Fine structure of excitons and electron-hole exchange energy in polymorphic CsPbBr3 single nanocrystals

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.

Homo- and Heterovalent Doping-Mediated Self-Trapped Exciton Emission and Energy Transfer in Mn-Doped Cs2Na1-xAgxBiCl6 Double Perovskites

Double perovskites exhibit low toxicity, intrinsic thermodynamic stability, and small carrier effective mass. Herein, a novel doping route was adopted to incorporate Mn ions into Cs₂Na_1-xAg_xBiCl₆ double perovskites for engineering the band gap and tailoring the energy transfer. The as-prepared Cs₂Na_1-xAg_xBiCl₆ (0 < x < 1) exhibited excellent photoluminescence and a broad self-trapped exciton (STE) band from 500 to 900 nm, which exhibited an abnormal emission peak blue shift with increasing temperature. For Mn-doped Cs₂Na_1-xAg_xBiCl₆, the two photoluminescence (PL) bands from d-d transition emission of Mn ions and STEs were always observed simultaneously in the PL window. The distinct energy-transfer channel from the Mn²⁺ ion guest to the double-perovskite host resulted in the dominant Mn²⁺ emission. Our results will be helpful for further understanding the nature of the photophysics of double perovskites.

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.

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.

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.

Underestimated Effect of a Polymer Matrix on the Light Emission of Single CsPbBr3 Nanocrystals

Lead-halide perovskite APbX₃ (A = Cs or organic cation; X = Cl, Br, I) nanocrystals (NCs) are the subject of intense research due to their exceptional characteristics as both classical and quantum light sources. Many challenges often faced with this material class concern the long-term optical stability, a serious intrinsic issue connected with the labile and polar crystal structure of APbX₃ compounds. When conducting spectroscopy at a single particle level, due to the highly enhanced contaminants (e.g., water molecules, oxygen) over the NC ratio, deterioration of NC optical properties occurs within tens of seconds with typically used excitation power densities (1-100 W/cm²) and in ambient conditions. Here, we demonstrate that choosing a suitable polymer matrix is of paramount importance for obtaining stable spectra from a single NC and for suppressing the dynamic photoluminescence blueshift. In particular, polystyrene (PS), the most hydrophobic among four tested polymers, leads to the best optical stability, one to two orders of magnitude higher than that obtained with poly(methyl methacrylate), a common polymeric encapsulant containing polar ester groups. Molecular mechanics simulations based on a force-field approximation corroborate the hypothesis that PS affords for a denser molecular packing at the NC surface. These findings underscore the often-neglected role of the sample preparation methodologies for the assessment of the optical properties of perovskite NCs at a single-particle level and guide the further design of robust single photon sources.

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.

Lattice Disorder-Engineered Energy Splitting between Bright and Dark Excitons in CsPbBr3 Quantum Wires

Excitons in nanostructured semiconductors often undergo strong electron-hole exchange interaction, resulting in bright-dark exciton splitting with the dark exciton usually being the lower energy state. This unfavorable state arrangement has become the major bottleneck for achieving high photoluminescence quantum yield (PLQY). However, the arrangement of dark and bright exciton states in lead halide perovskites is under intense debate due to the involvement of many complicated factors. We present here the first experimental evidence to demonstrate that the strain is a crucial factor in tuning the energy splitting of the bright and dark excitons, resulting in different PL properties.

Coherent spin dynamics of electrons and holes in CsPbBr3 perovskite crystals

The lead halide perovskites demonstrate huge potential for optoelectronic applications, high energy radiation detectors, light emitting devices and solar energy harvesting. Those materials exhibit strong spin-orbit coupling enabling efficient optical orientation of carrier spins in perovskite-based devices with performance controlled by a magnetic field. Here we show that elaborated time-resolved spectroscopy involving strong magnetic fields can be successfully used for perovskites. We perform a comprehensive study of high-quality lead halide perovskite CsPbBr₃ crystals by measuring the exciton and charge carrier g-factors, spin relaxation times and hyperfine interaction of carrier and nuclear spins by means of coherent spin dynamics. Owing to their ‘inverted’ band structure, perovskites represent appealing model systems for semiconductor spintronics exploiting the valence band hole spins, while in conventional semiconductors the conduction band electrons are considered for spin functionality.

Despite remarkable optical properties in lead halide perovskites, spin control in these materials is largely unexplored. Herein Belykh et al. study the coherent spin dynamics of electrons and holes in cesium lead bromide perovskites, and evidence interaction of electron and lattice nuclear spins.

