Correlation induced phonon softening in low density coupled bilayer   systems
  We predict a possible phonon softening instability in strongly correlated coupled semiconductor bilayer systems. By studying the plasmon-phonon coupling in coupled bilayer structures, we find that the renormalized acoustic phonon frequency may be softened at a finite wave vector due to many-body local field corrections, particularly in low density systems where correlation effects are strong. We discuss experimental possibilities to search for this predicted phonon softening phenomenon. 
E. H. Hwang and S. Das Sarma