Magnetoexciton in the Ellipsoidal Quantum Dots

This study presents a comprehensive theoretical analysis of exciton states within a strongly prolate GaAs ellipsoidal quantum dot, specifically focusing on the influence of an external magnetic field. Employing the variational method, we have developed an exciton trial wave function based on one-particle wave functions, allowing for precise computation of exciton energy and binding energies. These computations are explored as functions of both the minor semiaxis of the quantum dot and the varying strength of the external magnetic field. Additionally, we have calculated the total magnetization of the quantum dot by deriving the total energy with respect to the magnetic field, offering insights into the magnetic properties of the system. The study further extends to estimating the radiative lifetime of the magnetoexciton, which is analyzed as a function of the small geometrical parameter and the external magnetic field. The findings provide a detailed understanding of the interplay between quantum dot geometry, magnetic field strength, and exciton dynamics, contributing to the broader knowledge of quantum dot behavior in varying electromagnetic environments.