Photoluminescence ͑PL͒ has been used to study two-dimensional incompressible electron liquids in high magnetic fields for nearly two decades. However, some of the observed anomalies coincident with the fractional quantum Hall effect are still unexplained. We show that emission in these systems occurs from fractionally charged "quasiexciton" states formed from trions correlated with the surrounding electrons. Their binding and recombination depend on the state of both the electron liquid and the involved trion, predicting discontinuities in PL and sensitivity to sample parameters.

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Becuse of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole-dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another which leads to their dynamical binding. The interaction pseudopotentials V ↑↑ (k) and V ↑↓ (k) for two spin waves with equal wavevectors k and moving in the same or opposite directions have been calculated and shown to obey power laws V (k) ∝ k α at small k. A high value of α ↑↑ ≈ 4 explains the occurrence of linear bands in the spin excitation spectra of quantum Hall droplets.

Density of states (DOS) and absorption spectrum of weakly doped, narrow quantum wells in high magnetic fields are calculated by realistic exact diagonalization. The systems containing an electron-hole pair with and without an additional, second electron are compared. In DOS, the exciton-electron interaction is shown to fill the gaps between Landau levels and to yield additional discrete peaks corresponding to bound trion states. In absorption, interaction with the additional free electron causes no shift or renormalization of main, excitonic peaks. However, it results in additional, weaker peaks associated with bound trions in the lowest or higher Landau levels. The calculation is supplemented with experimental photoluminescence and photoluminescence-excitation studies of two-dimensional holes and electrons in high magnetic fields.

The energy spectra of negative trions (X − = 2e + h) in one-sided doped GaAs quantum wells are calculated. The maps of the trion binding energy ∆ as a function of well width w, electron concentration n, and the magnetic field B are obtained. The dependence of the trion ground state ("bright singlet" versus "dark triplet") on those parameters is established.