Anyonic ions, energy bands, and photoluminescence of fractional quantum Hall systems

A two-dimensional electron liquid interacting with free or localized valence-band holes located a distance d away from the electron layer is studied by exactly diagonalizing the Hamiltonian of a finite-size system. For a coplanar electron-hole system, our calculation does not show the usual sign of an imcompressible state or a fractional quantum Hall effect. For the case where the separation d is about 1.5 times the magnetic length, pronounced cusps are revealed in a plot of the ground-state energy versus the Landau-level degeneracy. Detailed analysis suggests that the ground state responsible for the cusps consists of anyonic ions (composed of Laughlin quasielectrons bound to a hole) weakly coupled to an incompressible fluid of the remaining electrons. The hypothesis of stable anyonic ions is further supported by the structure displayed in the photoluminescence (PL) spectrum. Three PL systems, namely, electron–free-hole (e-h), electron–localized-hole (e-${\mathit{A}}^{+}$), and electron–neutral-acceptor (e-${\mathit{A}}^0$), have been investigated as functions of separation d, filling factor ${\nu }_{\mathit{e}}$, and temperature T. Multipeaked spectra are obtained for all three systems; they can be understood in terms of quasielectron-hole recombination processes and the ‘‘band structure’’ of two-dimensional electrons in the fractional quantum Hall effect regime. The connections between the calculated spectrum and some recent experimental results are also discussed.