We investigated the elastic properties of the iron-based superconductor Ba(Fe 1Àx Co x ) 2 As 2 with eight Co concentrations. The elastic constant C 66 shows a large elastic softening associated with structural phase transition. C 66 was analyzed on the basis of the localized and itinerant pictures of Fe-3d electrons, which shows a strong electronlattice coupling and a possible mass enhancement in this system. The results are similar to those of unconventional superconductors, where the properties of the system are governed by quantum fluctuations associated with the zerotemperature critical point of long-range order, namely, the quantum critical point (QCP). In this system, the inverse of C 66 behaves just like the magnetic susceptibility in magnetic QCP systems. Although the QCPs of these existing superconductors are all ascribed to antiferromagnetism, our systematic studies on the canonical iron-based superconductor Ba(Fe 1Àx Co x ) 2 As 2 have revealed that there is a signature of ''structural quantum criticality'' in this material, which thus far has had no 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 iron 3d orbitals.

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