The slow zero-sound mode expected near the Mott transition in strongly interacting two-dimensional Fermi systems that are neutral is shown to persist as the physical sound mode in the case that the fermion carries electronic charge and is embedded in a positive ionic background. The latter sound velocity softens completely precisely at the Mott transition, indicating that a zone-center structural transition will occur in the system. We suggest that this phonon-softening mechanism is related to the structural transitions commonly observed in the oxide superconductors.

• Received 8 December 1993

DOI:https://doi.org/10.1103/PhysRevLett.73.1675