Quantum Size Effects on Magneto-Optical Absorption in Spherical Quantum Dots: Role of Confining Potential and Magnetic Field

Semiconducting quantum dots -- more fancifully dubbed artificial atoms -- are quasi-zero dimensional,
tiny, man-made systems with charge carriers {\em completely} confined in all three dimensions. The
scientific quest behind the synthesis of quantum dots is to create and control future electronic and
optical nanostructures engineered through tailoring size, shape, and composition.
The {\em complete} confinement -- or the lack of any degree of freedom for the electrons (and/or holes)
-- in quantum dots limits the exploration of {\em spatially localized} elementary excitations such as
plasmons to {\em direct} rather than {\em reciprocal} space.
Here we embark on a thorough investigation of
the magneto-optical absorption in semiconducting {\em spherical} quantum dots
characterized by a confining harmonic potential and an applied magnetic field in the symmetric gauge.
This is done within the framework of Bohm-Pines` random-phase approximation that enables us to derive
and discuss the full Dyson equation that takes proper account of the Coulomb interactions.
As an application of our theoretical strategy, we compute various single-particle and many-particle
phenomena such as the Fock-Darwin spectrum; Fermi energy; magneto-optical transitions; probability
distribution; and the magneto-optical absorption in the quantum dots.
It is observed that the role of an applied magnetic field on the absorption spectrum is comparable
to that of a confining potential. Increasing (decreasing) the strength of the magnetic field or the
confining potential is found to be analogous to shrinking (expanding) the size of the quantum dots:
resulting into a blue (red) shift in the absorption spectrum. The Fermi energy diminishes with both
increasing magnetic-field and dot-size; and exhibits saw-tooth-like oscillations at large values of
field or dot-size. Unlike laterally confined quantum dots, both (upper and lower) magneto-optical
transitions survive even in the extreme instances. However, the intra-Landau level transitions are
seen to be forbidden.
The spherical quantum dots have an edge over the strictly two-dimensional quantum dots in that the
additional (magnetic) quantum number makes the physics richer (but complex). A deeper grasp of the
Coulomb blockade, quantum coherence, and entanglement can lead to a better insight into promising
applications involving lasers, detectors, storage devices, and quantum computing$^{1,2}$.

1. M.S. Kushwaha, Electronics Letters {\bf 50}, 1305 (2014).

2. M.S. Kushwaha, AIP Advances {\bf 4}, 127151 (2014).

manvir@rice.edu