Perovskite solar cells with record power conversion efficiency are fabricated by alloying both hybrid and fully inorganic compounds. While the basic electronic properties of the hybrid perovskites are now well understood, key electronic parameters for solar cell performance, such as the exciton binding energy of fully inorganic perovskites, are still unknown. By performing magneto transmission measurements, we determine with high accuracy the exciton binding energy and reduced mass of fully inorganic CsPbX 3 perovskites (X=I, Br, and an alloy of these). The well behaved (continuous) evolution of the band gap with temperature in the range 4 − 270 K suggests that fully inorganic perovskites do not undergo structural phase transitions like their hybrid counterparts.The experimentally determined dielectric constants indicate that at low temperature, when the motion of the organic cation is frozen, the dielectric screening mechanism is essentially the same both for hybrid and inorganic perovskites, and is dominated by the relative motion of atoms within the lead-halide cage.

We have accurately determined the exciton binding energy and reduced mass of single crystals of methylammonium lead tri-iodide using magneto-reflectivity at very high magnetic fields. The single crystal has excellent optical properties with a narrow line width of ∼ 3 meV for the excitonic transitions and a 2s transition which is clearly visible even at zero magnetic field. The exciton binding energy of 16 ± 2 meV in the low temperature orthorhombic phase is almost identical to the value found in polycrystalline samples, crucially ruling out any possibility that the exciton binding energy depends on the grain size. In the room temperature tetragonal phase, an upper limit for the exciton binding energy of 12 ± 4 meV is estimated from the evolution of 1s-2s splitting at high magnetic field.

The critical filling factor ν c where Shubnikov-de Haas oscillations become spin split is investigated for a set of GaAs-GaAlAs heterojunctions. Finite temperature magnetoresistance measurements are used to extract the value of ν c at zero temperature. The critically point is where the disorder potential has the same magnitude as the exchange energy, leading to the empirical relationship ν c = g * n e τ s h/2m 0 . This is valid for all the samples studied, where the density n e and single particle lifetime τ s both vary by more than an order of magnitude and g * the exchange enhanced g-factor has a weak dependence on density. For each sample the spin gap energy shows a linear increase with magnetic field. Experiments in tilted magnetic field show the spin gap is the sum of the bare Zeeman energy and an exchange term. This explains why measurements of the enhanced g-factor from activation energy studies in perpendicular field and the coincidence method in tilted fields have previously disagreed.

Fractional quantum Hall effect energy gaps have been measured as a function of Zeeman energy. The gap at n 1͞3 decreases as the g factor is reduced by hydrostatic pressure. This behavior is similar to that at n 1 and shows that the excitations are spinlike. At small Zeeman energy, the excitation is consistent with the reversal of 3 spins and may be interpreted as a small composite Skyrmion. At 20 kbar, where g has changed sign, the 1͞3 gap appears to increase again. [S0031-9007(97)

Exciton fine structure splitting in semiconductors reflects the underlying symmetry of the crystal and quantum confinement. Since 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 split-ting as large as ∼ 200µ eV. This result provides an important starting point for the discussion of the origin of the large bright exciton fine structure observed in perovskite nanocrystals.In an ideally pure semiconductor, the lowest energy electronic excitation is a bound electronhole pair (exciton). The exchange interaction between electron and the hole spins lifts the degeneracy between dark singlet and bright multiplet excitonic states producing a fine structure. The physics of the fine structure splitting (FSS) has been the subject of intense in-1 arXiv:1909.06054v1 [cond-mat.mes-hall]