Exciton Fine Structure in Perovskite Nanocrystals

Measuring Exciton Fine-Structure in Randomly Oriented Perovskite Nanocrystal Ensembles Using Nonlinear Optical Spectroscopy: Theory

Lead halide perovskite nanocrystals (PNCs) exhibit unique optoelectronic properties, many of which originate from a purported bright-triplet exciton fine-structure. A major impediment to measuring this fine-structure is inhomogeneous spectral broadening, which has limited most experimental studies to single-nanocrystal spectroscopies. It is shown here that the linearly polarized single-particle selection rules in PNCs are preserved in nonlinear spectroscopies of randomly oriented ensembles. Simulations incorporating rotational averaging demonstrate that techniques such as transient absorption and two-dimensional coherent spectroscopy are capable of resolving exciton fine-structure in PNCs, even in the presence of inhomogeneous broadening and orientation disorder.

Morphological Control of 2D Hybrid Organic-Inorganic Semiconductor AgSePh

Silver phenylselenolate (AgSePh) is a hybrid organic-inorganic two-dimensional (2D) semiconductor exhibiting narrow blue emission, in-plane anisotropy, and large exciton binding energy. Here, we show that the addition of carefully chosen solvent vapors during the chemical transformation of metallic silver to AgSePh allows for control over the size and orientation of AgSePh crystals. By testing 28 solvent vapors (with different polarities, boiling points, and functional groups), we controlled the resulting crystal size from <200 nm up to a few μm. Furthermore, choice of solvent vapor can substantially improve the orientational homogeneity of 2D crystals with respect to the substrate. In particular, solvents known to form complexes with silver ions, such as dimethyl sulfoxide (DMSO), led to the largest lateral crystal dimensions and parallel crystal orientation. We perform systematic optical and electrical characterizations on DMSO vapor-grown AgSePh films demonstrating improved crystalline quality, lower defect densities, higher photoconductivity, lower dark conductivity, suppression of ionic migration, and reduced midgap photoluminescence at low temperature. Overall, this work provides a strategy for realizing AgSePh films with improved optical properties and reveals the roles of solvent vapors on the chemical transformation of metallic silver.

Dark and Bright Excitons in Halide Perovskite Nanoplatelets

Semiconductor nanoplatelets (NPLs), with their large exciton binding energy, narrow photoluminescence (PL), and absence of dielectric screening for photons emitted normal to the NPL surface, could be expected to become the fastest luminophores amongst all colloidal nanostructures. However, super-fast emission is suppressed by a dark (optically passive) exciton ground state, substantially split from a higher-lying bright (optically active) state. Here, the exciton fine structure in 2-8 monolayer (ML) thick Csn - 1 Pbn Br3n + 1 NPLs is revealed by merging temperature-resolved PL spectra and time-resolved PL decay with an effective mass model taking quantum confinement and dielectric confinement anisotropy into account. This approach exposes a thickness-dependent bright-dark exciton splitting reaching 32.3 meV for the 2 ML NPLs. The model also reveals a 5-16 meV splitting of the bright exciton states with transition dipoles polarized parallel and perpendicular to the NPL surfaces, the order of which is reversed for the thinnest NPLs, as confirmed by TR-PL measurements. Accordingly, the individual bright states must be taken into account, while the dark exciton state strongly affects the optical properties of the thinnest NPLs even at room temperature. Significantly, the derived model can be generalized for any isotropically or anisotropically confined nanostructure.

Evaluating Lead Halide Perovskite Nanocrystals as a Spin Laser Gain Medium

Spin-polarized charge endows conventional lasers with not only new functionalities but also reduced lasing thresholds thanks to the lifting of spin degeneracy. II-VI and III-V semiconductors have been extensively investigated as spin laser gain mediums; however, the degree of polarization is limited by the light hole and heavy hole degeneracy. Herein, we evaluate the potential of CsPbBr₃ nanocrystals─ones that are featured with low band-edge degeneracy and therefore a high degree of polarization as a result of inverted band structure and large spin-orbit coupling─as a gain medium for spin lasers. Our experiment and numerical modeling results reveal that, within the spin relaxation lifetime, the optical gain threshold can be depressed by polarizing the charge using circularly polarized photoexcitation. However, prolonging the spin relaxation lifetime is required to realize a spin laser.

