  It has been shown that coherent phonons can be used as a potent tool for
controlling and enhancing optoelectronic and transport properties of
nanostructured materials. Recent studies revealed that interaction of acoustic
phonons and fast-moving carriers in semiconductor heterostructures can be
accompanied by electron-phonon instabilities that cause ordinary and induced
Cherenkov effects. However, the development of such instabilities is still
poorly understood. Our study shows that other supersonic phenomena, beyond the
Cherenkov instability, are possible for non-equilibrium charge transport in the
miniband semiconductor superlattices (SLs) driven by an acoustic plane wave.
Using semiclassical nonperturbative methods and elements of the bifurcation
theory, we find the conditions for the onset of dynamical instabilities
(bifurcations) which are caused by the emission of specific SL phonons by
supersonic electrons, and their back action on the electrons. Notably, the
underlying radiation mechanism is connected either to normal or anomalous
Doppler effects in full accordance with the Ginzburg-Frank-Tamm theory. The
appearance of induced Doppler effects is also discussed in relation to the
formation of electron bunches propagating through the spatially periodic
structure of the SL. When the amplitude of the acoustic wave exceeds certain
threshold, the dynamical instabilities developed in the system are manifested
as drift velocity reversals, resonances in sound attenuation and absolute
negative mobility. We demonstrate that the discovered superluminal Doppler
phenomena can be utilized for tunable broadband amplification and generation of
GHz-THz electromagnetic waves, which creates a ground for development of novel
phononic devices.
