The absorption transition that creates the negatively charged exciton ${(X}^{-})$ in a two-dimensional electron gas is studied as a function of electron density $n_e$ and of magnetic field in a ${\mathrm{C}\mathrm{d}\mathrm{T}\mathrm{e}/\mathrm{C}\mathrm{d}}_{0.83}{\mathrm{Zn}}_{0.09}{\mathrm{Mg}}_{0.08}\mathrm{Te}$ quantum well. The sample is grown on a transparent substrate allowing transmission measurements. The density is varied from zero to $3\times {10}^{11}$ ${\mathrm{cm}}^{-2}$ by applying a voltage between a gold Schottky contact on the sample surface and an Ohmic back contact. In fixed high magnetic field (8 T), the variation of the $X^{-}$ absorption intensity has a triangular shape: It first increases linearly with $n_e,$ reaches a maximum at Landau level filling factor $\nu =1\mathrm{}$, then decreases approximately linearly with $n_e$ to disappear at $\nu \approx 2$. This is explained in a model that gives an $X^{-}$ absorption intensity proportional to the number of electrons in the lowest Landau level (degeneracy $2g)$ when $0<\mathrm{}\nu <1\mathrm{}$, but proportional to $2g-n_e,$ that is to the number of holes in this level, when $1<\mathrm{}\nu <2\mathrm{}$.

• Received 17 June 1997

DOI:https://doi.org/10.1103/PhysRevB.56.R12787