Enhancement of superconductivity by disorder in Remeika-type quasiskutterudites

Atomic-scale disorder is conventionally regarded as detrimental to superconductivity; however, under specific conditions, it can enhance superconducting properties. Here, we investigate the role of substitutional disorder in Remeika-type quasiskutterudites $R_3M_4$Sn$_{13}$ and $R_5M_6$Sn$_{18}$ ($R=$ Y, La, Lu; $M=$ Co, Rh, Ru) by combining measurements of magnetic susceptibility, electrical resistivity, and heat capacity with microscopic modeling. We demonstrate that increasing disorder leads to the emergence of locally superconducting regions characterized by an enhanced critical temperature $T_c^{\ast}$, exceeding the bulk transition temperature $T_c$. Both $T_c^\ast$ and $T_c$ exhibit a nonmonotonic dependence on dopant concentration and show a strong correlation with entropy isotherms measured as a function of disorder. The pronounced entropy maxima coincide with the largest separation between $T_c^{\ast}$ and $T_c$, establishing disorder as a thermodynamically controlled parameter governing superconductivity in these materials. Measurements of the upper critical field reveal distinct $H_{c2}(T)$ branches associated with the bulk and locally superconducting phases, providing direct experimental evidence for a percolative superconducting state. To interpret these observations, we propose a microscopic model that captures the interplay between the impurity-induced enhancement of local pairing and the disorder-driven suppression of global superconducting coherence. The model reproduces the experimentally observed nonmonotonic evolution of $T_c^{\ast}$ with disorder and supports a percolation-based interpretation of the superconducting transition. Our results demonstrate that controlled atomic disorder can serve as an effective materials-design parameter for tuning superconductivity in complex correlated systems.