Effective-mass model and magneto-optical properties in hybrid perovskites

Chiral europium halides with high-performance magnetic field tunable red circularly polarized luminescence at room temperature

Chiral organic-inorganic hybrid metal halides as promising circularly polarized luminescence (CPL) emitter candidates hold great potential for high-definition displays and future spin-optoelectronics. The recent challenge lies primarily in developing high-performance red CPL emitters. Here, coupling the f-f transition characteristics of trivalent europium ions (Eu3+) with chirality, we construct the chiral Eu-based halides, (R/S-3BrMBA)3EuCl6, which exhibit strong and predictable red emission with large photoluminescence quantum yield (59.8%), narrow bandwidth (≈2 nm), long lifetime (≈2 ms), together with large dissymmetry factor |glum| of 1.84 × 10-2. Compared with the previously reported chiral metal halides, these chiral Eu-based halides show the highest red CPL brightness. Furthermore, the degree of photoluminescence polarization in (R/S-3BrMBA)3EuCl6 can be manipulated by the external magnetic field. Particularly, benefiting from the field-generated Zeeman splitting and spin mixing at exciton states, an anomalously positive magneto-photoluminescence was observed at room temperature. This work provides an efficient strategy for constructing both high-performance and pure-red CPL emitters. It also opens the door for chiral rare-earth halides toward chiral optoelectronic and spintronic applications.

Spin-Orbital Ordering Effects of Light Emission in Organic-Inorganic Hybrid Metal Halide Perovskites

Organic-inorganic hybrid metal halide perovskites carrying strong spin-orbital coupling (SOC) have demonstrated remarkable light-emitting properties in spontaneous emission, amplified spontaneous emission (ASE), and circularly-polarized luminescence (CPL). Experimental studies have shown that SOC plays an important role in controlling the light-emitting properties in such hybrid perovskites. Here, the SOC consists of both orbital (L) and spin (S) momentum, leading to the formation of J (= L + S) excitons intrinsically involving orbital and spin momentum. In general, there are three issues in determining the effects of SOC on the light-emitting properties of J excitons. First, when the J excitons function as individual quasi-particles, the configurations of orbital and spin momentum directly decide the formation of bright and dark J excitons. Second, when the J excitons are mutually interacting as collective quasi-particles, the exciton-exciton interactions can occur through orbital and spin momentum. The exciton-exciton interactions through orbital and spin momentum give rise to different light-emitting properties, presenting SOC ordering effects. Third, the J excitons can develop ASE through coherent exciton-exciton interaction and CPL through exciton-helical ordering effect. This review article discusses the SOC effects in spontaneous emission, ASE, and CPL in organic-inorganic hybrid metal halide perovskites.

Two-dimensional chiral perovskites with large spin Hall angle and collinear spin Hall conductivity

Two-dimensional hybrid organic-inorganic perovskites with chiral spin texture are emergent spin-optoelectronic materials. Despite the wealth of chiro-optical studies on these materials, their charge-to-spin conversion efficiency is unknown. We demonstrate highly efficient electrically driven charge-to-spin conversion in enantiopure chiral perovskites (R/S-MB)2(MA)3Pb4I13 (〈n〉 = 4), where MB is 2-methylbutylamine, MA is methylamine, Pb is lead, and I is iodine. Using scanning photovoltage microscopy, we measured a spin Hall angle θsh of 5% and a spin lifetime of ~75 picoseconds at room temperature in 〈n〉 = 4 chiral perovskites, which is much larger than its racemic counterpart as well as the lower 〈n〉 homologs. In addition to current-induced transverse spin current, the presence of a coexisting out-of-plane spin current confirms that both conventional and collinear spin Hall conductivities exist in these low-dimensional crystals.

Emerging Spintronic Materials and Functionalities

The explosive growth of the information era has put forward urgent requirements for ultrahigh-speed and extremely efficient computations. In direct contrary to charge-based computations, spintronics aims to use spins as information carriers for data storage, transmission, and decoding, to help fully realize electronic device miniaturization and high integration for next-generation computing technologies. Currently, many novel spintronic materials have been developed with unique properties and multifunctionalities, including organic semiconductors (OSCs), organic-inorganic hybrid perovskites (OIHPs), and 2D materials (2DMs). These materials are useful to fulfill the demand for developing diverse and advanced spintronic devices. Herein, these promising materials are systematically reviewed for advanced spintronic applications. Due to the distinct chemical and physical structures of OSCs, OIHPs, and 2DMs, their spintronic properties (spin transport and spin manipulation) are discussed separately. In addition, some multifunctionalities due to photoelectric and chiral-induced spin selectivity (CISS) are overviewed, including the spin-filter effect, spin-photovoltaics, spin-light emitting devices, and spin-transistor functions. Subsequently, challenges and future perspectives of using these multifunctional materials for the development of advanced spintronics are presented.

