| Summary: | We discuss a variety of many-body approaches, within effective-mass and
k . p envelope-function formalisms, for calculating
correlated single excitons in semiconductor nanocrystals (NCs) to all orders in
the electron-hole Coulomb interaction. These approaches are applied to NCs of
the lead-halide perovskite CsPbBr3, which typically present excitons in
intermediate confinement with physical observables often strongly renormalized
by correlation (e.g., radiative decay rate enhanced by a factor of about 7
relative to a mean-field approach, for a NC of edge length 11 nm). The
many-body methods considered include the particle-hole Bethe-Salpeter equation,
configuration interaction with single excitations, and the random-phase
approximation with exchange (RPAE), which are shown to be closely related to
each other but to treat k . p corrections differently,
with RPAE being the most complete method. The methods are applied to calculate
the correlation energy, the radiative lifetime, and the long-range Coulomb
contribution to the fine structure of the ground-state exciton. In the limit of
large NC sizes, the numerical results are shown to agree well with analytical
results for this limit, where these are known. Correlated excited states of the
single exciton are used to calculate the one-photon absorption cross section;
the shape of the resulting cross-section curve (versus laser wavelength) at
threshold and up to an excitation energy of about 1 eV is in good agreement
with experimental cross sections. The equations for the methods are explicitly
adapted to spherical symmetry (involving radial integrals and angular factors)
and in this form permit a rapid computation for systems in intermediate
confinement.
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