Single-photon superradiance in individual caesium lead halide quantum dots.

The brightness of an emitter is ultimately described by Fermi's golden rule, with a radiative rate proportional to its oscillator strength times the local density of photonic states. As the oscillator strength is an intrinsic material property, the quest for ever brighter emission has relied on the local density of photonic states engineering, using dielectric or plasmonic resonators1,2. By contrast, a much less explored avenue is to boost the oscillator strength, and hence the emission rate, using a collective behaviour termed superradiance. Recently, it was proposed3 that the latter can be realized using the giant oscillator-strength transitions of a weakly confined exciton in a quantum well when its coherent motion extends over many unit cells. Here we demonstrate single-photon superradiance in perovskite quantum dots with a sub-100 picosecond radiative decay time, almost as short as the reported exciton coherence time4. The characteristic dependence of radiative rates on the size, composition and temperature of the quantum dot suggests the formation of giant transition dipoles, as confirmed by effective-mass calculations. The results aid in the development of ultrabright, coherent quantum light sources and attest that quantum effects, for example, single-photon emission, persist in nanoparticles ten times larger than the exciton Bohr radius.

Bright triplet excitons in caesium lead halide perovskites.

Nanostructured semiconductors emit light from electronic states known as excitons. For organic materials, Hund's rules state that the lowest-energy exciton is a poorly emitting triplet state. For inorganic semiconductors, similar rules predict an analogue of this triplet state known as the 'dark exciton'. Because dark excitons release photons slowly, hindering emission from inorganic nanostructures, materials that disobey these rules have been sought. However, despite considerable experimental and theoretical efforts, no inorganic semiconductors have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in caesium lead halide perovskites (CsPbX3, with X = Cl, Br or I) involves a highly emissive triplet state. We first use an effective-mass model and group theory to demonstrate the possibility of such a state existing, which can occur when the strong spin-orbit coupling in the conduction band of a perovskite is combined with the Rashba effect. We then apply our model to CsPbX3 nanocrystals, and measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright triplet character of the lowest exciton explains the anomalous photon-emission rates of these materials, which emit about 20 and 1,000 times faster than any other semiconductor nanocrystal at room and cryogenic temperatures, respectively. The existence of this bright triplet exciton is further confirmed by analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals, which are already used in lighting, lasers and displays, these excitons could lead to materials with brighter emission. More generally, our results provide criteria for identifying other semiconductors that exhibit bright excitons, with potential implications for optoelectronic devices.

Chiral Cation Doping for Modulating Structural Symmetry of 2D Perovskites.

Cation mixing in two-dimensional (2D) hybrid organic-inorganic perovskite (HOIP) structures represents an important degree of freedom for modifying organic templating effects and tailoring inorganic structures. However, the limited number of known cation-mixed 2D HOIP systems generally employ a 1:1 cation ratio for stabilizing the 2D perovskite structure. Here, we demonstrate a chiral-chiral mixed-cation system wherein a controlled small amount (<10%) of chiral cation S-2-MeBA (S-2-MeBA = (S)-(-)-2-methylbutylammonium) can be doped into (S-BrMBA)2PbI4 (S-BrMBA = (S)-(-)-4-bromo-α-methylbenzylammonium), modulating the structural symmetry from a higher symmetry (C2) to the lowest symmetry state (P1). This structural change occurs when the concentration of S-2-MeBA, measured by solution nuclear magnetic resonance, exceeds a critical level─specifically, for 1.4 ± 0.6%, the structure remains as C2, whereas 3.9 ± 1.4% substitution induces the structure change to P1 (this structure is stable to ∼7% substitution). Atomic occupancy analysis suggests that one specific S-BrMBA cation site is preferentially substituted by S-2-MeBA in the unit cell. Density functional theory calculations indicate that the spin splitting along different k-paths can be modulated by cation doping. A true circular dichroism band at the exciton energy of the 3.9% doping phase shows polarity inversion and a ∼45 meV blue shift of the Cotton-effect-type line-shape relative to (S-BrMBA)2PbI4. A trend toward suppressed melting temperature with higher doping concentration is also noted. The chiral cation doping system and the associated doping-concentration-induced structural transition provide a material design strategy for modulating and enhancing those emergent properties that are sensitive to different types of symmetry breaking.