On the optical anisotropy in 2D metal-halide perovskites

Two-dimensional metal-halide perovskites (MHPs) are versatile solution-processed organic/inorganic quantum wells where the structural anisotropy creates profound anisotropy in their electronic and excitonic properties and associated optical constants. We here employ a wholistic framework, based on semiempirical modeling (k·p/effective mass theory calculations) informed by hybrid density functional theory (DFT) and multimodal spectroscopic ellipsometry on (C₆H₅(CH₂)₂NH₃)₂PbI₄ films and crystals, that allows us to link the observed optical properties and anisotropy precisely to the underlying physical parameters that shape the electronic structure of a layered MHP. We find substantial frequency-dependent anisotropy in the optical constants and close correspondence between experiment and theory, demonstrating a high degree of in-plane alignment of the two-dimensional planes in both spin-coated thin films and cleaved single crystals made in this study. Hybrid DFT results elucidate the degree to which organic and inorganic frontier orbitals contribute to optical transitions polarized along a particular axis. The combined experimental and theoretical approach enables us to estimate the fundamental electronic bandgap of 2.65-2.68 eV in this prototypical 2D perovskite and to determine the spin-orbit coupling (Δ_SO = 1.20 eV) and effective crystal field (δ = -1.36 eV) which break the degeneracy of the frontier conduction band states and determine the exciton fine structure. The methods and results described here afford a better understanding of the connection between structure and induced optical anisotropy in quantum-confined MHPs, an important structure-property relationship for optoelectronic applications and devices.

Magnetic Effect of Dopants on Bright and Dark Excitons in Strongly Confined Mn-Doped CsPbI3 Quantum Dots

We investigated the magnetic effect of Mn²⁺ ions on an exciton of Mn-doped CsPbI₃ quantum dots (QDs), where we looked for the signatures of an exciton magnetic polaron known to produce a large effective magnetic field in Mn-doped CdSe QDs. In contrast to Mn-doped CdSe QDs that can produce ∼100 T of magnetic field upon photoexcitation, manifested as a large change in the energy and relaxation dynamics of a bright exciton, Mn-doped CsPbI₃ QDs exhibited little influence of a magnetic dopant on the behavior of a bright exciton. However, a μs-lived dark exciton in CsPbI₃ QDs showed 40% faster decay in the presence of Mn²⁺, equivalent to the effect of ∼3 T of an external magnetic field. While further study is necessary to fully understand the origin of the large difference in the magneto-optic property of an exciton in two systems, we consider that the difference in antiferromagnetic coupling of the dopants is an important contributing factor.

Dielectric Confinement and Exciton Fine Structure in Lead Halide Perovskite Nanoplatelets

Owing to their flexible chemical synthesis and the ability to shape nanostructures, lead halide perovskites have emerged as high potential materials for optoelectronic devices. Here, we investigate the excitonic band edge states and their energies levels in colloidal inorganic lead halide nanoplatelets, particularly the influence of dielectric effects, in a thin quasi-2D system. We use a model including band offset and dielectric confinements in the presence of Coulomb interaction. Short- and long-range contributions, modified by dielectric effects, are also derived, leading to a full modelization of the exciton fine structure, in cubic, tetragonal and orthorhombic phases. The fine splitting structure, including dark and bright excitonic states, is discussed and compared to recent experimental results, showing the importance of both confinement and dielectric contributions.

Optical Probing of Crystal Lattice Configurations in Single CsPbBr3 Nanoplatelets

Quantum-confined nanostructures of CsPbBr₃ with luminescence quantum efficiencies approaching unity have shown tremendous potential for lighting and quantum light applications. In contrast to CsPbBr₃ quantum dots, where the fine structure of the emissive exciton state has been intensely discussed, the relationship among lattice orientation, shape anisotropy, and exciton fine structure in lead halide nanoplatelets has not yet been established. In this work, we investigate the fine structure of the bright triplet exciton of individual CsPbBr₃ nanoplatelets by polarization-resolved micro- and magnetophotoluminescence spectroscopy at liquid helium temperature and find a large zero-field splitting of up to 2.5 meV. A unique relation between the crystal structure and the photoluminescence emission confirms the existence of two distinct crystal configurations in such nanoplatelets with different alignments of the crystal axes with respect to the nanoplatelet facets. Polarization-resolved experiments eventually allow us to determine the absolute orientation of an individual nanoplatelet on the substrate purely by optical means.

