  Quantum plasmonics of few electrons that was reported a few years ago in
photodoping experiments has received little or no attention in doped
nanomaterials both theoretically and experimentally. There are no studies of
quantum plasmonics of large quantum dots of the size of Bohr excitonic radius
or less that take electronic and geometric structure of the quantum dots. In
this work, we studied extensively the absorption spectra of a protype quantum
dot of sizeable ZnO of approximately 3.0 nm in diameter doped with Ga, and Al
in diluted limit with density functional theory (DFT) plus Hubbard corrections
(U). The localized surface plasmon resonances (LSPRs) were then determined from
the real part of the dielectric function by correlating the negative portion of
it to resonant spectral lines. Our results show the sensitivity of the spectral
lines to distribution of the dopants, the electronic structure of the dopants,
the polarization of the electric field, and size of the quantum dots. Even
though our findings are based on stoichiometrically simple ZnO, it shows that
the DFT + U method with numerical atomic basis can be used at reasonable
computational cost to study quantum plasmonics of few electrons taking into
account electronic and geometric structures, which is missing currently. The
method can be extended to study magneto-optics of diluted magnetic
semiconductor QDs.