Weak Dispersion of Exciton Landé Factor with Band Gap Energy in Lead Halide Perovskites: Approximate Compensation of the Electron and Hole Dependences

The optical properties of lead halide perovskite semiconductors in vicinity of the bandgap are controlled by excitons, so that investigation of their fundamental properties is of critical importance. The exciton Landé or g-factor gX is the key parameter, determining the exciton Zeeman spin splitting in magnetic fields. The exciton, electron, and hole carrier g-factors provide information on the band structure, including its anisotropy, and the parameters contributing to the electron and hole effective masses. Here, gX is measured by reflectivity in magnetic fields up to 60 T for lead halide perovskite crystals. The materials band gap energies at a liquid helium temperature vary widely across the visible spectral range from 1.520 up to 3.213 eV in hybrid organic-inorganic and fully inorganic perovskites with different cations and halogens: FA0.9Cs0.1PbI2.8Br0.2, MAPbI3, FAPbBr3, CsPbBr3, and MAPb(Br0.05Cl0.95)3. The exciton g-factors are found to be nearly constant, ranging from +2.3 to +2.7. Thus, the strong dependences of the electron and hole g-factors on the bandgap roughly compensate each other when combining to the exciton g-factor. The same is true for the anisotropies of the carrier g-factors, resulting in a nearly isotropic exciton g-factor. The experimental data are compared favorably with model calculation results.

Coherent Carrier Spin Dynamics in FAPbBr3 Perovskite Crystals

Coherent spin dynamics of electrons and holes are studied in hybrid organic-inorganic lead halide perovskite FAPbBr3 bulk single crystals using the time-resolved Kerr ellipticity technique at cryogenic temperatures. The Larmor spin precession of the carrier spins in a magnetic field is monitored to measure the Landé g-factors of electrons (+2.44) and holes (+0.41). These g-factors are highly isotropic. The measured spin dephasing times amount to a few nanoseconds, and the longitudinal hole spin relaxation time is 470 ns. The important role of the strong hyperfine interaction between carrier spins and nuclear spins is demonstrated via dynamic nuclear polarization. At low temperatures, electron and hole spin relaxation predominantly occurs via the hyperfine interaction, whose importance significantly decreases at temperatures above 12 K. We overview the spin dynamics in various lead halide perovskite crystals and polycrystalline films and conclude on their common features provided by charge carrier localization at cryogenic temperatures.

Bright Excitonic Fine Structure in Metal-Halide Perovskites: From Two-Dimensional to Bulk

The optical response of two-dimensional (2D) perovskites, often referred to as natural quantum wells, is primarily governed by excitons, whose properties can be readily tuned by adjusting the perovskite layer thickness. We have investigated the exciton fine structure splitting in the archetypal 2D perovskite (PEA)2(MA)n-1PbnI3n+1 with varying numbers of inorganic octahedral layers n = 1, 2, 3, and 4. We demonstrate that the in-plane excitonic states exhibit splitting and orthogonally oriented dipoles for all confinement regimes. The evolution of the exciton states in an external magnetic field provides further insights into the g-factors and diamagnetic coefficients. With increasing n, we observe a gradual evolution of the excitonic parameters characteristic of a 2D to three-dimensional transition. Our results provide valuable information concerning the evolution of the optoelectronic properties of 2D perovskites with the changing confinement strength.

Rashba Spin Splitting Limiting the Application of 2D Halide Perovskites for UV-Emitting Devices

Layered lead halide perovskites have attracted much attention as promising materials for a new generation of optoelectronic devices. To make progress in applications, a full understanding of the basic properties is essential. Here, we study 2D-layered (BA)2PbX4 by using different halide anions (X = I, Br, and Cl) along with quantum confinement. The obtained cell parameter evolution, supported by experimental measurements and theoretical calculations, indicates strong lattice distortions of the metal halide octahedra, breaking the local inversion symmetry in (BA)2PbCl4, which strongly correlates with a pronounced Rashba spin-splitting effect. Optical measurements reveal strong photoluminescence quenching and a drastic reduction in the PL quantum yield in this larger band gap compound. We suggest that these optical results are closely related to the appearance of the Rashba effect due to the existence of a local electric dipole. The results obtained in ab initio calculations showed that the (BA)2PbCl4 possesses electrical polarization of 0.13 μC/cm2 and spin-splitting energy of about 40 meV. Our work establishes that local octahedra distortions induce Rashba spin splitting, which explains why obtaining UV-emitting materials with high PLQY is a big challenge.

Ab Initio Predictions of Spin Relaxation, Dephasing, and Diffusion in Solids

Spin relaxation, dephasing, and diffusion are at the heart of spin-based information technology. Accurate theoretical approaches to simulate spin lifetimes (τs), determining how fast the spin polarization and phase information will be lost, are important to the understanding of the underlying mechanism of these spin processes, and invaluable in searching for promising candidates of spintronic materials. Recently, we develop a first-principles real-time density-matrix (FPDM) approach to simulate spin dynamics for general solid-state systems. Through the complete first-principles descriptions of light-matter interaction and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent spin-orbit coupling, as well as ab initio Landé g-factor, our method can predict τs at various conditions as a function of carrier density and temperature, under electric and magnetic fields. By employing this method, we successfully reproduce experimental results of disparate materials and identify the key factors affecting spin relaxation, dephasing, and diffusion in different materials. Specifically, we predict that germanene has long τs (∼100 ns at 50 K), a giant spin lifetime anisotropy, and spin-valley locking effect under electric fields, making it advantageous for spin-valleytronic applications. Based on our theoretical derivations and ab initio simulations, we propose a new useful electronic quantity, named spin-flip angle θ↑↓, for the understanding of spin relaxation through intervalley spin-flip scattering processes. Our method can be further applied to other emerging materials and extended to simulate exciton spin dynamics and steady-state photocurrents due to photogalvanic effect.