Rashba exciton in a 2D perovskite quantum dot

The Rashba effect has been proposed to give rise to a bright exciton ground state in halide perovskite nanocrystals (NCs), resulting in very fast radiative recombination at room temperature and extremely fast radiative recombination at low temperature. In this paper we find the dispersion of the "Rashba exciton", i.e., the exciton whose bulk dispersion reflects large spin-orbit Rashba terms in the conduction and valence bands and thus has minima at non-zero quasi-momenta. Placing Rashba excitonsin quasi-2D cylindrical quantum dots, we calculate size-dependent levels of confined excitons and their oscillator transition strengths. We consider the implications of this model for two-dimensional hybrid organic-inorganic perovskites, discuss generalizations of this model to 3D NCs, and establish criteria under which a bright ground exciton state could be realized.

Brightening of Dark States in CsPbBr3 Quantum Dots Caused by Light-Induced Magnetism

Lead halide perovskite quantum dots (QDs) have shown great potential for optoelectronic and quantum photonic applications. Although controversy remains about the electronic fine structures of bulk perovskites due to the strong spin-orbit coupling affecting the conduction bands, compelling evidence indicates that the ground states of perovskite QDs remain dark, limiting their applications in optoelectronic devices. Here, it is demonstrated that photoexcitation can induce large intrinsic magnetic fields in Mn-doped CsPbBr₃ perovskite QDs. Equivalent to applying an external magnetic field, the light-induced field causes giant Zeeman splitting to the bright triplet states and brightens the dark singlet ground state, thus effectively rendering a partially bright ground state in the doped QDs. These findings here may contribute to the understanding of the electronic fine structures in perovskite QDs and demonstrate a potential approach for creating semiconductor nanostructures that can serve as bright light sources.

Temperature-Independent Dielectric Constant in CsPbBr3 Nanocrystals Revealed by Linear Absorption Spectroscopy

Fundamental photophysical behavior in CsPbBr₃ nanocrystals (NCs), especially at low temperatures, is under active investigation. While many studies have reported temperature-dependent photoluminescence, comparatively few have focused on understanding the temperature-dependent absorption spectrum. Here, we report the temperature-dependent (35-300 K) absorption and photoluminescence spectra of zwitterionic ligand-capped CsPbBr₃ NCs with four different edge lengths (d = 4.9, 7.2, 8.1, and 13.2 nm). The two lowest-energy excitonic transitions are quantitatively modeled over the full temperature range within the effective mass approximation considering the quasi-cubic NC shape and nonparabolicity of the electronic bands. Significantly, we find that the effective dielectric constant determined from the best fit model parameters is independent of temperature. Moreover, we observe a temperature-dependent Stokes shift that saturates at a finite value of Δ ≈ 10 meV at low temperatures for d = 7.2 nm NCs, which is absent in bulk CsPbBr₃ films. Overall, these observations highlight differences between the temperature-dependent dielectric behavior of NC and bulk perovskites and point to the need for a more unified theoretical understanding of absorption and emission in halide perovskites.

