Thermoelectric amplification of phonons in bulk semiconductors under a strong magnetic field

We consider the problem of phonon instability in an electron-phonon system of a semiconductor in a temperature field upon variation of a strong (quantizing) static magnetic field. It is found that the phonons may become unstable when certain values for the temperature gradient-drift velocity and the magnetic field are exceeded. However, even after the thresholds are exceeded, it is predicted that there exist alternate bands of the magnetic field, in which the phonons are unstable in one band, stable in the next band, unstable again in the following band, etc. These alternate bands have their origin in the discreteness of the Landau levels of the electrons. An application is made for a GaAs sample.