Lattice distortion inducing exciton splitting and coherent quantum beating in CsPbI3 perovskite quantum dots.

Anisotropic exchange splitting in semiconductor quantum dots results in bright-exciton fine-structure splitting important for quantum information processing. Direct measurement of fine-structure splitting usually requires single/few quantum dots at liquid-helium temperature because of its sensitivity to quantum dot size and shape, whereas measuring and controlling fine-structure splitting at an ensemble level seem to be impossible unless all the dots are made to be nearly identical. Here we report strong bright-exciton fine-structure splitting up to 1.6 meV in solution-processed CsPbI3 perovskite quantum dots, manifested as quantum beats in ensemble-level transient absorption at liquid-nitrogen to room temperature. The splitting is robust to quantum dot size and shape heterogeneity, and increases with decreasing temperature, pointing towards a mechanism associated with orthorhombic distortion of the perovskite lattice. Effective-mass-approximation calculations reveal an intrinsic 'fine-structure gap' that agrees well with the observed fine-structure splitting. This gap stems from an avoided crossing of bright excitons confined in orthorhombically distorted quantum dots that are bounded by the pseudocubic {100} family of planes.

Alkyl-Aryl Cation Mixing in Chiral 2D Perovskites.

We report 2D hybrid perovskites comprising a blend of chiral arylammonium and achiral alkylammonium spacer cations (1:1 mole ratio). These new perovskites feature an unprecedented combination of chirality and alkyl-aryl functionality alongside noncovalent intermolecular interactions (e.g., CH···π interactions), determined by their crystal structures. The mixed-cation perovskites exhibit a circular dichroism that is markedly different from the purely chiral cation analogues, offering new avenues to tune the chiroptical properties of known chiral perovskites, instead of solely relying on otherwise complex chemical syntheses of new useable chiral cations. Further, the ability to dilute the density of chiral cations by mixing with achiral cations may offer a potential way to tailor the spin-based properties in 2D hybrid perovskites, such as Rashba-Dresselhaus spin splitting and chirality-induced spin selectivity and magnetization effects.

Tuning Spin-Polarized Lifetime in Two-Dimensional Metal-Halide Perovskite through Exciton Binding Energy.

Metal-halide perovskite semiconductors have attracted attention for opto-spintronic applications where the manipulation of charge and spin degrees of freedom have the potential to lower power consumption and achieve faster switching times for electronic devices. Lower-dimensional perovskites are of particular interest since the lower degree of symmetry of the metal-halide connected octahedra and the large spin-orbit coupling can potentially lift the spin degeneracy. To achieve their full application potential, long spin-polarized lifetimes and an understanding of spin-relaxation in these systems are needed. Here, we report an intriguing spin-selective excitation of excitons in a series of 2D lead iodide perovskite (n = 1) single crystals by using time- and polarization-resolved transient reflection spectroscopy. Exciton spin relaxation times as long as ∼26 ps at low excitation densities and at room temperature were achieved for a system with small binding energy, 2D EOA2PbI4 (EOA = ethanolamine). By tuning the excitation density and the exciton binding energy, we identify the dominant mechanism as the D'yakonov-Perel (DP) mechanism at low exciton densities and the Bir-Aronov-Pikus (BAP) mechanism at high excitation densities. Together, these results provide new design principles to achieve long spin lifetimes in metal-halide perovskite semiconductors.

Effect of Anisotropic Confinement on Electronic Structure and Dynamics of Band Edge Excitons in Inorganic Perovskite Nanowires.

Inorganic lead halide perovskite nanostructures show promise as the active layers in photovoltaics, light emitting diodes, and other optoelectronic devices. They are robust in the presence of oxygen and water, and the electronic structure and dynamics of these nanostructures can be tuned through quantum confinement. Here we create aligned bundles of CsPbBr3 nanowires with widths resulting in quantum confinement of the electronic wave functions and subject them to ultrafast microscopy. We directly image rapid one-dimensional exciton diffusion along the nanowires, and we measure an exciton trap density of roughly one per nanowire. Using transient absorption microscopy, we observe a polarization-dependent splitting of the band edge exciton line, and from the polarized fluorescence of nanowires in solution, we determine that the exciton transition dipole moments are anisotropic in strength. Our observations are consistent with a model in which splitting is driven by shape anisotropy in conjunction with long-range exchange.

