Analytical Ground-State of an Exciton Trapped in a Circular Parabolic Quantum Dot in the Presence of a Magnetic Field

Abstract

The quasi-exact properties of an exciton are investigated theoretically in the presence of an external magnetic field using the effective-mass approach in GaAs parabolic quantum dot. The energy spectrum is obtained analytically as a function of the dot radius, interaction strength and magnetic field. It is established that, a steady bound state of an exciton in the ground state exists under the effect of a strong magnetic field; also I noticed that the exciton binding energy decreases by increasing both the radius of the dot and the magnetic field strength and the reduction becomes pronounced for larger dots. As expected, it has been found that the exciton total energy decreases with increasing the size of the dot and it enhances by increasing the magnetic field. It appears that the exciton total energy strongly depends on the magnetic field for dots with big size. The magnetic field effect on the exciton size also has been studied. It is shown that the increase in the magnetic field leads to a reduction in the exciton size; due to magnetic field confinement, while the size of an exciton reach its bulk limit as the dot size increases. Moreover, it is shown that, if the dot radius is sufficiently large the oscillator strength saturates and it becomes insensitive to the magnetic field while the increase in the magnetic field gradually weakened the oscillator strength. I have calculated the ground-state distribution for both the electron and the hole. It is found that the localization of the electron/hole increases in the presence of a magnetic field. Moreover, the ground-state optical-absorption intensity is investigated. Finally, the dependence of the lowest five states of an exciton on both the dot radius and the magnetic field are discussed.