Observability of localized magnetoplasmons in quantum dots: Scrutinizing the eligibility of far-infrared, Raman, and electron-energy-loss spectroscopies

We investigate a one-component, quasi-zero dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de-Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy-loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn’s theorem (GKT) in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energies capable of being explored with the FIR, Raman, and/or electron-energy-loss spectroscopy. This implies that either of these probes is competent in observing the localized magnetoplasmons in the system. As an application of the rigorous analytical diagnosis of the system, we have presented various pertinent single-particle, such as Fock-Darwin spectrum, Fermi energy, zigzag excitation spectrum, and magneto-optical transitions, and the many-particle phenomena, such as magneto-optical absorption, Raman intensity, and electron energy-loss probability. In the latter, the energy position of the resonance peaks is observed to be independent of the electron-electron interactions and hence of the number of electrons in the quantum dot in compliance with the GKT. It is found that both confinement potential and magnetic field play a decisive role in influencing the aforementioned many-particle phenomena. Specifically, increasing (decreasing) the strength of the confining potential is found to be analogous to shrinking (expanding) the size of the quantum dots and results into a blue (red) shift in the respective spectra. Intensifying the magnetic field has two-fold effects in the resonance spectra associated with all three spectroscopies considered here: the lower resonance peak observes a red shift, whereas the higher one experiences a blue shift. This is a unique and intriguing behavior observed in the quantum dots with complete confinement. A deeper insight into the physics of the quantum dots is paving the way for their implementation in such diverse fields as quantum computing and medical imaging