Enhanced Exciton Quantum Coherence in Single CsPbBr3 Perovskite Quantum Dots using Femtosecond Two-Photon Near-Field Scanning Optical Microscopy

Cesium-halide perovskite quantum dots (QDs) have gained tremendous interest as quantum emitters in quantum information processing applications due to their optical and photophysical properties. However, engineering excitonic states in quantum dots requires a deep knowledge of the coherent dynamics of their excitons at a single-particle level. Here, we use femtosecond time-resolved two-photon near-field scanning optical microscopy (NSOM) to reveal coherences involving a single cesium lead bromide perovskite QD (CsPbBr₃) at room temperature. We show that, compared to other nonperovskite nanoparticles, the electronic coherence on a single perovskite QD has a relatively long lifetime of ca. 150 fs, whereas CdSe QDs have exciton coherence times shorter than 75 fs at room temperature. One possible explanation for the longer coherence time observed for the CsPbBr₃ perovskite system is related to the exciton fine structure of these perovskite QDs compared to other nanoparticles. These perovskite QDs exhibit interesting optical properties that differ from those of the traditional QDs including bright triplet exciton states. In fact, due to the small amplitude of the energy gap fluctuations of dipole-allowed triplet states in perovskite QDs, the coherent superposition could be preserved for longer times. Furthermore, single-particle excitation approach implemented in this work allows us to remove effects of heterogeneity that are usually present in ensemble averaging experiments at room temperature. The realization of quantum-mechanical phase-coherence of a charge carrier that can operate at room temperature is an issue of great importance for the potential application of coherent electronic phenomena in electronic and optoelectronic devices. These interesting findings provide further evidence of the great potential of these perovskite QDs as candidates for quantum computing and information processing applications.

State of the Art and Prospects for Halide Perovskite Nanocrystals

Metal-halide perovskites have rapidly emerged as one of the most promising materials of the 21st century, with many exciting properties and great potential for a broad range of applications, from photovoltaics to optoelectronics and photocatalysis. The ease with which metal-halide perovskites can be synthesized in the form of brightly luminescent colloidal nanocrystals, as well as their tunable and intriguing optical and electronic properties, has attracted researchers from different disciplines of science and technology. In the last few years, there has been a significant progress in the shape-controlled synthesis of perovskite nanocrystals and understanding of their properties and applications. In this comprehensive review, researchers having expertise in different fields (chemistry, physics, and device engineering) of metal-halide perovskite nanocrystals have joined together to provide a state of the art overview and future prospects of metal-halide perovskite nanocrystal research.

Nanoparticles, Nanocrystals, and Quantum Dots: What are the Implications of Size in Colloidal Nanoscale Materials?

Semiconductor nanoparticles (NP) or nanocrystals (NC) have been investigated for many decades, with particular acceleration in interest upon the discovery of quantum confinement effects thereby yielding quantum dots (QD) from certain well-grown NC. The term NP is commonly used in the case of metal and wide gap semiconductor nanocrystals. The term NC is commonly used in semiconductor nanocrystals, whether covalent II-VI or ionic perovskites, that are colloidally grown. The term QD applies to select semiconductor nanocrystals for whom their size is on the order of the excitonic Bohr radius. In the case of colloidal particles on the nanometer length scale, these terms are often used carelessly and interchangeably. The words have specific meaning in relationship to specific physical effects which give rise to specific key processes that can be measured. Here, we provide a Perspective on the ways in which size confers function across different families of NP. In this way, we aim to find ways to identify their similarities and differences by providing the correct semantics for discussion of the salient processes.

Revealing the Exciton Fine Structure in Lead Halide Perovskite Nanocrystals

Lead-halide perovskite nanocrystals (NCs) are attractive nano-building blocks for photovoltaics and optoelectronic devices as well as quantum light sources. Such developments require a better knowledge of the fundamental electronic and optical properties of the band-edge exciton, whose fine structure has long been debated. In this review, we give an overview of recent magneto-optical spectroscopic studies revealing the entire excitonic fine structure and relaxation mechanisms in these materials, using a single-NC approach to get rid of their inhomogeneities in morphology and crystal structure. We highlight the prominent role of the electron-hole exchange interaction in the order and splitting of the bright triplet and dark singlet exciton sublevels and discuss the effects of size, shape anisotropy and dielectric screening on the fine structure. The spectral and temporal manifestations of thermal mixing between bright and dark excitons allows extracting the specific nature and strength of the exciton–phonon coupling, which provides an explanation for their remarkably bright photoluminescence at low temperature although the ground exciton state is optically inactive. We also decipher the spectroscopic characteristics of other charge complexes whose recombination contributes to photoluminescence. With the rich knowledge gained from these experiments, we provide some perspectives on perovskite NCs as quantum light sources.

