Electron states in a GaAs quantum dot in a magnetic field

TLDR

Self‑consistent Poisson–Schrödinger calculations were performed for electron states in a fully confined GaAs/AlxGa1−xAs quantum dot. The Hartree‑approximation equations were solved to obtain potential profiles, energy levels, and dot charge as functions of gate voltage and perpendicular magnetic field, with electron number constrained to integers in the Coulomb‑blockade regime. The calculations show a nearly circular confining potential, energy levels largely independent of dot charge at fixed gate voltage, and magnetic‑field evolution resembling that of a parabolic potential.

Abstract

Self-consistent numerical solutions of the Poisson and Schr\"odinger equations have been obtained for electron states in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure with confinement in all three spatial dimensions. The equations are solved in the Hartree approximation, omitting exchange and correlation effects. Potential profiles, energy levels, and the charge in the quantum dot are obtained as functions of the applied gate voltage and magnetic field. First, the zero-magnetic-field case is considered, and the quantum-dot charge is allowed to vary continuously as the gate voltage is swept. Then, in connection with the phenomenon of Coulomb blockade, the number of electrons in the quantum dot is constrained to integer values. Finally, the calculation is extended to examine the evolution of levels in a magnetic field applied perpendicular to the heterojunction. Our results indicate that the confining potential has nearly circular symmetry despite the square geometry of the gate, that the energy levels are quite insensitive to the charge in the quantum dot at a fixed gate voltage, and that the evolution of levels with increasing magnetic field is similar to that found for a parabolic potential.