Pressure-Induced Free Exciton Emission in a Quasi-Zero-Dimensional Hybrid Lead Halide

Structural dimensionality and electronic dimensionality play a crucial role in determining the type of excitonic emission in hybrid metal halides (HMHs). It is important but challenging to achieve free exciton (FE) emission in zero-dimensional (0D) HMHs based on the control over the electronic dimensionality. In this work, a quasi-0D HMH (C7 H15 N2 Br)2 PbBr4 with localized electronic dimensionality is prepared as a prototype model. With increasing pressure onto (C7 H15 N2 Br)2 PbBr4 , the broad and weak self-trapped exciton (STE) emission at ambient conditions is considerably enhanced before 3.6 GPa, which originates from more distorted [PbBr4 ]2- seesaw units upon compression. Notably, a narrow FE emission in (C7 H15 N2 Br)2 PbBr4 appears at 3.6 GPa, and then this FE emission is gradually strengthened up to 8.4 GPa. High pressure structural characterizations reveal that anisotropic contraction of (C7 H15 N2 Br)2 PbBr4 results in a noticeable reduction in the distance between adjacent [PbBr4 ]2- seesaw units, as well as an obvious enhancement of crystal stiffness. Consequently, the electronic connectivity in (C7 H15 N2 Br)2 PbBr4 is sufficiently promoted above 3.6 GPa, which is also supported with theoretical calculations. The elevation of electronic connectivity and enhanced stiffness together lead to pressure-induced FE emission and subsequent emission enhancement in quasi-0D (C7 H15 N2 Br)2 PbBr4 .

Spin Coherence and Spin Relaxation in Hybrid Organic-Inorganic Lead and Mixed Lead-Tin Perovskites

Metal halide perovskites make up a promising class of materials for semiconductor spintronics. Here we report a systematic investigation of coherent spin precession, spin dephasing and spin relaxation of electrons and holes in two hybrid organic-inorganic perovskites MA0.3FA0.7PbI3 and MA0.3FA0.7Pb0.5Sn0.5I3 using time-resolved Faraday rotation spectroscopy. With applied in-plane magnetic fields, we observe robust Larmor spin precession of electrons and holes that persists for hundreds of picoseconds. The spin dephasing and relaxation processes are likely to be sensitive to the defect levels. Temperature-dependent measurements give further insights into the spin relaxation channels. The extracted electron Landé g-factors (3.75 and 4.36) are the biggest among the reported values in inorganic or hybrid perovskites. Both the electron and hole g-factors shift dramatically with temperature, which we propose to originate from thermal lattice vibration effects on the band structure. These results lay the foundation for further design and use of lead- and tin-based perovskites for spintronic applications.

Impact of Bychkov-Rashba Spin Splitting on Dual Emissions for Lead Halide Perovskite Nanowires

Bychkov-Rashba spin-orbit coupling (SOC) is decisive for photoinduced photoluminescence (PL) in terms of double emissions. It turns out to be remarkable for one-dimensional lead halide perovskite nanowires (PeNWs). This is primarily due to large surface to volume ratios and structural symmetry breaking fields in the reduced dimension. Systematic studies of the effect of Rashba SOC on PL and its discrimination with the self-trapped exciton in wide temperature and illumination intensity ranges are considerably important and, heretofore, have not been performed. Here, highly crystalline methylammonium lead triiodine (MAPbI3) PeNWs are demonstrated to be able to produce remarkable dual emissions at low temperatures. With extensive analyses by a photoelectrical device-based spin-photogalvanic effect and magnetophotoluminescence, the Rashba effect is proven to be the only factor that governs the dual emissions. We believe a complete understanding of the PL character of PeNWs is beneficial for the development of novel perovskite nanophotonic devices.

Spin-Flip Raman Scattering on Electrons and Holes in Two-Dimensional (PEA)2 PbI4 Perovskites

The class of Ruddlesden-Popper type (PEA)2 PbI4 perovskites comprises 2D structures whose optical properties are determined by excitons with a large binding energy of about 260 meV. It complements the family of other 2D semiconductor materials by having the band structure typical for lead halide perovskites, that can be considered as inverted compared to conventional III-V and II-VI semiconductors. Accordingly, novel spin phenomena can be expected for them. Spin-flip Raman scattering is used here to measure the Zeeman splitting of electrons and holes in a magnetic field up to 10 T. From the recorded data, the electron and hole Landé factors (g-factors) are evaluated, their signs are determined, and their anisotropies are measured. The electron g-factor value changes from +2.11 out-of-plane to +2.50 in-plane, while the hole g-factor ranges between -0.13 and -0.51. The spin flips of the resident carriers are arranged via their interaction with photogenerated excitons. Also the double spin-flip process, where a resident electron and a resident hole interact with the same exciton, is observed showing a cumulative Raman shift. Dynamic nuclear spin polarization induced by spin-polarized holes is detected in corresponding changes of the hole Zeeman splitting. An Overhauser field of the polarized nuclei acting on the holes as large as 0.6 T can be achieved.

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.