Synthesis and Properties of Strongly Quantum-Confined Cesium Lead Halide Perovskite Nanocrystals

ConspectusSemiconducting metal halide perovskite (MHP) nanocrystals have emerged as an important new class of materials as the source of photons and charges for various applications that can outperform many other semiconductor nanocrystals utilized for the same purposes. However, the majority of the studies of MHP nanocrystals focused on weakly or nonconfined systems, where the quantum confinement giving rise to various size-dependent and confinement-enhanced photophysical properties cannot be explored readily. This was partially due to the challenge in producing strongly quantum-confined MHP nanocrystals, since the traditional kinetic control approach was less effective for the size control. Recent synthetic progress in MHP nanocrystals utilizing the equilibrium-based size control achieved the precise control of quantum confinement with high ensemble uniformity, enabling the exploration of the unique properties of MHP nanocrystals under strong quantum confinement. In this Account, we review the recent progress made in the synthesis of strongly quantum-confined cesium lead halide nanocrystals and investigation of the properties of exciton modified by strong quantum confinement. The main body of this Account discusses the key results of the research in this field in two separate sections. Section 2 describes the thermodynamic equilibrium-based synthesis method to control the size of cesium lead halide perovskite quantum dots in strongly confined regime. Size control in anisotropic nanocrystals with one- and two-dimensional quantum confinement is also discussed. Section 3 covers the following three topics that highlight the effects of quantum confinement on various spectroscopic properties of excitons in cesium lead halide perovskite nanocrystals: (1) Size-dependent absorption cross section of cesium lead halide quantum dots; (2) confinement effect on exciton fine structure and access to the dark exciton exhibiting intense and long-lived photoluminescence; (3) activation of forbidden exciton transition via dynamic lattice distortion by the photoexcited charge carriers enhanced by quantum confinement. The impact of strong quantum confinement goes beyond the properties of excitons covered in this Account and is expected to expand the functionality of MHP nanocrystals as the source of photons and charges. For instance, realization of the possible enhancement of photon down- and upconversion and hot carrier generation via quantum confinement will further increase the usefulness of strongly confined MHP nanocrystals in their applications.

Aging of Self-Assembled Lead Halide Perovskite Nanocrystal Superlattices: Effects on Photoluminescence and Energy Transfer

Excitonic coupling, electronic coupling, and cooperative interactions in self-assembled lead halide perovskite nanocrystals were reported to give rise to a red-shifted collective emission peak with accelerated dynamics. Here we report that similar spectroscopic features could appear as a result of the nanocrystal reactivity within the self-assembled superlattices. This is demonstrated by studying CsPbBr₃ nanocrystal superlattices over time with room-temperature and cryogenic micro-photoluminescence spectroscopy, X-ray diffraction, and electron microscopy. It is shown that a gradual contraction of the superlattices and subsequent coalescence of the nanocrystals occurs over several days of keeping such structures under vacuum. As a result, a narrow, low-energy emission peak is observed at 4 K with a concomitant shortening of the photoluminescence lifetime due to the energy transfer between nanocrystals. When exposed to air, self-assembled CsPbBr₃ nanocrystals develop bulk-like CsPbBr₃ particles on top of the superlattices. At 4 K, these particles produce a distribution of narrow, low-energy emission peaks with short lifetimes and excitation fluence-dependent, oscillatory decays. Overall, the aging of CsPbBr₃ nanocrystal assemblies dramatically alters their emission properties and that should not be overlooked when studying collective optoelectronic phenomena nor confused with superfluorescence effects.

