Spatial correlation of an electron and hole in quasi-two-dimensional electronic system in a strong magnetic field and its relationship to the light-scattering tensor

The spatial correlation of light-generated electrons and holes in a quasi-two-dimensional electron gas in a strong magnetic field is investigated in an approximation linear in the intensity of the exciting light. The correlation is due to the interaction of the electrons and holes with longitudinal optical (LO) phonons. The theory permits calculating, on the basis of a special diagrammatic technique, two distribution functions of an electron-hole pair with respect to the distance between the electron and the hole after the emission of N phonons: first, the function determining the total number of pairs which have emitted N phonons and, second, the function related to the rank-4 light-scattering tensor in interband resonance Raman scattering of light. A special feature of the system is that the electron and hole energy levels are discrete. The calculation is performed for a square quantum well with infinitely high barriers. The distribution function and the total number of electron-hole pairs before the emission of phonons as well as the distribution function corresponding to two-phonon resonance Raman scattering are calculated. The theory predicts the appearance of several close-lying peaks in the excitation spectrum under resonance conditions. The number of peaks is related to the number of the Landau level participating in the optical transition. The distance between peaks is determined by the electron-phonon coupling constant. Far from resonance there is one peak, which is much weaker than the peaks obtained under resonance conditions. Zh. éksp. Teor. Fiz. 111, 2194–2214 (June 1997)