Ground state properties of a two-electron system in a three-dimensional GaAs quantum dot with Gaussian confinement in a magnetic field

Abstract

The ground state properties of a system of two interacting electrons trapped in a three-dimensional GaAs quantum dot with Gaussian confinement under the influence of an externally applied magnetic field (B) are obtained using a variational method with a Chandrashekhr-like wave function containing only three variational parameters and involving a modified Jastrow correlation factor. The phase diagram for the two-electron singlet bound state is obtained in the parameter space of the confinement potential. The pair density function is calculated as a function of the electron-electron separation for a couple of magnetic fields and its peak positions are obtained to study the behaviour of the size of the electron pair as a function of the confinement length and the depth of the potential. The size of the electron pair is also obtained directly by calculating the expectation value of the electron-electron separation with respect to the system wave function. Finally, the behaviour of the ground state energy is studied as a function of the electron effective mass and the dielectric constant of a quantum dot.