Theory of exciton spectra of incompressible quantum liquids

Energy and optical spectra of excitons against a background of incompressible quantum liquids (IQL’s) are investigated by finite-size computations in a spherical geometry and by symmetry arguments based on the composite fermion theory. Properties of excitons are governed by the parameter h/l, where h is a separation between electron and hole confinement planes and l is a magnetic length. When h/l≲1, the energy spectrum comprises a single exciton branch ${\mathit{L}}_0$ and a quasicontinuum above it. With increasing h/l a multiple-branch exciton spectrum develops. Different branches ${\mathit{L}}_{\mathit{m}}$ may be classified by the index m, which identifies the minimum angular momentum, ${\mathit{L}}_{\mathit{m}}$, of the ${\mathit{L}}_{\mathit{m}}$ branch. There are two types of branches. The branches of the first type are symmetrically compatible with a model of an exciton as a neutral entity consisting of a valence hole and several fractionally charged quasiparticles. All these anyon branches have m values exceeding some critical value (m≥3 for the ν=1/3 IQL), and they are generically related to some specific states from the low-energy sector of the electron subsystem, and drop down below the original ${\mathit{L}}_0$ branch with increasing h/l. Comparative investigation of the number-of-particle dependencies of the electron and exciton spectra shows that these properties survive in the macroscopic limit and establishes a connection between anyon branches and the basic low-energy physics of IQL’s.