Quantum and Dielectric Confinement Effects in Lower-Dimensional Hybrid Perovskite Semiconductors

Hybrid halide perovskites are now superstar materials leading the field of low-cost thin film photovoltaics technologies. Following the surge for more efficient and stable 3D bulk alloys, multilayered halide perovskites and colloidal perovskite nanostructures appeared in 2016 as viable alternative solutions to this challenge, largely exceeding the original proof of concept made in 2009 and 2014, respectively. This triggered renewed interest in lower-dimensional hybrid halide perovskites and at the same time increasingly more numerous and differentiated applications. The present paper is a review of the past and present literature on both colloidal nanostructures and multilayered compounds, emphasizing that availability of accurate structural information is of dramatic importance to reach a fair understanding of quantum and dielectric confinement effects. Layered halide perovskites occupy a special place in the history of halide perovskites, with a large number of seminal papers in the 1980s and 1990s. In recent years, the rationalization of structure-properties relationship has greatly benefited from new theoretical approaches dedicated to their electronic structures and optoelectronic properties, as well as a growing number of contributions based on modern experimental techniques. This is a necessary step to provide in-depth tools to decipher their extensive chemical engineering possibilities which surpass the ones of their 3D bulk counterparts. Comparisons to classical semiconductor nanostructures and 2D van der Waals heterostructures are also stressed. Since 2015, colloidal nanostructures have undergone a quick development for applications based on light emission. Although intensively studied in the last two years by various spectroscopy techniques, the description of quantum and dielectric confinement effects on their optoelectronic properties is still in its infancy.

Luminescent perovskites: recent advances in theory and experiments

This review summarizes previous research on luminescent perovskites, including oxides and halides, with different structural dimensionality. The relationship between the crystal structure, electronic structure and properties is discussed in detail.

Solvothermal synthesis of cesium lead halide perovskite nanowires with ultra-high aspect ratios for high-performance photodetectors

One-dimensional (1D) inorganic perovskite nanowires (NWs) have attracted promising attention for application in the fields of photodetection, lasers and lighting due to their outstanding optoelectronic properties. However the direct synthesis of highly pure all-inorganic perovskite NWs with well-defined morphologies and compositions still remains challenging. Here we report the controllable synthesis of brightly emitting cesium lead halide CsPbX₃ (X = Cl, Br) NWs and their assembly into high-performance photodetector nanodevices. High quality CsPbX₃ NWs have been directly synthesized via a solvothermal method without using post-synthetic anion-exchange reactions. The NWs are single-crystalline, with uniform diameters of ∼10 nm and lengths of up to tens of microns, showing ultra-high aspect ratios. Both CsPbCl₃ and CsPbBr₃ NWs show excellent photoluminescence (PL) characteristics with narrow emission spectra and high PL quantum yields (PLQYs). The photodetectors constructed on the CsPbX₃ NWs and interdigital electrodes (with interdigitation widths up to 100 μm) exhibit promising photoelectric properties, achieving high switching ratios (5.8 × 10³ for CsPbCl₃ NW devices and 1.1 × 10³ for CsPbBr₃ NW devices) and fast response time. The present solvothermal approach is controllable, convenient, and is easily realized for quantifiable preparation, and can further promote the application of the all-inorganic perovskite NWs in the optoelectronic field.

Unraveling exciton-phonon coupling in individual FAPbI3 nanocrystals emitting near-infrared single photons

Formamidinium lead iodide (FAPbI3) exhibits the narrowest bandgap energy among lead halide perovskites, thus playing a pivotal role for the development of photovoltaics and near-infrared classical or quantum light sources. Here, we unveil the fundamental properties of FAPbI3 by spectroscopic investigations of nanocrystals of this material at the single-particle level. We show that these nanocrystals deliver near-infrared single photons suitable for quantum communication. Moreover, the low temperature photoluminescence spectra of FAPbI3 nanocrystals reveal the optical phonon modes responsible for the emission line broadening with temperature and a vanishing exciton-acoustic phonon interaction in these soft materials. The photoluminescence decays are governed by thermal mixing between fine structure states, with a two-optical phonon Raman scattering process. These results point to a strong Frölich interaction and to a phonon glass character that weakens the interactions of charge carriers with acoustic phonons and thus impacts their relaxation and mobility in these perovskites.