Subband spectrum of a parabolic quantum well in a perpendicular magnetic field

We have calculated self-consistent electron wave functions and eigenenergies in a wide parabolic quantum well subject to a perpendicular magnetic field. The spectra from these calculations naturally divide into three regions of magnetic-field strength. These regions are distinguished by different relative magnitudes of subband spacings and ħ${\mathrm{\omega }}_{\mathit{c}}$. In each region, the eigenenergies and Fermi energy exhibit distinctive behavior as a function of field. We find that in low and intermediate fields, the usual Landau-level fan diagram with rigid eigenenergies is incorrect. We conclude that the system adopts a different physical evolution in each region of the magnetic field. This is reflected in the evolution of the shape of the electron-gas slab and the self-consistent potential in each region.