Multidimensional coherent spectroscopy reveals triplet state coherences in cesium lead-halide perovskite nanocrystals

Advances in optoelectronics require materials with novel and engineered characteristics. A class of materials that has garnered tremendous interest is metal-halide perovskites, stimulated by meteoric increases in photovoltaic efficiencies of perovskite solar cells. In addition, recent advances have applied perovskite nanocrystals (NCs) in light-emitting devices. It was found recently that, for cesium lead-halide perovskite NCs, their unusually efficient light emission may be due to a unique excitonic fine structure composed of three bright triplet states that minimally interact with a proximal dark singlet state. To study this fine structure without isolating single NCs, we use multidimensional coherent spectroscopy at cryogenic temperatures to reveal coherences involving triplet states of a CsPbI₃ NC ensemble. Picosecond time scale dephasing times are measured for both triplet and inter-triplet coherences, from which we infer a unique exciton fine structure level ordering composed of a dark state energetically positioned within the bright triplet manifold.

Coherent Spin Precession and Lifetime-Limited Spin Dephasing in CsPbBr3 Perovskite Nanocrystals

Carrier spins in semiconductor nanocrystals are promising candidates for quantum information processing. Using a combination of time-resolved Faraday rotation and photoluminescence spectroscopies, we demonstrate optical spin polarization and coherent spin precession in colloidal CsPbBr₃ nanocrystals that persists up to room temperature. By suppressing the influence of inhomogeneous hyperfine fields with a small applied magnetic field, we demonstrate inhomogeneous hole transverse spin-dephasing times (T₂^*) that approach the nanocrystal photoluminescence lifetime, such that nearly all emitted photons derive from coherent hole spins. Thermally activated LO phonons drive additional spin dephasing at elevated temperatures, but coherent spin precession is still observed at room temperature. These data reveal several major distinctions between spins in nanocrystalline and bulk CsPbBr₃ and open the door for using metal-halide perovskite nanocrystals in spin-based quantum technologies.

The dark exciton ground state promotes photon-pair emission in individual perovskite nanocrystals

Cesium lead halide perovskites exhibit outstanding optical and electronic properties for a wide range of applications in optoelectronics and for light-emitting devices. Yet, the physics of the band-edge exciton, whose recombination is at the origin of the photoluminescence, is not elucidated. Here, we unveil the exciton fine structure of individual cesium lead iodide perovskite nanocrystals and demonstrate that it is governed by the electron-hole exchange interaction and nanocrystal shape anisotropy. The lowest-energy exciton state is a long-lived dark singlet state, which promotes the creation of biexcitons at low temperatures and thus correlated photon pairs. These bright quantum emitters in the near-infrared have a photon statistics that can readily be tuned from bunching to antibunching, using magnetic or thermal coupling between dark and bright exciton sublevels.

The optical and electronic properties of cesium lead halide perovskite nanocrystals are dictated by the band-edge exciton, whose physics is not elucidated. Here, the authors unveil its fine structure and demonstrate that the ground dark singlet state promotes the creation of biexcitons at low temperatures and thus correlated photon pairs.

Intense Dark Exciton Emission from Strongly Quantum-Confined CsPbBr3 Nanocrystals

Dark exciton as the lowest-energy (ground) exciton state in metal halide perovskite nanocrystals is a subject of much interest. This is because the superior performance of perovskites as the photon source combined with long lifetime of dark exciton can be attractive for many applications of exciton. However, the direct observation of the intense and long-lived dark exciton emission, indicating facile access to dark ground exciton state, has remained elusive. Here, we report the intense photoluminescence from dark exciton with microsecond lifetime in strongly confined CsPbBr₃ nanocrystals and reveal the crucial role of confinement in accessing the dark ground exciton state. This study establishes the potential of strongly quantum-confined perovskite nanostructures as the excellent platform to harvest the benefits of extremely long-lived dark exciton.

Transition from Doublet to Triplet Excitons in Single Perovskite Nanocrystals

Lead halide perovskite nanocrystals (NCs) have emerged as novel semiconductor nanostructures possessing great potential for optoelectronic, photovoltaic, and quantum information processing applications. Success in these applications requires a comprehensive understanding of the perovskite NCs' electronic structures, which mysteriously exhibit either doublet or triplet peaks of exciton luminescence at the single-particle level. Here we show that the transition from doublet- to triplet-exciton peaks can be triggered in single CsPbI₃ NCs from the same batch of samples when they are stored in the ambient environment. We propose theoretically that the doublet-exciton peaks originate from two in-plane dipole moments, while the optical transition arising from the out-of-plane dipole moment becomes prominent only after the crystal-field splitting is strongly reduced by the structural transformation in the deterioration process. Furthermore, the quantum-confinement effect is strongly reinforced in the single CsPbI₃ NCs with a triplet-exciton configuration, leading to enhanced Auger recombination and allowing us to extract the emission-energy dependence of the exciton-energy-level fine structure.

