Evidence of a structural quantum critical point in (CaSr)RhSn from a lattice dynamics study

Cheung, Y. W.*; Hu, Y. J.*; Imai, Masaki*; Tanioku, Yasuaki*; Kanagawa, Hibiki*; Murakawa, Joichi*; Moriyama, Kodai*; Zhang, W.*; Lai, K. T.*; Yoshimura, Kazuyoshi*; Grosche, M. F.*; Kaneko, Koji   ; Tsutsui, Satoshi*; Goh, S. K.*

Approaching a quantum critical point has been an effective route to stabilize superconductivity. While the role of magnetic QCPs has been extensively discussed, similar exploration of a structural QCP is scarce. Using inelastic X-ray scattering, we examine the phonon spectrum of the nonmagnetic quasi-skutterudite (CaSr)RhSn, which represents a precious system to explore the interplay between structural instabilities and superconductivity by tuning the Ca concentration x. We unambiguously detect the softening of phonon modes around the M point on cooling towards the structural transition. Intriguingly, at x = 0:85, the soft mode energy squared at the M point extrapolates to zero at -5.7 K, providing the first compelling microscopic evidence of a structural QCP in (CaSr)RhSn. The enhanced phonon density-of-states at low energy provides the essential ingredient for realizing strong-coupling superconductivity near the structural QCP.