Strong Coupling Superconductivity in the Vicinity of the Structural Quantum Critical Point in (Ca${}_x$Sr${}_{1-x}$)${}_3$Rh${}_4$Sn${}_{13}$

Abstract

The family of the superconducting quasi-skutterudites (Ca${}_x$Sr${}_{1-x}$)${}_3$Rh${}_4$Sn${}_{13}$ features a structural quantum critical point at $x_c=0.9$, around which a dome-shaped variation of the superconducting transition temperature $T_c$ is found. Using specific heat, we probe the normal and the superconducting states of the entire series straddling the quantum critical point. Our analysis indicates a significant lowering of the effective Debye temperature on approaching $x_c$, which we interpret as a result of phonon softening accompanying the structural instability. Furthermore, a remarkably large enhancement of $2\Delta /k_B{T}_c$ and $\Delta C/\gamma T_c$ beyond the Bardeen-Cooper-Schrieffer (BCS) values is found in the vicinity of the structural quantum critical point. The phase diagram of (Ca${}_x$Sr${}_{1-x}$)${}_3$Rh${}_4$Sn${}_{13}$ thus provides a model system to study the interplay between structural quantum criticality and strong electron-phonon coupling superconductivity.

6 pages, accepted for publication in Phys. Rev. Lett

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