tunability of these fundamental parameters, we conclude this Perspective with the most notable strategies for attaining 2D perovskites with reduced bandgaps to better suit photovoltaic applications.

Polaron transport in hybrid CH3NH3PbI3 perovskite thin films

A comprehensive study of the transport properties of a prototypical CH3NH3PbI3 thin film is presented. The polaron-longitudinal optical (LO) phonon scattering mechanism, based on Low-Pines's polaron mobility, was studied to elucidate the charge-carrier mobility. We found that the calculated mobilities showed very good quantitative agreement with the experimental data measured in thin film samples using photoconductivity techniques. In THz mobility, the calculated results yielded room-temperature (RT) mobilities of ∼650 cm2 V-1 s-1 (single crystal) and ∼220 cm2 V-1 s-1 (disordered thin film) at a low quantum yield (φ) and 32 cm2 V-1 s-1 (high-quality thin film) at φ = 1. The dynamic disorder due to organic reorientation was included in the calculations. Its effect provided a power law mobility of μ ∝ Tm and satisfactorily supported temperature-dependent mobility over the temperature range of 80-370 K. In the orthorhombic and tetragonal phases, the charge-carrier mobilities with dynamic disorder were approximately 47% and 22% lower than those obtained from phases without dynamic disorder. The RT mobility was 26 cm2 V-1 s-1 at φ = 1. In the low-temperature orthorhombic phase, the structural phase transition was considered. The mobility followed a power law with m = -1.7. In the tetragonal and cubic phases, the mobility also followed a power law, but with m = -1.1, which is an intermediate range in optical phonon scattering. When combined with recent theoretical analysis, we also found three limitations of power law mobility with exponents between -0.46 and -1.1 for polaron-LO phonon scattering, -1.2 and -1.6 for bare carrier-LO phonon scattering, and -1.7 and -2.0 for carrier scattering off optical phonons and lattice fluctuations. This work not only provides a description of temperature-dependent mobility in CH3NH3PbI3 thin films, but also gives new insights into THz photoconductivity and the relationship between LO phonon scattering and power law mobility.

Photoinduced phase separation in the lead halides is a polaronic effect

We present a perspective on recent observations of the photoinduced phase separation of halides in multi-component lead-halide perovskites. The spontaneous phase separation of an initial homogeneous solid solution under steady-state illumination conditions is found experimentally to be reversible, stochastic, weakly dependent on morphology, yet strongly dependent on composition and thermodynamic state. Regions enriched in a specific halide species that form upon phase separation are self-limiting in size, pinned to specific compositions, and grow in number in proportion to the steady-state carrier concentration until saturation. These empirical observations of robustness rule out explanations based on specific defect structures and point to the local modulation of an existing miscibility phase transition in the presence of excess charge carriers. A model for rationalizing existing observations based on the coupling between composition, strain, and charge density fluctuations through the formation of polarons is reviewed.

Does Dipolar Motion of Organic Cations Affect Polaron Dynamics and Bimolecular Recombination in Halide Perovskites?

The role of dipolar motion of organic cations in the A-sites of halide perovskites has been debated in an effort to understand why these materials possess such remarkable properties. Here, we show that the dipolar motion of cations such as methylammonium (MA) or formamidinium (FA) versus cesium (Cs) does not influence large polaron binding energies, delocalization lengths, formation times, or bimolecular recombination lifetimes in lead bromide perovskites containing only one type of A-site cation. We directly probe the transient absorption spectra of large polarons throughout the entire mid-infrared and resolve their dynamics on time scales from sub-100 fs to sub-μs using time-resolved mid-infrared spectroscopy. Our findings suggest that the improved optoelectronic properties reported of halide perovskites with mixed A-site cations may result from synergy among the cations and how their mixture modulates the structure and dynamics of the inorganic lattice rather than from the dipolar properties of the cations themselves.

