Screening effect on the Landau-level broadening for electrons in GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As heterojunctions

A self-consistent scheme is developed for studying the screening effect on Landau-level broadening of a two-dimensional electron gas in a strong magnetic field due to long-range impurity potentials. Numerical calculation of the Landau-level widths is performed for GaAs?(hy${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As heterojunctions with the strength of the magnetic field varying from 2 to 18 T. Our results show that the Landau levels become extremely narrow when the magnetic field is strong enough such that the Fermi level lies near the center of the lowest Landau level. However, in other regions of lower magnetic field, the level widths are usually several times broader than those obtained from the short-range impurity potential. This latter result is qualitatively in agreement with the recent de Haas–van Alphen effect experiment of Eisenstein et al.