Optical absorption by incoherent and coherent ensembles of spin excitations in an unpolarised quantum Hall system

In connection with recent studies of extremely long-living spin-cyclotron excitations that are actually magnetoexcitons in the quantum Hall electron gas, we discuss the contribution to light absorption related to the presence of a magnetoexcitonic ensemble in this purely electronic system. The distribution of magnetoexcitons in an ‘incoherent’ phase, as well as absorption of light, is determined by a smooth random potential inevitably present in a quantum well. Since weakly interacting excitations have to obey the Bose–Einstein statistics, one may expect the appearance of a coherent phase where all magnetoexcitons are in the same state. The absorption of light is still determined by disorder in the system, but it turns out to be about an order of magnitude higher. A comparative analysis is made of both incoherent and coherent cases. The condition for coherent–incoherent phase transition is discussed. It is expected to be strongly related to long-distance inter-excitonic correlations. The latter are accounted in terms of virial correction (i.e. depending on magnetoexciton concentration) for the single magnetoexciton energy found within the approximation of a slightly non-ideal gas.