Exciton Fine Structure in Perovskite Nanocrystals.

The bright emission observed in cesium lead halide perovskite nanocrystals (NCs) has recently been explained in terms of a bright exciton ground state [ Becker et al. Nature 2018 , 553 , 189 - 193 ], a claim that would make these materials the first known examples in which the exciton ground state is not an optically forbidden dark exciton. This unprecedented claim has been the subject of intense experimental investigation that has so far failed to detect the dark ground-state exciton. Here, we review the effective-mass/electron-hole exchange theory for the exciton fine structure in cubic and tetragonal CsPbBr3 NCs. In our calculations, the crystal field and the short-range electron-hole exchange constant were calculated using density functional theory together with hybrid functionals and spin-orbit coupling. Corrections associated with long-range exchange and surface image charges were calculated using measured bulk effective mass and dielectric parameters. As expected, within the context of the exchange model, we find an optically inactive ground exciton level. However, in this model, the level order for the optically active excitons in tetragonal CsPbBr3 NCs is opposite to what has been observed experimentally. An alternate explanation for the observed bright exciton level order in CsPbBr3 NCs is offered in terms of the Rashba effect, which supports the existence of a bright ground-state exciton in these NCs. The size dependence of the exciton fine structure calculated for perovskite NCs shows that the bright-dark level inversion caused by the Rashba effect is suppressed by the enhanced electron-hole exchange interaction in small NCs.

Explaining the Unusual Photoluminescence of Semiconductor Nanocrystals Doped via Cation Exchange.

Aliovalent doping of CdSe nanocrystals (NCs) via cation exchange processes has resulted in interesting and novel observations for the optical and electronic properties of the NCs. However, despite over a decade of study, these observations have largely gone unexplained, partially due to an inability to precisely characterize the physical properties of the doped NCs. Here, electrostatic force microscopy was used to determine the static charge on individual, cation-doped CdSe NCs in order to investigate their net charge as a function of added cations. While the NC charge was relatively insensitive to the relative amount of doped cation per NC, there was a remarkable and unexpected correlation between the average NC charge and PL intensity, for all dopant cations introduced. We conclude that the changes in PL intensity, as tracked also by changes in NC charge, are likely a consequence of changes in the NC radiative rate caused by symmetry breaking of the electronic states of the nominally spherical NC due to the Coulombic potential introduced by ionized cations.

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.

Band-Edge Exciton in CdSe and Other II-VI and III-V Compound Semiconductor Nanocrystals - Revisited.

In this Mini Review, we summarize major corrections to the dark-bright exciton theory [ Efros et al. Phys. Rev B 1996 , 54 , 4843 - 4856 ], which should be used for quantitative description of the band edge exciton in II-VI and III-V compound quantum-dot nanocrystals (NCs). The theory previously did not take into account the long-range exchange interaction, resulting in the under-estimation of the splitting between the upper bright and lower dark or quasi-dark exciton, as reported by several experimental groups. Another type of correction originates from the closeness in energy of the ground, 1S3/2, and the first excited, 1P3/2, hole levels in a spherical NC, resulting in significant energetic overlap of the levels from the 1S3/21Se and 1P3/21Se exciton manifolds connected with the ground 1Se electron level. The thermal occupation of the optically forbidden 1P3/21Se exciton levels changes the radiative decay time of the NCs at both helium and room temperatures. We demonstrate the role of both effects in CdSe NCs and compare our predictions with available experimental data.

n-Type PbSe Quantum Dots via Post-Synthetic Indium Doping.

