The spin interaction of a hole confined in a quantum dot with the surrounding nuclei is described in terms of an effective magnetic field. We show that, in contrast to the Fermi contact hyperfine interaction for conduction electrons, the dipole-dipole hyperfine interaction is anisotropic for a hole, for both pure or mixed hole states. We evaluate the coupling constants of the hole-nuclear interaction and demonstrate that they are only one order of magnitude smaller than the coupling constants of the electron-nuclear interaction. We also study, theoretically, the hole spin dephasing of an ensemble of quantum dots via the hyperfine interaction in the framework of frozen fluctuations of the nuclear field, in absence or in presence of an applied magnetic field. We also discuss experiments which could evidence the dipole-dipole hyperfine interaction and give information on hole mixing. 2 I -INTRODUCTIONThe spin of an individual electron, confined in a quantum dot (QD), is currently considered as a potential candidate for the realization of spintronic and quantum information processing in solid-state-based devices [1][2][3]. While in bulk or quantum wells, the electronic spin is efficiently relaxed by processes related to spin-orbit coupling, such as the D'YakonovPerel mechanism [4], the spatial confinement of carriers in semiconductor QDs significantly reduces the relaxation and decoherence processes. Recently, the hyperfine coupling with the spins of the lattice nuclei has been identified as the ultimate limit, at low temperature, to the electron spin relaxation or decoherence in QDs.For conduction electrons, the hyperfine interaction has a Fermi contact character, and is at the origin of ensemble dephasing times of the order of one nanosecond in III-V QDs [5][6][7][8][9].For holes, the Fermi contact coupling is massively suppressed because of the p-symmetry of the valence band states. The hyperfine interaction is then induced by the weaker long-range dipole-dipole coupling [10], so that much longer relaxation and decoherence times are expected [11].Recent progresses in the preparation and reading of an ensemble of hole spins [12] or of a single hole spin, confined in QD, offer the opportunity to study their dynamics. By inserting single QDs in n-i-Schottky diode structures, D. Heiss et al. [13] and A.J. Ramsay et al.[14] have evidenced the possibility to initialize and store hole spins, as previously done with conduction electrons [15], while measuring the time dependence of their polarization.In the present work, we show that, while being weaker than the electron Fermi contact interaction, the long-range dipole-dipole coupling between holes and nuclei can be an efficient decoherence mechanism, and leads to ensemble dephasing times of the order of ten nanoseconds in III-V QDs.The paper is organized as follows: In section II, the hyperfine dipole-dipole coupling between nuclear spins and the spin of a hole is written in terms of an effective nuclear magnetic field acting on the hole spin. In this section, differe...

All inorganic CsPbX3 (X = Cl, Br, I) nanocrystals (NCs) belong to the novel class of confined metal-halide perovskites which are currently arousing enthusiasm and stimulating huge activity across several fields of optoelectronics due to outstanding properties. A deep knowledge of the band-edge excitonic properties of these materials is thus crucial to further optimize their performances. Here, high-resolution photoluminescence (PL) spectroscopy of single bromide-based NCs reveals the exciton fine structure in the form of sharp peaks that are linearly polarized and grouped in doublets or triplets, which directly mirror the adopted crystalline structure, tetragonal (D4h symmetry) or orthorhombic (D2h symmetry). Intelligible equations are found that show how the fundamental parameters (spin-orbit coupling, ΔSO, crystal field term, T, and electron-hole exchange energy, J) rule the energy spacings in doublets and triplets. From experimental data, fine estimations of each parameter are obtained. The analysis of the absorption spectra of an ensemble of NCs with a "quasi-bulk" behavior leads to ΔSO = 1.20 ± 0.06 eV and T = -0.34 ± 0.05 eV in CsPbBr3. The study of individual luminescence responses of NCs having sizes comparable to the exciton Bohr diameter, 7 nm, allows us to estimate the value of J to be around ≈3 meV in both tetragonal and orthorhombic phases. This value is already enhanced by confinement.