Few-Particle Excitons

A theory of an anyon exciton consisting of a valence hole and several quasi-electrons is presented. Detailed study of three-particle and four-particle magnetoexcitons is performed. Multiple-branch energy spectra are obtained. A full classification scheme for the exciton states is developed. Exact analytical solutions of the four-particle problem have been found for some limiting cases. It is shown that the angular momentum of the exciton ground state is growing with increasing distance h between electron and hole confinement planes. The model describes a number of properties established by few-particle computations, including an abrupt change in emission with increasing h. Distribution of electron density around a hole is calculated. For nonzero exciton quasimomentum the electron density shows a spectacular splitting on bundles. For h bigger than the magnetic length the anyon exciton model gives an insight into the features of magnetoexciton against the background of an incompressible quantum liquid.