  I construct a simple model to demonstrate that when the many-electron quantum
state of a material is near a quantum phase transition and the vibrational
motion of a phonon explores the potential energy surface near the transition
point, then an impenetrable barrier appears at the potential energy surface
which restricts the phonon from crossing the transition point and abnormally
increases the phonon frequency. The ensuing anomalous enhancement of the
electron phonon coupling is general and independent of the specific nature of
the electronic quantum phase transition. Understanding and modelling this
strong electron-phonon coupling may potentially lead to the design of phonon
superconductors with high critical temperatures by choosing their parameters
appropriately near an electronic quantum phase transition.
