Splitting of Landau levels of a 2D electron due to electron-phonon interactions

We show that in a very strong magnetic field $B$ electron-phonon interaction gives rise to a splitting of Landau levels of a 2D electron into a series of infinitely degenerate sublevels. We provide both qualitative and quantitative description of this phenomenon. The cases of interaction with acoustic and polar optical phonons are considered. The energy distance between nearest sublevels in both cases tends to zero as $B^{-1/2}$ at large $B$.Comment: 4 pages, LaTe

Metastable bound state of a pair of two-dimensional spatially separated electrons in anti-parallel magnetic fields

We propose a new mechanism for binding of two equally charged carriers in a double-layer system subjected by a magnetic field of a special form. A field configuration for which the magnetic fields in adjacent layers are equal in magnitude and opposite in direction is considered. In such a field an additional integral of motion - the momentum of the pair P arises. For the case when in one layer the carrier is in the zero (n=0) Landau level while in the other layer - in the first (n=1) Landau level the dependence of the energy of the pair on its momentum E(P} is found. This dependence turns out to be nonmonotonic one : a local maximum and a local minimum appears, indicating the emergence of a metastable bound state of two carrier with the same sign of electrical charge.Comment: 7 page