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

Impact of Bright-Dark Exciton Thermal Population Mixing on the Brightness of CsPbBr3 Nanocrystals

Understanding the interplay between bright and dark exciton states is crucial for deciphering the luminescence properties of low-dimensional materials. The origin of the outstanding brightness of lead halide perovskites remains elusive. Here, we analyze temperature-dependent time-resolved photoluminescence to investigate the population mixing between bright and dark exciton sublevels in individual CsPbBr3 nanocrystals in the intermediate confinement regime. We extract bright and dark exciton decay rates and show quantitatively that the decay dynamics can only be reproduced with second-order phonon transitions. Furthermore, we find that any exciton sublevel ordering is compatible with the most likely population transfer mechanism. The remarkable brightness of lead halide perovskite nanocrystals rather stems from a reduced asymmetry between bright-to-dark and dark-to-bright conversion originating from the peculiar second-order phonon-assisted transitions that freeze bright-dark conversion at low temperatures together with the very fast radiative recombination and favorable degeneracy of the bright exciton state.

Visualizing the Low-Energy Electronic Structure of Prototypical Hybrid Halide Perovskite through Clear Band Measurements

Organic-inorganic hybrid perovskites (OIHPs) are a promising class of materials that rival conventional semiconductors in various optoelectronic applications. However, unraveling the precise nature of their low-energy electronic structures continues to pose a significant challenge, primarily due to the absence of clear band measurements. Here, we investigate the low-energy electronic structure of CH3NH3PbI3 (MAPI3) using angle-resolved photoelectron spectroscopy combined with ab initio density functional theory. We successfully visualize the electronic structure of MAPI3 near the bulk valence band maximum by using a laboratory photon source (He Iα, 21.2 eV) at low temperature and explore its fundamental properties. The observed valence band exhibits a highly isotropic and parabolic band characterized by small effective masses of 0.20-0.21 me, without notable spectral signatures associated with a large polaron or the Rashba effect, subjects that are intensely debated in the literature. Concurrently, our spin-resolved measurements directly disprove the giant Rashba scenario previously suggested in a similar perovskite compound by establishing an upper limit for the Rashba parameter (αR) of 0.28 eV Å. Our results unveil the unusually complex nature of the low-energy electronic structure of OIHPs, thereby advancing our fundamental understanding of this important class of materials.

Tailoring the Electron and Hole Landé Factors in Lead Halide Perovskite Nanocrystals by Quantum Confinement and Halide Exchange

The tunability of the optical properties of lead halide perovskite nanocrystals makes them highly appealing for applications. Halide anion exchange and quantum confinement enable tailoring of the band gap. For spintronics, the Landé g-factors of electrons and holes are essential. Using empirical tight-binding and k·p methods, we calculate them for nanocrystals of all-inorganic lead halide perovskites CsPbX3 (X = I, Br, Cl). The hole g-factor band gap dependence follows the universal law found for bulk perovskites, while for electrons, a considerable modification is predicted. Based on the k·p analysis, we conclude that this difference arises from the interaction of the bottom conduction band with the spin-orbit split electron states. These predictions are confirmed experimentally for electron and hole g-factors in CsPbI3 nanocrystals in a glass matrix, measured by time-resolved Faraday ellipticity in a magnetic field at cryogenic temperatures.

Exciton Fine Structure of CsPbCl3 Nanocrystals: An Interplay of Electron-Hole Exchange Interaction, Crystal Structure, Shape Anisotropy, and Dielectric Mismatch

In the semiconducting perovskite materials family, the cesium-lead-chloride compound (CsPbCl₃) supports robust excitons characterized by a blue-shifted transition and the largest binding energy, thus presenting a high potential to achieve demanding solid-state room-temperature photonic or quantum devices. Here we study the fundamental emission properties of cubic-shaped colloidal CsPbCl₃ nanocrystals (NCs), examining in particular individual NC responses using micro-photoluminescence in order to unveil the exciton fine structure (EFS) features. Within this work, NCs with average dimensions ⟨L_α⟩ ≈ 8 nm (α = x, y, z) are studied with a level of dispersity in their dimensions that allows disentangling the effects of size and shape anisotropy in the analysis. We find that most of the NCs exhibit an optical response under the form of a doublet with crossed polarized peaks and an average inter-bright-state splitting, Δ_BB ≈ 1.53 meV, but triplets are also observed though being a minority. The origin of the EFS patterns is discussed in the frame of the electron-hole exchange model by taking into account the dielectric mismatch at the NC interface. The different features (large dispersity in the Δ_BB values and occasional occurrence of triplets) are reconciled by incorporating a moderate degree of shape anisotropy, observed in the structural characterization, by preserving the relatively high degree of the NC lattice symmetry. The energy distance between the optically inactive state and the bright manifold, Δ_BD, is also extracted from time-resolved photoluminescence measurements (Δ_BD ≈ 10.7 meV), in good agreement with our theoretical predictions.