Fine Structure Splitting of Phonon-Assisted Excitonic Transition in (PEA)2PbI4 Two-Dimensional Perovskites

Two-dimensional van der Waals materials exhibit particularly strong excitonic effects, which causes them to be an exceptionally interesting platform for the investigation of exciton physics. A notable example is the two-dimensional Ruddlesden-Popper perovskites, where quantum and dielectric confinement together with soft, polar, and low symmetry lattice create a unique background for electron and hole interaction. Here, with the use of polarization-resolved optical spectroscopy, we have demonstrated that the simultaneous presence of tightly bound excitons, together with strong exciton-phonon coupling, allows for observing the exciton fine structure splitting of the phonon-assisted transitions of two-dimensional perovskite (PEA)2PbI4, where PEA stands for phenylethylammonium. We demonstrate that the phonon-assisted sidebands characteristic for (PEA)2PbI4 are split and linearly polarized, mimicking the characteristics of the corresponding zero-phonon lines. Interestingly, the splitting of differently polarized phonon-assisted transitions can be different from that of the zero-phonon lines. We attribute this effect to the selective coupling of linearly polarized exciton states to non-degenerate phonon modes of different symmetries resulting from the low symmetry of (PEA)2PbI4 lattice.

Magnetically Tunable Spontaneous Superradiance from Mesoscopic Perovskite Emitter Clusters

Perovskite emitters are promising materials as next-generation optical sources due to their low fabrication cost and high quantum yield. In particular, the superradiant emission from a few coherently coupled perovskite emitters can be used to produce a bright entangled photon source. Here, we report the observation of superradiance from mesoscopic (<55) CsPbBr₃ perovskite emitters, which have a much smaller ensemble size than the previously reported results (>10⁶ emitters). The superradiance is spontaneously generated by off-resonance excitation and detected by time-resolved photoluminescence and second-order photon correlation measurements. We observed a remarkable magnetic tunability of the superradiant photon bunching, indicating a magnetic field-induced decoherence process. The experimental results can be well explained using a theoretical framework based on the microscopic master equation. Our findings shed light on the superradiance mechanism in perovskite emitters and enable low-cost quantum light sources based on perovskite.

Spin-photogalvanic effect in chiral lead halide perovskites

Low-temperature solution-made chiral lead halide perovskites (LHPs) have spontaneous Bychkov-Rashba spin orbit coupling (SOC) and chiral-induced spin selectivity (CISS) qualities. Their coexistence may give rise to considerable spin and charge conversion capabilities for spin-orbitronic applications. In this study, we demonstrate the spin-photogalvanic effect for (R-MBA)₂PbI₄ and (S-MBA)₂PbI₄ polycrystalline film-based lateral devices (100 μm channel length). The light helicity dependence of the short-circuit photocurrent exhibits the circular photogalvanic effect (CPGE) and linear photogalvanic effect (LPGE) with decent two-fold symmetry for a complete cycle in a wide temperature range from 4 K to 300 K. Because of the Rashba SOC and the material helicity, the effect is converse for the two chiral LHPs. In addition, its magnitude and sign can be effectively tuned by constant magnetic fields. The Rashba effect, CISS-generated unbalanced spin transport, and chiral-induced magnetization are mutually responsible for it. Our study evidently proves the future prospect of using chiral LHPs for spin-orbitronics.

Biexciton dynamics in halide perovskite nanocrystals

Lead halide perovskite nanocrystals are attracting considerable interest as next-generation optoelectronic materials. Optical responses of nanocrystals are determined by excitons and exciton complexes such as trions and biexcitons. Understanding of their dynamics is indispensable for the optimal design of optoelectronic devices and the development of new functional properties. Here, we summarize the recent advances on the exciton and biexciton photophysics in lead halide perovskite nanocrystals revealed by femtosecond time-resolved spectroscopy and single-dot spectroscopy. We discuss the impact of the biexciton dynamics on controlling and improving the optical gain.

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.

Submillisecond Spin Relaxation in CsPb(Cl,Br)3 Perovskite Nanocrystals in a Glass Matrix

Lead halide perovskite nanocrystals in a glass matrix are a promising platform for optoelectronic applications due to their excellent optical properties combined with outstanding stability against the environment. We reveal the potential of this system for spintronics by studying the electron spin properties of CsPb(Cl,Br)₃ nanocrystals in a fluorophosphate glass matrix. Using optical spin orientation and spin depolarization with a radio frequency field, we measure longitudinal spin relaxation time, T₁, reaching several hundreds of microseconds at low temperatures. This time T₁ corresponds to a spin state with a small g factor, which we attribute to a weakly exchange-coupled electron-hole pair with antiparallel spins.

The Landé factors of electrons and holes in lead halide perovskites: universal dependence on the band gap

The Landé or g-factors of charge carriers are decisive for the spin-dependent phenomena in solids and provide also information about the underlying electronic band structure. We present a comprehensive set of experimental data for values and anisotropies of the electron and hole Landé factors in hybrid organic-inorganic (MAPbI₃, MAPb(Br_0.5Cl_0.5)₃, MAPb(Br_0.05Cl_0.95)₃, FAPbBr₃, FA_0.9Cs_0.1PbI_2.8Br_0.2, MA=methylammonium and FA=formamidinium) and all-inorganic (CsPbBr₃) lead halide perovskites, determined by pump-probe Kerr rotation and spin-flip Raman scattering in magnetic fields up to 10 T at cryogenic temperatures. Further, we use first-principles density functional theory (DFT) calculations in combination with tight-binding and k ⋅ p approaches to calculate microscopically the Landé factors. The results demonstrate their universal dependence on the band gap energy across the different perovskite material classes, which can be summarized in a universal semi-phenomenological expression, in good agreement with experiment.

