Collective Excitations in Asymmetric Parabolic Quantum Wells
  We study within the linear response theory the far-infrared optical absorption spectrum and the collective excitations of an asymmetric, wide parabolic Al$_x$Ga$_{1-x}$As quantum well, consisting of two half-parabolas of different curvatures, in the presence of an in-plane magnetic field. We employ a self-consistent-field approach in the local-density approximation using parameter values of a recent experimental study. At low $N_s$, there is only one resonance corresponding to the lowest inter-Landau-level transition, and at high $N_s$ we obtain two resonances at frequencies corresponding to the different curvatures of the well, in good agreement with experiment. We also calculate the optical spectra without any magnetic field and find similar trends as a function of $N_s$, i.e., one resonance at low $N_s$ and two main resonances at high $N_s$.} 
P. I. Tamborenea and S. Das Sarma