We developed a postsynthetic treatment to produce impurity n-type doped PbSe QDs with In3+ as the substitutional dopant. Increasing the incorporated In content is accompanied by a gradual bleaching of the interband first-exciton transition and concurrently the appearance of a size-dependent, intraband absorption, suggesting the controlled introduction of delocalized electrons into the QD band edge states under equilibrium conditions. We compare the optical properties of our In-doped PbSe QDs to cobaltocene treated QDs, where the n-type dopant arises from remote reduction of the PbSe QDs and observe similar behavior. Spectroelectrochemical measurements also demonstrate characteristic n-type signatures, including both an induced absorption within the electrochemical bandgap and a shift of the Fermi-level toward the conduction band. Finally, we demonstrate that the In3+ dopants can be reversibly removed from the PbSe QDs, whereupon the first exciton bleach is recovered. Our results demonstrate that PbSe QDs can be controllably n-type doped via impurity aliovalent substitutional doping.

Photoluminescence Enhancement through Symmetry Breaking Induced by Defects in Nanocrystals.

We present a theoretical model for the effect of symmetry breaking introduced by the doping of semiconductor nanocrystals with Coulomb impurities. The presence of a Coulomb center breaks the nanocrystal symmetry and affects its optical properties through the mixing of the hole spin and parity sublevels, breaking the selection rules responsible for the exciton dark state in undoped nanocrystals. After reviewing the effects on the exciton fine structure and optical selection rules using symmetry theory, we present a perturbative model to quantify the effects. We find that the symmetry breaking proceeds by two mechanisms: First, mixing by even parity terms in the Coulomb multipole expansion results in an exciton fine structure consisting of three optically active doublets which are polarized along x, y, and z axes with a ground optically passive dark exciton state, and second, odd parity terms which break inversion symmetry significantly activate optical transitions which are optically forbidden in the unperturbed nanocrystal due to both spin and parity selection rules. In the case of small sized "quasi-spherical" nanocrystals, the introduction of a single positively charged Coulomb center is shown here to result in significant enhancement of the radiative decay rate at room temperatures by up to a factor of 10.

Identification of Semiconductor Nanocrystals with Bright Ground-State Excitons.

While semiconductor nanocrystals provide versatile fluorescent materials for light-emitting devices, their brightness suffers from the "dark exciton"─an optically inactive electronic state into which nanocrystals relax before emitting. Recently, a theoretical mechanism, the Rashba effect, was discovered that can overcome this limitation by inverting the lowest-lying levels and creating a bright excitonic ground state. However, no methodology is available to systematically identify materials that exhibit this inversion, hindering the development of superbright nanocrystals and their devices. Here, based on a detailed understanding of the Rashba mechanism, we demonstrate a procedure that reveals previously unknown "bright-exciton" nanocrystals. We first define physical criteria to reduce over 500,000 known solids to 173 targets. Higher-level first-principles calculations then refine this list to 28 candidates. From these, we select five with high oscillator strength and develop effective-mass models to determine the nature of their lowest excitonic state. We confirm that four of the five solids yield bright ground-state excitons in nanocrystals. Thus, our results provide a badly needed roadmap for experimental investigation of bright-exciton nanomaterials.

Rashba splitting in organic-inorganic lead-halide perovskites revealed through two-photon absorption spectroscopy.

The Rashba splitting in hybrid organic-inorganic lead-halide perovskites (HOIP) is particularly promising and yet controversial, due to questions surrounding the presence or absence of inversion symmetry. Here we utilize two-photon absorption spectroscopy to study inversion symmetry breaking in different phases of these materials. This is an all-optical technique to observe and quantify the Rashba effect as it probes the bulk of the materials. In particular, we measure two-photon excitation spectra of the photoluminescence in 2D, 3D, and anionic mixed HOIP crystals, and show that an additional band above, but close to the optical gap is the signature of new two-photon transition channels that originate from the Rashba splitting. The inversion symmetry breaking is believed to arise from ionic impurities that induce local electric fields. The observation of the Rashba splitting in the bulk of HOIP has significant implications for the understanding of their spintronic and optoelectronic device properties.

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 [Formula: see text] = 2.52 and [Formula: see text]= 2.63 for electrons, whereas [Formula: see text]= 0.28 and [Formula: see text]= 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.

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.

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 (ΔSO = 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.

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.

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.