The Landé factors govern all the spin-related basic phenomena and are the key parameters which guide spintronics applications. Here, Kirstein et al. demonstrate a universal dependence of the Landé factors on the bandgap energy of several perovskite materials.

Achieving Up-Conversion Amplified Spontaneous Emission through Spin Alignment between Coherent Light-Emitting Excitons in Perovskite Microstructures

Metal hybrid perovskites have presented interesting infrared-to-visible up-conversion light-emitting lasing properties through multi-photon absorption. Here, when the optical pumping switches between circular and linear polarization, up-conversion amplified spontaneous emission (ASE) intensity exhibits large and small amplitudes, respectively, leading to a positive up-conversion ΔASE in the CsPbBr3 perovskite microrods. This observed phenomenon demonstrates that the coherent interaction between coherent light-emitting excitons is indeed established at the up-conversion ASE regime in the CsPbBr3 perovskite microrods. In addition, the positive up-conversion ΔASE indicates the orbital magnetic dipoles between coherent light-emitting excitons are conserved during up-conversion ASE action. Essentially, the up-conversion ΔASE results provide evidence that shows up-conversion ASE can be realized by the orbit−orbit polarization interaction between light-emitting excitons. Moreover, up-conversion ASE proportionally increased as the pumping fluence increased, which shows that orbit–orbit polarization interaction can be gradually enhanced between coherent light-emitting excitons by increasing pumping density in the CsPbBr3 perovskite microrods. Substantially, our studies provide a fundamental understanding of the spin alignment between coherent light-emitting excitons towards developing spin-dependent nonlinear lasing actions in metal halide perovskites.

Unexpected Anisotropy of the Electron and Hole Landé g-Factors in Perovskite CH3NH3PbI3 Polycrystalline Films

In this work, we studied, at low temperature, the coherent evolution of the localized electron and hole spins in a polycrystalline film of CH3NH3PbI3 (MAPI) by using a picosecond-photo-induced Faraday rotation technique in an oblique magnetic field. We observed an unexpected anisotropy for the electron and hole spin. We determined the electron and hole Landé factors when the magnetic field was applied in the plane of the film and perpendicular to the exciting light, denoted as transverse ⟂ factors, and when the magnetic field was applied perpendicular to the film and parallel to the exciting light, denoted as parallel ∥ factors. We obtained |ge,⟂|=2.600 ± 0.004, |ge,∥|=1.604 ± 0.033 for the electron and |gh,⟂|=0.406 ± 0.002, |gh,∥|=0.299 ± 0.007 for the hole. Possible origins of this anisotropy are discussed herein.

Omnidirectional exciton diffusion in quasi-2D hybrid organic-inorganic perovskites

Exciton transport plays a central role in optoelectronic and photonic devices. In quasi-two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs), tightly bound excitons are found to diffuse within 2D layers rapidly with a non-monotonic temperature dependence. Surprisingly, the interlayer exciton diffusion is quite effective as well despite the large interlayer distance. This is in sharp contrast to electron transport, where the interlayer mobility is several orders of magnitude smaller than the intralayer one. Here, we show that the unusual exciton diffusion behaviors can be systematically modeled via the excitonic band structure arising from a long-range dipolar coupling. Coherent exciton motion is interrupted by scattering of impurities at low temperatures and of acoustic/optical phonons at high temperatures. Acoustic and optical phonons modulate the dipole-dipole distance and the dipole orientation, respectively. The ratio of intralayer and interlayer diffusion constants, D_xx/D_zz, is comparable to a_z/a_x with a_z and a_x being the interlayer and intralayer lattice constants of 2D HOIPs, respectively. The efficient and omnidirectional exciton diffusion suggests a great potential of 2D HOIPs in novel excitonic and polaritonic applications.

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.

Magnetic-field manipulation of circularly polarized photoluminescence in chiral perovskites

The introduction of chiral organic ligands into hybrid organic-inorganic perovskites (HOIPs) results in chiral perovskites, which exhibit natural optical activities (NOAs) such as circularly polarized luminescence (CPL). CPL can be observed in achiral HOIPs under a magnetic field as well. Here, we systematically study the temperature- and magnetic field-dependence of both circular polarization and total intensity in chiral HOIPs. Pronounced CPL polarization is observed in polycrystalline films of chiral HOIPs, which can be further tuned by an applied magnetic field. The magnetic field also modifies the total intensity of CPL, giving rise to magneto-PL in chiral HOIPs, which is observable even at room temperature. The observed field and temperature-dependence of polarization can be well accounted for by a recently developed theory of chiral HOIPs, where the materials' helicity gives rise to a novel spin-orbit coupling (SOC). The observed MPL can be quantitatively accounted for by the interplay of exciton fine structures and the magnetic field. Our study suggests that the magnetic field provides an effective means to manipulate both the polarization and intensity of CPL in chiral HOIPs, which can be exploited for novel device applications.

