Band and branch inversion phenomena in GaAs–Al x Ga 1–x As superlattices

A detailed analysis of the symmetry properties of the Bloch envelope functions in GaAs–Al x Ga 1–x As superlattices (SL) for finite values of k ⟂ is made. It is pointed out that in the ( E , k , k ⟂ ) space, where k is the SL wave vector, the energy spectrum is built up of independent branches. Each one of these branches contains two curves of definite parity placed at the planes k = 0 and k = π/d , where d is the SL period. It is shown that with increasing magnitude of k ⟂ , an interchange of symmetries between branches (similar to the well known band inversion phenomenon) may occur at the plane k = 0 or k = π/d. Furthermore, it is also shown that a magnetic field may induce interchange of symmetries between contiguous bands.