Spectral Fingerprint of Quantum Confinement in Single CsPbBr3 Nanocrystals

Lead halide perovskite nanocrystals are promising materials for classical and quantum light emission. To understand these outstanding properties, a thorough analysis of the band-edge exciton emission is needed, which is not reachable in ensemble and room-temperature studies because of broadening effects. Here, we report on a cryogenic-temperature study of the photoluminescence of single CsPbBr₃ nanocrystals in the intermediate quantum confinement regime. We reveal the size-dependence of the spectral features observed: the bright triplet exciton energy splittings, the trion and biexciton binding energies, and the optical phonon replica spectrum. In addition, we show that bright triplet energy splittings are consistent with a pure exchange model and that the variety of polarization properties and spectra recorded can be rationalized simply by considering the orientation of the emitting dipoles and the populations of the emitting states.

Universal scaling laws for charge-carrier interactions with quantum confinement in lead-halide perovskites

Lead halide perovskites open great prospects for optoelectronics and a wealth of potential applications in quantum optical and spin-based technologies. Precise knowledge of the fundamental optical and spin properties of charge-carrier complexes at the origin of their luminescence is crucial in view of the development of these applications. On nearly bulk Cesium-Lead-Bromide single perovskite nanocrystals, which are the test bench materials for next-generation devices as well as theoretical modeling, we perform low temperature magneto-optical spectroscopy to reveal their entire band-edge exciton fine structure and charge-complex binding energies. We demonstrate that the ground exciton state is dark and lays several millielectronvolts below the lowest bright exciton sublevels, which settles the debate on the bright-dark exciton level ordering in these materials. More importantly, combining these results with spectroscopic measurements on various perovskite nanocrystal compounds, we show evidence for universal scaling laws relating the exciton fine structure splitting, the trion and biexciton binding energies to the band-edge exciton energy in lead-halide perovskite nanostructures, regardless of their chemical composition. These scaling laws solely based on quantum confinement effects and dimensionless energies offer a general predictive picture for the interaction energies within charge-carrier complexes photo-generated in these emerging semiconductor nanostructures.

Confinement-Tunable Transition Dipole Moment Orientation in Perovskite Nanoplatelet Solids and Binary Blends

Tuning the transition dipole moment (TDM) orientation in low-dimensional semiconductors is of fundamental and practical interest, as it enables high-efficiency nanophotonics and light-emitting diodes. However, despite recent progress in nanomaterials physics and chemistry, material systems that allow continuous tuning of the TDM orientation remain rare. Here, combining k-space photoluminescence spectroscopy and multiscale modeling, we demonstrate that the TDM orientation in lead halide perovskite (LHP) nanoplatelet (NPL) solids is largely confinement-tunable through the NPL geometry that regulates the anisotropy of Bloch states, dielectric confinement, and exciton fine structure. We further quantified the role of uniaxial ordering during NPL assembly in modifying the macroscopic emission directionality of thin films, which is especially important in actual optoelectronic devices. Our theoretical framework successfully corroborates the previous prediction of exciton bright level order reversal with experimental evidence of a counterintuitive reduction of in-plane dipole ratio in ultrathin (one- and two-monolayer-thick) NPLs, even at room temperature. More interestingly, the NPLs retain their TDM orientation in binary blends irrespective of interparticle energy transfer, owing to the phase segregation and NPL-NPL decoupling, enabling the design of films whose fluorescence exhibits an intrinsic angle-dependent color gradient.

Thickness-Dependent Dark-Bright Exciton Splitting and Phonon Bottleneck in CsPbBr3-Based Nanoplatelets Revealed via Magneto-Optical Spectroscopy

The optimized exploitation of perovskite nanocrystals and nanoplatelets as highly efficient light sources requires a detailed understanding of the energy spacing within the exciton manifold. Dark exciton states are particularly relevant because they represent a channel that reduces radiative efficiency. Here, we apply large in-plane magnetic fields to brighten optically inactive states of CsPbBr3-based nanoplatelets for the first time. This approach allows us to access the dark states and directly determine the dark-bright splitting, which reaches 22 meV for the thinnest nanoplatelets. The splitting is significantly less for thicker nanoplatelets due to reduced exciton confinement. Additionally, the form of the magneto-PL spectrum suggests that dark and bright state populations are nonthermalized, which is indicative of a phonon bottleneck in the exciton relaxation process.