Lead-Dominated Hyperfine Interaction Impacting the Carrier Spin Dynamics in Halide Perovskites

The outstanding optical quality of lead halide perovskites inspires studies of their potential for the optical control of carrier spins as pursued in other materials. Entering largely uncharted territory, time-resolved pump-probe Kerr rotation is used to explore the coherent spin dynamics of electrons and holes in bulk formamidinium caesium lead iodine bromide (FA0.9 Cs0.1 PbI2.8 Br0.2 ) and to determine key parameters characterizing interactions of their spins, such as the g-factors and relaxation times. The demonstrated long spin dynamics and narrow g-factor distribution prove the perovskites as promising competitors for conventional semiconductors in spintronics. The dynamic nuclear polarization via spin-oriented holes is realized and the identification of the lead (207 Pb) isotope in optically detected nuclear magnetic resonance proves that the hole-nuclei interaction is dominated by the lead ions. A detailed theoretical analysis accounting for the specifics of the lead halide perovskite materials allows the evaluation of the underlying hyperfine interaction constants, both for electrons and holes. Recombination and spin dynamics evidence that at low temperatures, photogenerated electrons and holes are localized at different regions of the perovskite crystal, resulting in their long lifetimes up to 44 μs. The findings form the base for the tailored development of spin-optoelectronic applications for the large family of lead halide perovskites and their nanostructures.

Packing-Shape Effects of Optical Properties in Amplified Spontaneous Emission through Dynamics of Orbit-Orbit Polarization Interaction in Hybrid Perovskite Quantum Dots Based on Self-Assembly

This paper reports packing-shape effects of amplified spontaneous emission (ASE) through orbital polarization dynamics between light-emitting excitons by stacking perovskite (MAPbBr₃) quantum dots (QDs sized between 10 nm and 14 nm) into rod-like and diamond-like aggregates. The rod-like packing shows a prolonged photoluminescence (PL) lifetime (184 ns) with 3 nm red-shifted peak (525 nm) as compared to the diamond-like packing (PL peak, 522 nm; lifetime, 19 ns). This indicates that the rod-like packing forms a stronger interaction between QDs with reduced surface-charged defects, leading to surface-to-inside property-tuning capability with an ASE. Interestingly, the ASE enabled by rod-like packing shows an orbit-orbit polarization interaction between light-emitting excitons, identified by linearly/circularly polarized pumping conditions. More importantly, the polarization dynamics is extended to the order of nanoseconds in the rod-like assembly, determined by the observation that within the ASE lifetime (2.54 ns) the rotating pumping beam polarization direction largely affects the coherent interaction between light-emitting excitons.

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.

Coherent Spin Dynamics of Electrons and Holes in CsPbBr3 Colloidal Nanocrystals

The spin dynamics in CsPbBr₃ lead halide perovskite nanocrystals are studied by picosecond pump-probe Faraday rotation in an external magnetic field. Coherent Larmor precession of electrons and holes with spin dephasing times of ∼600 ps is detected in a transversal magnetic field. The longitudinal spin relaxation time in weak magnetic fields reaches 80 ns at a temperature of 5 K. In this regime, the carrier spin dynamics is governed by nuclear spin fluctuations characterized by an effective hyperfine field strength of 25 mT. The Landé factors determining the carrier Zeeman splittings are g_e = +1.73 for electrons and g_h = +0.83 for holes. A comparison with a CsPbBr₃ polycrystalline film and bulk single crystals evidences that the spatial confinement of electrons and holes in the nanocrystals only slightly affects their g factors and spin dynamics.

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.

Manganese doping for enhanced magnetic brightening and circular polarization control of dark excitons in paramagnetic layered hybrid metal-halide perovskites

Materials combining semiconductor functionalities with spin control are desired for the advancement of quantum technologies. Here, we study the magneto-optical properties of novel paramagnetic Ruddlesden-Popper hybrid perovskites Mn:(PEA)2PbI4 (PEA = phenethylammonium) and report magnetically brightened excitonic luminescence with strong circular polarization from the interaction with isolated Mn2+ ions. Using a combination of superconducting quantum interference device (SQUID) magnetometry, magneto-absorption and transient optical spectroscopy, we find that a dark exciton population is brightened by state mixing with the bright excitons in the presence of a magnetic field. Unexpectedly, the circular polarization of the dark exciton luminescence follows the Brillouin-shaped magnetization with a saturation polarization of 13% at 4 K and 6 T. From high-field transient magneto-luminescence we attribute our observations to spin-dependent exciton dynamics at early times after excitation, with first indications for a Mn-mediated spin-flip process. Our findings demonstrate manganese doping as a powerful approach to control excitonic spin physics in Ruddlesden-Popper perovskites, which will stimulate research on this highly tuneable material platform with promise for tailored interactions between magnetic moments and excitonic states.

Strong spin-orbit coupling inducing Autler-Townes effect in lead halide perovskite nanocrystals

Manipulation of excitons via coherent light-matter interaction is a promising approach for quantum state engineering and ultrafast optical modulation. Various excitation pathways in the excitonic multilevel systems provide controllability more efficient than that in the two-level system. However, these control schemes have been restricted to limited control-light wavelengths and cryogenic temperatures. Here, we report that lead halide perovskites can lift these restrictions owing to their multiband structure induced by strong spin-orbit coupling. Using CsPbBr₃ perovskite nanocrystals, we observe an anomalous enhancement of the exciton energy shift at room temperature with increasing control-light wavelength from the visible to near-infrared region. The enhancement occurs because the interconduction band transitions between spin-orbit split states have large dipole moments and induce a crossover from the two-level optical Stark effect to the three-level Autler-Townes effect. Our finding establishes a basis for efficient coherent optical manipulation of excitons utilizing energy states with large spin-orbit splitting.

Here, Yumoto et al. demonstrate that for a halide perovskite with large spin-orbit splitting the optical Stark effect can give way to a three level Autler-Townes effect in the near-infrared region. The multiband nature of the effect potentially allows for further optical control over quantum states.

