Strong Coupling Superconductivity in the Vicinity of the Structural Quantum Critical Point in (Ca_xSr_1-x)₃Rh₄Sn₁₃

The family of the superconducting quasiskutterudites (Ca_xSr_1-x)₃Rh₄Sn₁₃ 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 2Δ/k_BT_c and ΔC/γT_c beyond the Bardeen-Cooper-Schrieffer values is found in the vicinity of the structural quantum critical point. The phase diagram of (Ca_xSr_1-x)₃Rh₄Sn₁₃ thus provides a model system to study the interplay between structural quantum criticality and strong electron-phonon coupling superconductivity.