The one-photon absorption cross section of nanocrystals (NCs) of the inorganic perovskite CsPbBr 3 is studied theoretically using a multiband k • p envelope-function model combined with a treatment of intercarrier correlation by many-body perturbation theory. A confined exciton is described first within the Hartree-Fock (HF) approximation and correlation between the electron and hole is then included in leading order by computing the first-order vertex correction to the electron-photon interaction. The vertex correction is found to give an enhancement of the near-threshold absorption cross section by a factor of up to 4 relative to the HF (mean-field) value of the cross section, for NCs with an edge length L = 9-12 nm (regime of intermediate confinement). The vertex-correction enhancement factors are found to decrease with increasing exciton energy; the absorption cross section for photons of energy ω = 3.1 eV (about 0.7 eV above threshold) is enhanced by a factor of only 1.4-1.5 relative to the HF value. The k • p corrections to the absorption cross section are also significant; they are found to increase the cross section at an energy ω = 3.1 eV by about 30% relative to the value found in the effective-mass approximation. The theoretical absorption cross section at ω = 3.1 eV, assuming a Kane parameter E P = 20 eV, is found to be intermediate among the set of measured values (which vary among themselves by nearly an order of magnitude) and to obey a power-law dependence σ (1) (ω) ∝ L 2.9 on the NC edge length L, in good agreement with experiment. The dominant contribution to the theoretical exponent 2.9 is shown to be the density of final-state excitons. We also calculate the radiative lifetimes of the ground-state 1S e -1S h exciton of NCs of CsPbBr 3 and CsPbI 3 , finding an overestimate by a factor of up to about two (for E P = 20 and 17 eV, respectively) compared to the available experimental data, which vary among themselves by about ±40%. The sources of theoretical uncertainty and the possible reasons for the discrepancies with experiment are discussed. The main theoretical uncertainty in these calculations is in the value of the Kane parameter E P .

We calculate the shift in emission frequency of the trion and biexciton (relative to that of the single exciton) for nanocrystals (NCs) of inorganic perovskites CsPbBr3 and CsPbI3. The calculations use an envelope-function k · p model combined with self-consistent Hartree-Fock and a treatment of the intercarrier correlation energy in the lowest (second) order of many-body perturbation theory. The carriers in the trion and biexciton are assumed to have relaxed nonradiatively to the ground state at the band edge before emission occurs. The theoretical trion shifts for both CsPbBr3 and CsPbI3 are found to be in fair agreement with available experimental data, which include low-temperature single-dot measurements, though are perhaps systematically small by a factor of order 1.5, which can plausibly be explained by a combination of a slightly overestimated dielectric constant and omitted third-and higher-order terms in the correlation energy. Taking this level of agreement into account, we estimate that the ground-state biexciton shift for CsPbBr3 is a redshift of order 10-20 meV for NCs with an edge-length of 12 nm. This value is intermediate among the numerous high-temperature measurements on NCs of CsPbBr3, which vary from large redshifts of order 100 meV to blueshifts of several meV.

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

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We present calculations of the two-photon absorption cross section σ (2) (ω) for nanocrystals (NCs) of the inorganic perovskite CsPbBr 3 for photon energies ω ranging from the absorption threshold at 2ω ≈ 2.3 eV up to 2ω = 3.1 eV. The calculations employ a 4 × 4 k • p envelope-function model, with final-state excitons described in a self-consistent Hartree-Fock approximation. The k • p corrections to σ (2) (ω) are found to be rather large, giving a reduction of about 30% in the cross section at the largest energies considered. The cross section is shown to be independent of polarization in the effective-mass approximation (EMA), but including k • p corrections leads to a small difference in σ (2) (ω) between circular and linear polarization, which rises to about 16% at 2ω = 3.1 eV. The theoretical cross section follows closely a power-law dependence on NC size, σ (2) (ω) ∝ L α , with theoretical exponents α = 3.4 (EMA) or α = 3.2 (4 × 4 k • p model), in excellent agreement with experiment. The dominant contribution to the exponent α is shown to be the number of final-state excitons per unit energy. Measured values of the absolute (normalized) cross section σ (2) (ω) show a large spread of values, differing by as much as a factor of 25 for some NC sizes. Our calculations strongly favor a group of measurements at the lower end of the reported range of σ (2) (ω).