In-plane optical anisotropy due to conduction band electron wavefunctions

Photoluminescence measurements were carried out on Be $\delta$-doped GaAs/Al$_{0.33}$Ga$_{0.67}$As heterostructure at 1.6 K in magnetic fields ($B$) up to 5 T. Luminescence originating from recombination of a two-dimensional electron gas (2DEG) and photo excited holes localized on Be acceptors was analyzed. The degree of circular polarization ($\gamma_C$) of the luminescence from fully occupied Landau levels was determined as a function of $B$ and the 2DEG concentration, $n_s$. At $B$ constant, $\gamma_C$ decreased with the increase of $n_s$. Two mechanisms of the $\gamma_C(n_s)$ dependence are discussed: a) the Stark effect on a photo excited hole bound to Be acceptor and b) the in-plane anisotropy of the intensity of optical transitions. A quantitative analysis shows that the influence of the Stark effect on $\gamma_C$ is negligible in the present experiment. We propose that the $\gamma_C(n_s)$ dependence results from the $C_{2v}$ symmetry of conduction band electron wavefunctions and we give qualitative arguments supporting this interpretation.