Bright Exciton Fine-Structure in Two-Dimensional Lead Halide Perovskites

The fast-growing field of atomically thin semiconductors urges a new understanding of two-dimensional excitons, which entirely determine their optical responses. Here, taking layered lead halide perovskites as an example of unconventional two-dimensional semiconductors, by means of versatile optical spectroscopy measurements, we resolve fine-structure splitting of bright excitons of up to ∼2 meV, which is among the largest values in two-dimensional semiconducting systems. The large fine-structure splitting is attributed to the strong electron-hole exchange interaction in layered perovskites, which is proven by the optical emission in high magnetic fields of up to 30 T. Furthermore, we determine the g-factors for these bright excitons as ∼+1.8. Our findings suggest layered lead halide perovskites are an ideal platform for studying exciton spin-physics in atomically thin semiconductors that will pave the way toward exciton manipulation for novel device applications.

Universal Size-Dependent Stokes Shifts in Lead Halide Perovskite Nanocrystals

Size-dependent photoluminescence Stokes shifts (ΔE_s) universally exist in CsPbX₃ (X = Cl^-, Br^-, or I^-) perovskite nanocrystals (NCs). ΔE_s values, which range from ∼15 to 100 meV for NCs with average edge lengths (l) from approximately 13 to 3 nm, are halide-dependent such that ΔE_s(CsPbI₃) > ΔE_s(CsPbBr₃) ≳ ΔE_s(CsPbCl₃). Observed size-dependent Stokes shifts are not artifacts of ensemble size distributions as demonstrated through measurements of single CsPbBr₃ NC Stokes shifts (⟨ΔE_s⟩ = 42 ± 5 meV), which are in near quantitative agreement with associated ensemble (l = 6.8 ± 0.8 nm) ΔE_s values (ΔE_s ≈ 50 meV). Transient differential absorption measurements additionally illustrate no significant spectral dynamics on the picosecond time scale that would contribute to ΔE_s. This excludes polaron formation as being responsible for ΔE_s. Altogether, the results point to an origin for ΔE_s, intrinsic to the size-dependent electronic properties of individual perovskite NCs.

Multiband Model for Tetragonal Crystals: Application to Hybrid Halide Perovskite Nanocrystals

We investigate the theoretical band structure of organic-inorganic perovskites APbX₃ with tetragonal crystal structure. Using D_4h point group symmetry properties, we derive a general 16-band Hamiltonian describing the electronic band diagram in the vicinity of the wave-vector point corresponding to the direct band gap. For bulk crystals, a very good agreement between our predictions and experimental physical parameters, as band gap energies and effective carrier masses, is obtained. Extending this description to three-dimensional confined hybrid halide perovskite, we calculate the size dependence of the excitonic radiative lifetime and fine structure. We describe the exciton fine structure of cube-shaped nanocrystals by an interplay of crystal-field and electron-hole exchange interaction (short- and long-range parts) enhanced by confinement. Using very recent experimental results on FAPbBr₃ nanocrystals, we extract the bulk short-range exchange interaction in this material and predict its value in other hybrid compounds. Finally, we also predict the bright-bright and bright-dark splittings as a function of nanocrystal size.