Transient quantum beatings of trions in hybrid organic tri-iodine perovskite single crystal

Utilizing the spin degree of freedom of photoexcitations in hybrid organic inorganic perovskites for quantum information science applications has been recently proposed and explored. However, it is still unclear whether the stable photoexcitations in these compounds correspond to excitons, free/trapped electron-hole pairs, or charged exciton complexes such as trions. Here we investigate quantum beating oscillations in the picosecond time-resolved circularly polarized photoinduced reflection of single crystal methyl-ammonium tri-iodine perovskite (MAPbI₃) measured at cryogenic temperatures. We observe two quantum beating oscillations (fast and slow) whose frequencies increase linearly with B with slopes that depend on the crystal orientation with respect to the applied magnetic field. We assign the quantum beatings to positive and negative trions whose Landé g-factors are determined by those of the electron and hole, respectively, or by the carriers left behind after trion recombination. These are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{[001]}^{e}$$\end{document}g[001]e = 2.52 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${g}_{[1\bar{1}0]}^{e}\,$$\end{document}g[11¯0]e= 2.63 for electrons, whereas \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\big|{g}_{[001]}^{h}\big|\,$$\end{document}g[001]h= 0.28 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\big|{g}_{[1\bar{1}0]}^{h}\big|\,$$\end{document}g[11¯0]h= 0.57 for holes. The obtained g-values are in excellent agreement with an 8-band K.P calculation for orthorhombic MAPbI₃. Using the technique of resonant spin amplification of the quantum beatings we measure a relatively long spin coherence time of ~ 11 (6) nanoseconds for electrons (holes) at 4 K.

Understanding photo-physics giving rise to quantum beating oscillations in hybrid organic-inorganic perovskites aids their applications in spintronics and quantum information science. Here, authors demonstrate that quantum beatings observed in single crystal perovskite at cryogenic temperatures are originating from positive and negative trions.

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.

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.

Brightening of dark excitons in 2D perovskites

Optically inactive dark exciton states play an important role in light emission processes in semiconductors because they provide an efficient nonradiative recombination channel. Understanding the exciton fine structure in materials with potential applications in light-emitting devices is therefore critical. Here, we investigate the exciton fine structure in the family of two-dimensional (2D) perovskites (PEA)₂SnI₄, (PEA)₂PbI₄, and (PEA)₂PbBr₄. In-plane magnetic field mixes the bright and dark exciton states, brightening the otherwise optically inactive dark exciton. The bright-dark splitting increases with increasing exciton binding energy. Hot photoluminescence is observed, indicative of a non-Boltzmann distribution of the bright-dark exciton populations. We attribute this to the phonon bottleneck, which results from the weak exciton–acoustic phonon coupling in soft 2D perovskites. Hot photoluminescence is responsible for the strong emission observed in these materials, despite the substantial bright-dark exciton splitting.

Energy Tuning of Electronic Spin Coherent Evolution in Methylammonium Lead Iodide Perovskites

We investigated the coherent evolution of the electronic spin at low temperature in high-quality CH₃NH₃PbI₃ polycrystalline films by picosecond-resolved photoinduced Faraday rotation. We show that this coherent evolution can be tuned by choosing the pump-probe energy within the lowest optical-absorption band, and we explain it as the result of two main contributions: the localized electron and the localized hole. Their corresponding amplitude ratios are not constant across the lowest absorption band-an observation which disqualifies a free exciton from being at the origin of the electronic spin coherent evolution. We measured a spin coherence time of localized electrons (holes) of 4.4 ns (3.7 ns) at 1.635 eV, which evolves to about 7 ns at 1.612 eV (the hole coherence time remains almost constant at lower energies). Finally, we provide a global image of the spin coherent evolution in bulk metal halide perovskite, which overcomes recent controversies.

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.

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.

Anisotropic shape of CsPbBr3 colloidal nanocrystals: from 1D to 2D confinement effects

We synthesized strongly anisotropic CsPbBr₃ nanocrystals with very narrow emission and absorption lines associated to confinement effects along one or two dimensions, called respectively nanoplatelets (NPLs) and nanosticks (NSTs). Transmission Electron Microscopy (TEM) images, absorption and photoluminescence (PL) spectra taken at low temperature are very precise tools to determine which kind of confinement has to be considered and to deduce the shape, the size and the thickness of nanocrystals under focus. We show that the energy of the band-edge absorption and PL peaks versus the inverse of the square of the NPL thickness has a linear behaviour from 11 monolayers (MLs) i.e. a thickness of 6.38 nm, until 4 MLs (2.32 nm) showing that self-energy correction compensates the increase of the exciton binding energy in thin NPLs as already observed in Cadmium chalcogenides-based NPLs. We also show that slight changes in the morphology of NSTs leads to a very drastic modification of their absorption spectra. Time-resolved PL of NSTs has a non-monotonous behaviour with temperature. At 5 K, a quasi-single exponential with a lifetime of 80 ps is obtained; at intermediate temperature, the decay is bi-exponential and at 150 K, a quasi-single exponential decay is recovered (≈0.4 ns). For NSTs, the exciton interaction with LO phonons governs the broadening of the absorption and PL peaks at room temperature and is stronger than in chalcogenides quantum dots and NPLs.