Optoelectronic Properties of Two-Dimensional Bromide Perovskites: Influences of Spacer Cations

Two-dimensional (2D) halide perovskites have displayed unique emission properties, making them potential candidates for next-generation light-emitting devices. Here, we combine nonadiabatic molecular dynamics and time-domain density functional theory to investigate the fundamental mechanisms of carrier recombination processes. Considering monolayer bromide perovskites with dissimilar organic spacer molecules, n-butylammonium (BA) and phenylethylammonium (PEA) cations, we find a strong correlation between temperature-induced structural fluctuations and nonradiative carrier recombination rates in these materials. The more flexible geometry of (BA)₂PbBr₄ compared to that of (PEA)₂PbBr₄, results in faster electron-hole recombination and shorter carrier lifetime, diminishing the photoluminescence quantum yield for softer 2D perovskites. Reduced structural fluctuations in relatively rigid (PEA)₂PbBr₄ not only indicate of a longer carrier lifetime but also suggest a narrower emission line width, implying a higher purity of the emitted light. Our ab initio modeling of excited state properties in 2D perovskites conveys material designing strategies to fine-tune perovskite emissions for solid-state lighting applications.

Temperature and Gate Dependence of Carrier Diffusion in Single Crystal Methylammonium Lead Iodide Perovskite Microstructures

We investigate temperature-dependent photogenerated carrier diffusion in single-crystal methylammonium lead iodide microstuctures via scanning photocurrent microscopy. Carrier diffusion lengths increased abruptly across the tetragonal to orthorhombic phase transition and reached 200 ± 50 μm at 80 K. In combination with the microsecond carrier lifetime measured by a transient photocurrent method, an enormous carrier mobility value of 3 × 10⁴ cm²/V s was extracted at 80 K. The observed highly nonlocal photocurrent and the rapid increase of the carrier diffusion length at low temperatures can be understood by the formation and efficient transport of free excitons in the orthorhombic phase as a result of reduced optical phonon scattering due to the dipolar nature of the excitons. Carrier diffusion lengths were tuned by a factor of 8 by gate voltage and increased with increasing majority carrier (electron) concentration, consistent with the exciton model.

Optical Properties of Layered Hybrid Organic-Inorganic Halide Perovskites: A Tight-Binding GW-BSE Study

We present a many-body calculation of the band structure and optical spectrum of the layered hybrid organic-inorganic halide perovskites in the Ruddlesden-Popper phase with the general formula A₂^'A_n-1M_nX_3n+1, where n controls the thickness of the primarily inorganic perovskite layers. We calculate the mean-field band structure with spin-orbit coupling, quasi-particle corrections within the GW approximation, and optical spectra using the Bethe-Salpeter equation. The model is parametrized by first-principles calculations and classical electrostatic screening, enabling an accurate but cost-effective study of large unit cells and corresponding n-dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing n, and the nonhydrogenic character of the excitonic Rydberg series is analyzed. For methylammonium lead iodide perovskites with butylammonium spacers, our n-dependent 1s and 2s exciton energy levels are in good agreement with those from recently reported experiments, and the 1s exciton binding energy is calculated to be 302 meV for n = 1, 97 meV for n = 5, and 37 meV for n = ∞ (bulk MAPbI₃). A calculation for an exfoliated n = 1 bilayer predicts a very large 1s exciton binding energy of 444 meV.

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.

High open-circuit voltages in lead-halide perovskite solar cells: experiment, theory and open questions

One of the most significant features of lead-halide perovskites is their ability to have comparably slow recombination despite the fact that these materials are mostly processed from solution at room temperature. The slow recombination allows achieving high open-circuit voltages when the lead-halide perovskite layers are used in solar cells. This perspective discusses the state of the art of our understanding and of experimental data with regard to recombination and open-circuit voltages in lead-halide perovskites. A special focus is put onto open questions that the community has to tackle to design future photovoltaic and optoelectronic devices based on lead-halide perovskites and other semiconductors with similar properties. This article is part of a discussion meeting issue 'Energy materials for a low carbon future'.

Breakdown of the Static Picture of Defect Energetics in Halide Perovskites: The Case of the Br Vacancy in CsPbBr3

We consider the Br vacancy in CsPbBr₃ as a prototype for the impact of structural dynamics on defect energetics in halide perovskites (HaPs). Using first-principles molecular dynamics based on density functional theory, we find that the static picture of defect energetics breaks down; the energy level associated with a Br vacancy is found to be intrinsically dynamic, oscillating by as much as 1 eV on the picosecond time scale at room temperature. These significant energy fluctuations are correlated with the distance between the neighboring Pb atoms across the vacancy and with the electrostatic potential at these Pb atomic sites. We expect this unusually strong coupling of structural dynamics and defect energetics to bear important implications for both experimental and theoretical analyses of defect characteristics in HaPs. It may also hold significant ramifications for carrier transport and defect tolerance in this class of photovoltaic materials.