Hidden symmetry and magnetospectroscopy of quantum wells near filling factorν=2

The magnetoluminescence spectra of symmetric quantum wells containing an electron gas show an abrupt changeover from Landau-level behavior (i.e., linear shift of energy with magnetic field) to quadratic (excitonlike) behavior as the field is increased. This so-called “Mott transition” occurs when the electron filling factor ${\nu }_e$ is 2, i.e., when the lowest Landau level is just filled. We show that the changeover is a natural consequence of the hidden symmetry that has been shown to hold in two-dimensional systems at high fields. This symmetry is broken when the integer parts of ${\nu }_e/2\mathrm{}$ and ${\nu }_h/2\mathrm{}$ differ $({\nu }_h,$ the hole filling factor, is very small in these experiments). This symmetry breaking can also account for the new emission bands that are observed in such spectra when ${\nu }_e$ becomes larger than 2, and these bands can be described, at least qualitatively, in the framework of the magnetoexciton theory. These bands include the red-shifted magnetoplasmon and shake-up satellites and the blue-shifted cyclotron satellites. We also discuss the possible existence of a new type of trion (charged exciton), associated with the electron $n_e=1\mathrm{}$ Landau level, and conclude that these trions should be observable.