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Nature of structural instabilities in superconducting Sr$$_3$$Ir$$_4$$Sn$$_{13}$$

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

A quantum critical point appears as a second-order phase transition which takes place at zero temperature. In contrast to heavy-fermion systems in which magnetism often plays a vital role, recent studies revealed that structural instabilities can drive a system to a quantum critical point as well. In quasi-skutterudite (Ca,Sr)$$_3T_4$$Sn$$_{13}$$ ($$T$$=Rh, Ir), Sr$$_3$$Ir$$_4$$Sn$$_{13}$$ exhibits superconductivity around $$T_{rm sc}$$$${sim}$$5 K and a structural transition at $$T^*{simeq}$$147 K. Applying physical or chemical pressure on Sr$$_3$$Ir$$_4$$Sn$$_{13}$$ suppresses $$T^*$$ rapidly, and a quasi-linear $$T$$ dependence of electrical resistivity, signature of non-Fermi liquid behavior, was observed where $$T^*$$ extrapolates to 0~K. The isomorphs (Ca$$_x$$Sr$$_{1-x}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ exhibits similar behavior, where the criticality can be reached by $$x{sim}$$0.9 without external pressure. Neutron scattering experiments in Sr$$_3$$Ir$$_4$$Sn$$_{13}$$ evidences the second order nature of the structural transition at $$T^*$$ by the observation of a continuous evolution of superlattice peak below $$T^*$$ and a gradual increase of critical scattering upon approaching to $$T^*$$ by cooling. Increase of $$x$$ in (Ca$$_x$$Sr$$_{1-x}$$)$$_3$$Rh$$_4$$Sn$$_{13}$$ toward the quantum critical point leads to the systematic variation of the critical exponents of the order parameter. In addition, this substitution induces the phonon softening around the M point towards zero energy revealed by inelastic X-ray scattering experiment. We will present systematic variations in both elastic and inelastic channels upon approaching to the quantum critical point.



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