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 Physics of Interlayer Exciton Delocalization in Ruddlesden-Popper Lead Halide Perovskites

Two-dimensional (2D) lead halide Ruddlesden-Popper perovskites (RPP) have recently emerged as a prospective material system for optoelectronic applications. Their self-assembled multi quantum-well structure gives rise to the novel interwell energy funnelling phenomenon, which is of broad interests for photovoltaics, light-emission applications, and emerging technologies (e.g., spintronics). Herein, we develop a realistic finite quantum-well superlattice model that corroborates the hypothesis of exciton delocalization across different quantum-wells in RPP. Such delocalization leads to a sub-50 fs coherent energy transfer between adjacent wells, with the efficiency depending on the RPP phase matching and the organic large cation barrier lengths. Our approach provides a coherent and comprehensive account for both steady-state and transient dynamical experimental results in RPPs. Importantly, these findings pave the way for a deeper understanding of these systems, as a cornerstone crucial for establishing material design rules to realize efficient RPP-based devices.

External Field-Tunable Internal Orbit-Orbit Interaction in Flexible Perovskites

In hybrid metal halide perovskites, electrons carry both orbital and spin momenta through s-p wave function hybridization. This leads to a hypothesis that the orbit-orbit interaction between excitons can occur through orbital magnetic dipoles forming short-range interaction or through orbital polarizations forming long-range interaction to influence optoelectronic properties. This Letter reports an interesting phenomenon: the orbit-orbit interaction can be electrically switched between orbital magnetic dipoles and orbital polarizations in a flexible perovskite (MAPbI_3-xCl_x) solar cell by scanning an external voltage between forward and reverse biases (0.2 and -0.2 V). Essentially, this phenomenon presents an external mechanism for electrically controlling the internal orbit-orbit interaction in hybrid perovskites. It was further observed that this bias-switchable orbit-orbit interaction is sensitive to temperature, becoming negligible when the temperature is decreased from 300 to 250 K. This observation indicates that the mobile ions driven by an external electrical field provide an intrinsic mechanism for electrically switching the orbit-orbit interaction through polarization and spin parameters while applying an external voltage between forward and reverse biases. These results provide a comprehensive understanding of tuning the orbit-orbit interaction in flexible perovskites toward developing orbitronic actions.

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.

Chirality-Induced Spin-Orbit Coupling, Spin Transport, and Natural Optical Activity in Hybrid Organic-Inorganic Perovskites

Hybrid organic-inorganic perovskites (HOIPs) with chiral organic ligands exhibit highly spin-dependent transport and strong natural optical activity (NOA). Here we show that these remarkable features can be traced to a chirality-induced spin-orbit coupling (SOC), H_so = ατk_zσ_z, which connects the carrier's spin (σ_z), its wave vector (k_z), and the material's helicity (τ) along the screw direction with strength α controlled by the geometry of the organic ligands. This SOC leads to a macroscopic spin polarization in the presence of an electrical current and is responsible for the observed spin-selective transport. NOA originates from a coupling between the exciton's center-of-mass wave vector K_z and its circular polarization j_z^ex, H_so^' = α'τK_zj_z^ex, contributed jointly from the electron's and the hole's SOCs in an exciton. Our model provides a roadmap to achieve a strong and tunable chirality in HOIPs for novel applications utilizing carrier spin and photon polarization.

Magneto-Optical Detection of Photoinduced Magnetism via Chirality-Induced Spin Selectivity in 2D Chiral Hybrid Organic-Inorganic Perovskites

The recent convergence of chiral molecules with metal halide perovskite frameworks gives rise to an interesting family of chiral systems: two-dimensional, chiral hybrid organic-inorganic perovskites (chiral-HOIPs). While possessing photovoltaic properties of traditional HOIPs, this class of materials is endowed with chirality through its organic ligands in which the degeneracy of the electron spin in charge transport is broken. That is, the chirality-induced spin selectivity (CISS) effect manifests, making it a promising platform to bridge opto-spintronic studies and the CISS effect. In this work, chiral-HOIP/NiFe heterostructures are studied by means of the magneto-optical Kerr effect using a Sagnac interferometer. Upon illumination of the chiral-HOIPs, the Kerr signal at the chiral-HOIP/NiFe interface changes, and a linear dependence of the response on the magnetic field is observed. The sign of the slope was found to depend on the chirality of the HOIPs. The results demonstrate the utility of chiral-HOIP materials for chiral opto-spintronic applications.

How Exciton Interactions Control Spin-Depolarization in Layered Hybrid Perovskites

Using circularly polarized broadband transient absorption, time-resolved circular photoluminescence, and transient Faraday rotation spectroscopy, we report that spin-dependent interactions have a significant impact on exciton energies and spin depolarization times in layered Ruddlesden-Popper hybrid metal-halide perovskites. In BA₂FAPb₂I₇, we report that room-temperature spin lifetimes are largest (3.2 ps) at a carrier density of ∼10¹⁷ cm^-3 with increasing depolarization rates at higher exciton densities. This indicates that many-body interactions reduce spin-lifetimes and outcompete the effect of D'yakonov-Perel precessional relaxation that has been previously reported at lower carrier densities. We further observe a dynamic circular dichroism that arises from a photoinduced polarization in the exciton distribution between total angular momentum states. Our findings provide fundamental and application relevant insights into the spin-dependent exciton-exciton interactions in layered hybrid perovskites.

