Renormalization effects in the dense neutral magnetoplasma of quantum wells with two filled subbands

Optical studies of the neutral electron-hole (eh) magnetoplasma in undoped $\frac{{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}}{\mathrm{GaAs}}$ quantum wells (QW's) have been performed in magnetic fields up to 12 T. Three experimental situations were investigated over a wide range of plasma densities with subband splittings that were smaller, slightly larger, and much larger than the cyclotron energy. For dense ($n_{\mathrm{eh}}\approx 5\times {10}^{12}$ ${\mathrm{cm}}^{-2\mathrm{}}$) and hot ($T\approx 200-300$ K) photoexcited plasmas, the zeroth Landau-level (LL) transition energies of both sub-bands are in agreement with results of random-phase-approximation calculations neglecting excitonic effects. The stronger renormalization of the first subband is mainly due to the difference in the screened exchange contribution to the renormalization of the band gap. Excitonic corrections become important with decreasing density. They appear first near the Fermi edge and influence the initial or the final state of the optical transitions, depending on the filling of the corresponding LL's. In narrow QW's they lead to a much stronger renormalization of the zeroth LL in the second subband. The excitonic effects decrease with increasing QW width and decreasing magnetic field. At 4 T and a QW width of 30 nm they are negligible already at $n_{\mathrm{eh}}\approx 5\times {10}^{11}$ ${\mathrm{cm}}^{-2\mathrm{}}$. In this case, the strong difference between the renormalization of the zeroth and the first LL observed at small plasma densities is connected with the much smaller binding energy of the $2s$ magnetoexcitons in the empty QW.