Ever since the discovery of the quantum Hall effects, effort has been made to study these correlated states by means of optics. Both Raman spectroscopy and photoluminescence have proven invaluable. Focussing on the latter, the following picture emerges after almost three decades of development: Both in the vicinity of integer and fractional quantum Hall (FQHE) states anomalous photoluminescence multiple-peak structures emerge if the quantum well is sufficiently wide and anisotropic (e.g., doped on one side only). The transfer of oscillator strength between nearby peaks occurs in a range of magnetic field roughly defined by the edges of the Hall plateaus where charged excitations (electrons, holes, composite fermion quasiparticles or quasiholes) become mobile. The featureless photoluminescence traces for narrow or symmetric wells is understood in terms of the "hidden symmetry", which states that if the electron-electron and the electron-hole interactions are identical (apart from sign), the neutral exciton complexes decouple from the rest of the electron gas, and the electron-hole recombination energy is insensitive to the electronic state.
A combination of theory and experiment has identified as many as four bound electron-hole complexes in the initial state near integer fillings: the neutral exciton X, the singlet trion (charged exciton) Xs-, and the dark and bright triplet trions Xdt- and Xtb-. (The life-time of the valence-band hole created by irradiation is apparently long enough so that the recombination starts from a stationary state of the hole and the electron gas.)
Near fractional quantum Hall states there are three regimes of the effective separation of the valence-band hole and electron wave functions in the direction transverse to the samples. For small separation d < dc1, "hidden symmetry" rules, and photoluminescence characterizes the decoupled bound complexes and does not probe the correlated electron liquid. For large separation d > dc2, excitons do not form, but the hole can bind at most two fractionally charged composite fermion quasiparticles. In the most interesting intermediate range dc1 < d < dc2 charged trions can be involved in the formation of the correlated liquid, giving rise to fractionally charged quasiexcitons. In particular, the observed transfer of oscillator strength to a second photoluminescence peak at the nu > 1/3 edge of the Hall plateau was interpreted as the appearence of a transition from a fractionally charged exciton QX-, which can form only if mobile composite fermion quasiparticles appear at the high- edge of the Hall plateau.
Theory has so far focussed on the simplest state at nu=1/3, even though the photoluminescence peak anomalies have been seen at nu=2/3, 2/5, 3/5 and 3/7. The relevance of composite fermions to the photoluminescence problem is testified by the observation that the states corresponding to the same number of filled CF Landau levels, 2/3 and 2/5, and 3/5 and 3/7, exhibit similar behavior. Therefore, relying upon the composite fermion theory, we extend the theory of photoluminescence in FQHE liquids to all relevant fractions, and also study FQHE states without full spin-polarization. Eventually, we aim at exploring the notorious nu=5/2 state from this aspect.
Reliable background in quantum mechanics and solid-state physics, programming skills, experience with computer algebra softwares.