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.

Extremely Long Spin Lifetime of Light-Emitting States in Quasi-2D Perovskites through Orbit-Orbit Interaction

This paper reports an extremely long spin relaxation time of optically polarized light-emitting states at room temperature in quasi-2D perovskites [(PEA)₂(MA)₄Pb₅Br₁₆ with n = 5], when the long-range orbit-orbit interaction between excited states is developed through orbital polarization. Our studies found that the quasi-2D perovskite [(PEA)₂(MA)₄Pb₅Br₁₆ with n = 5] demonstrates a long-range orbit-orbit interaction between excited states to conserve the spins of optically polarized light-emitting states, identified by the positive change on photoluminescence intensity (+ΔPL) in steady state upon switching the photoexcitation from linear to circular polarization. Meanwhile, the PL circular polarization (σ⁺σ⁺ - σ⁺σ^-) can maintain in nanosecond under fixed photoexcitation (σ⁺). In contrast, the 2D/3D mixed perovskite (n > 5) shows a short-range orbit-orbit interaction between excited states through orbital magnetic dipoles, identified by the -ΔPL by switching from linear to circular photoexcitation. At the same time, the spin lifetime of light-emitting states becomes undetectable.

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.

Optical deformation potential and self-trapped excitons in 2D hybrid perovskites

Self-trapped excitons (STEs) in two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) emit broadband white light, suggesting the great potential of 2D HOIPs in low-cost lighting and display applications. A prerequisite for understanding STEs' properties is a correct identification of the underlying interaction that leads to the STEs. Here, we show that the long-range polar coupling between electrons and optical phonons is quenched in 2D HOIPs' tightly bound excitons and cannot effect STEs. Rather, the STEs are induced by a short-range optical deformation potential (ODP) arising from the phonon-modulated Pb-X quantum-well thickness. Interaction between transition dipoles in adjacent PbX6 (X = Br or I) octahedra gives rise to highly anisotropic intra- and inter-layer exciton bandwidths. In flat (001) 2D HOIPs, both the ODP and the exciton bandwidths are susceptible to out-of-plane PbX6 tilting but not to the in-plane one, and their interplay can quantitatively account for the observed temperature and structure dependences of luminescence associated with STEs. In corrugated (011) 2D HOIPs, the exciton bandwidth is further reduced and the resultant STEs have a stronger lattice distortion and broader luminescence spectrum. Our results reveal the mechanism of STE formation and suggest ways of tuning STEs and associated broadband luminescence in 2D HOIPs.

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.

Ferroelectricity and Rashba Effect in a Two-Dimensional Dion-Jacobson Hybrid Organic-Inorganic Perovskite

Hybrid organic-inorganic perovskites (HOIPs) are a new generation of high-performance materials for solar cells and light emitting diodes. Beyond these applications, ferroelectricity and spin-related properties of HOIPs are increasingly attracting interests. The presence of strong spin-orbit coupling, allied with symmetry breaking ensured by remanent polarization, should give rise to Rashba-type splitting of electronic bands in HOIP. However, the report of both ferroelectricity and Rashba effect in HOIP is rare. Here we report the observation of robust ferroelectricity and Rashba effect in two-dimensional Dion-Jacobson perovskites.

Using Mechanical Stress to Investigate the Rashba Effect in Organic-Inorganic Hybrid Perovskites

Organic-inorganic hybrid perovskites simultaneously possess strong spin-orbit coupling (SOC) and structure inversion asymmetry, establishing a Rashba effect to influence light emission and photovoltaics. Here, we use mechanical bending as a convenient approach to investigate the Rashba effect through SOC in perovskite (MAPbI_3-xCl_x) films by elastically deforming grains. It is observed that applying a concave bending can broaden the line shape of the magnetophotocurrent, increasing the internal magnetic parameter B₀ from 121 to 205 mT, which indicates an enhancement on SOC. Interestingly, the PL lifetime is found to be enlarged from 9.9 to 14.8 ns under this bending, which suggests that introducing compressive strain can essentially increase the Rashba effect through SOC, leading to an increase upon indirect band transition. Furthermore, the PL peak associated with the Rashba effect is shifted from 776 to 780 nm under this mechanical bending. Therefore, mechanical bending provides a convenient experimental method to approach the Rashba effect in hybrid perovskites.

The ground exciton state of formamidinium lead bromide perovskite nanocrystals is a singlet dark state

Lead halide perovskites have emerged as promising new semiconductor materials for high-efficiency photovoltaics, light-emitting applications and quantum optical technologies. Their luminescence properties are governed by the formation and radiative recombination of bound electron-hole pairs known as excitons, whose bright or dark character of the ground state remains unknown and debated. While symmetry analysis predicts a singlet non-emissive ground exciton topped with a bright exciton triplet, it has been predicted that the Rashba effect may reverse the bright and dark level ordering. Here, we provide the direct spectroscopic signature of the dark exciton emission in the low-temperature photoluminescence of single formamidinium lead bromide perovskite nanocrystals under magnetic fields. The dark singlet is located several millielectronvolts below the bright triplet, in fair agreement with an estimation of the long-range electron-hole exchange interaction. Nevertheless, these perovskites display an intense luminescence because of an extremely reduced bright-to-dark phonon-assisted relaxation.