  We investigated the elastic properties of the iron-based superconductor
Ba(Fe1-xCox)2As2 with eight Co concentrations. The elastic constant C66 shows
large elastic softening associated with the structural phase transition. The
C66 was analyzed base on localized and itinerant pictures of Fe-3d electrons,
which shows the strong electron-lattice coupling and a possible mass
enhancement in this system. The results resemble those of unconventional
superconductors, where the properties of the system are governed by the quantum
fluctuations associated with the zero-temperature critical point of the
long-range order; namely, the quantum critical point (QCP). In this system, the
inverse of C66 behaves just like the magnetic susceptibility in the magnetic
QCP systems. While the QCPs of these existing superconductors are all ascribed
to antiferromagnetism, our systematic studies on the canonical iron-based
superconductor Ba(Fe1-xCox)2As2 have revealed that there is a signature of
"structural quantum criticality" in this material, which is so far without
precedent. The elastic constant anomaly is suggested to concern with the
emergence of superconductivity. These results highlight the strong
electron-lattice coupling and effect of the band in this system, thus
challenging the prevailing scenarios that focus on the role of the iron
3d-orbitals.