Quasicubic model for metal halide perovskite nanocrystals

We present an analysis of quantum confinement of carriers and excitons, and exciton fine structure, in metal halide perovskite (MHP) nanocrystals (NCs). Starting with coupled-band k · P theory, we derive a nonparabolic effective mass model for the exciton energies in MHP NCs valid for the full size range from the strong to the weak confinement limits. We illustrate the application of the model to CsPbBr₃ NCs and compare the theory against published absorption data, finding excellent agreement. We then apply the theory of electron-hole exchange, including both short- and long-range exchange interactions, to develop a model for the exciton fine structure. We develop an analytical quasicubic model for the effect of tetragonal and orthorhombic lattice distortions on the exchange-related exciton fine structure in CsPbBr₃, as well as some hybrid organic MHPs of recent interest, including formamidinium lead bromide (FAPbBr₃) and methylammonium lead iodide (MAPbI₃). Testing the predictions of the quasicubic model using hybrid density functional theory (DFT) calculations, we find qualitative agreement in tetragonal MHPs but significant disagreement in the orthorhombic modifications. Moreover, the quasicubic model fails to correctly describe the exciton oscillator strength and with it the long-range exchange corrections in these systems. Introducing the effect of NC shape anisotropy and possible Rashba terms into the model, we illustrate the calculation of the exciton fine structure in CsPbBr₃ NCs based on the results of the DFT calculations and examine the effect of Rashba terms and shape anisotropy on the calculated fine structure.

Stable Ultraconcentrated and Ultradilute Colloids of CsPbX3 (X = Cl, Br) Nanocrystals Using Natural Lecithin as a Capping Ligand

Attaining thermodynamic stability of colloids in a broad range of concentrations has long been a major thrust in the field of colloidal ligand-capped semiconductor nanocrystals (NCs). This challenge is particularly pressing for the novel NCs of cesium lead halide perovskites (CsPbX₃; X = Cl, Br) owing to their highly dynamic and labile surfaces. Herein, we demonstrate that soy lecithin, a mass-produced natural phospholipid, serves as a tightly binding surface-capping ligand suited for a high-reaction yield synthesis of CsPbX₃ NCs (6–10 nm) and allowing for long-term retention of the colloidal and structural integrity of CsPbX₃ NCs in a broad range of concentrations—from a few ng/mL to >400 mg/mL (inorganic core mass). The high colloidal stability achieved with this long-chain zwitterionic ligand can be rationalized with the Alexander–De Gennes model that considers the increased particle–particle repulsion due to branched chains and ligand polydispersity. The versatility and immense practical utility of such colloids is showcased by the single NC spectroscopy on ultradilute samples and, conversely, by obtaining micrometer-thick, optically homogeneous dense NC films in a single spin-coating step from ultraconcentrated colloids.

Direct Synthesis of Quaternary Alkylammonium-Capped Perovskite Nanocrystals for Efficient Blue and Green Light-Emitting Diodes

Cesium lead halide nanocrystals (CsPbX3 NCs) are new inorganic light sources covering the entire visible spectral range and exhibiting near-unity efficiencies. While the last years have seen rapid progress in green and red electroluminescence from CsPbX3 NCs, the development of blue counterparts remained rather stagnant. Controlling the surface state of CsPbX3 NCs had proven to be a major factor governing the efficiency of the charge injection and for diminishing the density of traps. Although didodecyldimethylammonium halides (DDAX; X = Br, Cl) had been known to improve the luminescence of CsPbX3 NCs when applied postsynthetically, they had not been used as the sole long-chain ammonium ligand directly in the synthesis of these NCs. Herein we report a facile, direct synthesis of DDAX-stabilized CsPbX3 NCs. We then demonstrate blue and green light-emitting diodes, characterized by the electroluminescence at 463-515 nm and external quantum efficiencies of 9.80% for green, 4.96% for sky-blue, and 1.03% for deep-blue spectral regions.

Giant Fine Structure Splitting of the Bright Exciton in a Bulk MAPbBr3 Single Crystal

Exciton fine structure splitting in semiconductors reflects the underlying symmetry of the crystal and quantum confinement. Because the latter factor strongly enhances the exchange interaction, most work has focused on nanostructures. Here, we report on the first observation of the bright exciton fine structure splitting in a bulk semiconductor crystal, where the impact of quantum confinement can be specifically excluded, giving access to the intrinsic properties of the material. Detailed investigation of the exciton photoluminescence and reflection spectra of a bulk methylammonium lead tribromide single crystal reveals a zero magnetic field splitting as large as ∼200 μeV. This result provides an important starting point for the discussion of the origin of the large bright exciton fine structure splitting observed in perovskite nanocrystals.