Photoluminescence in the Fractional Quantum Hall Effect

Abstract

The fractional quantum Hall effect results from a correlated ground state of interacting electrons confined to a layer and subject to a strong transverse magnetic field. It exhibits dissipationaless conduction ρ_xx = 0 and quantization of the Hall resistance R_H = hv/e , with v-the Landau level filling number-a rational fraction. This paper will address the magneto-optics of quantum Hall states. For ideal system of coplanar electrons and holes the photoluminescence (PL) spectrum occurs at the isolated magnetoexciton binding energy, independent of the underlying electron density and therefore does not reflect any of the features associated with the fractional quantum Hall effect. If, however, the electron and hole layers are far enough apart the PL spectrum coincides with the single particle spectral (tunneling) density of states ρ(ω). For quantum Hall states at primary fillings v = 1/m, ρ(ω) exhibits a single characteristic peak. In the presence of quasi-particle excitations the PL spectrum develops an additional peak with intensity proportional to the number of quasi-particles and shifted in energy from the main peak by the quasi-particle quasi-hole gap.