The basic state of two layered heterostructure at high magnetic field

It is shown that the electron states in the two layered heterostructure at high magnetic field (when it is possible to neglect Coulomb interaction) can be classified by the energy levels of the size quantization. We construct the basic electron state when the electron states with the lowest energy of the size quantization have the density of the half filled Ll. That defines the electron chemical potential and gives the possibility to describe the wave functions of all electrons including the energy distribution of the two dimensional part. That gives the electron distribution consistent with the experimental results S. Luin et al., Phys. Rev. Let. 94, 146804 (2005).