Enhancement of superconductivity by disorder in Remeika-type quasiskutterudites

Abstract

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.

Figures (8)

• Figure 1: Plot of Rietveld refinement for Y$_{4.5}$Ca$_{0.5}$Rh$_{6}$Sn$_{18}$ (tetragonal structure $I4_1/acd$, the lattice parameters in (Å): $a=13.7678(1)$, $c=27.5430(8)$) obtained with the weighted-profile $R$ factor $R_{wp}=1.9$%. Black dots - observed pattern, red line - calculated, blue ticks - Bragg peaks positions, magenta line - the difference.
• Figure 2: $T-x$ diagram for the series of Y$_{5-x}$Ca$_x$Rh$_6$Sn$_{18}$ compounds with tetragonal structure $I4_1/acd$. (a) Superconducting critical temperatures $T_c$ and $T_c^{\ast}$ are divided by $T_c(x=0)\equiv T_c(0)$ for Y$_5$Rh$_6$Sn$_{18}$. The blue points represent the locally disordered $T_c^{\ast}$ phase, the orange points represent the bulk $T_c$ phase, and the green open squares show $\frac{1}{T_c(0)}(T_c^{\ast}-T_c)+1$. The solid lines are the best approximations by third degree polynomial. The red rhombic points show disorder-driven enhancement in $T_c$ calculated by a multiband model in an unconventional multiband $s_{\pm}$ SC vs. disorder concentration in atomic % (the data taken from Ref. Gastiasoro2018), while the black triangles show the $T-x$ change consistent with Abrikosov and Gor’kov theory Abricosov1961 (the data taken from Ref. Gastiasoro2018). The respective points are connected by the lines. (b) Entropy isotherms $S$ at $T=5$, 10 and 12 K as a function of Ca at. % (and $x$).
• Figure 3: (a) $T-x$ diagram for the series of La$_{3-x}$Ca$_x$Rh$_4$Sn$_{13}$ compounds. The blue points indicate the beginning of the transition between normal and SC phase at $T_c^{\ast}$. The red points represent the temperature $T_{\Delta}$ of the maxima of the $f(\Delta)$ function for each component of the series. The green points show the bulk$T_c$ phase. The purple and dark blue dotted curves show disorder-driven enhancement in $T_c$ calculated by a multiband GA model for Ca dopants in La$_{3-x}$Ca$_x$Rh$_4$Sn$_{13}$ (lower at. % scale) and La dopants in Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$ (upper at. % scale), respectively (the data taken from Ref. Gastiasoro2018). (b) La$_{3-x}$Ca$_x$Rh$_4$Sn$_{13}$, entropy isotherms $S_T$ as a function of Ca dopant in at. % (and $x$).
• Figure 4: The upper critical field $H_{c2}$ vs. $T^\ast$ for Ca$_{3}$Rh$_4$Sn$_{13}$. The $H-T$ data are approximated by GL equation $H_{c2}(T)=H_{c2}(0)\frac{1-t^2}{1+t^2}$, where $t=\frac{T}{T_c}$.
• Figure 5: The upper critical field $H_{c2}^{\ast}$ vs. $T$ for Ca$_{3}$Rh$_4$Sn$_{13}$ doped with La. (a) Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$; the $H-T$ data are approximated by GL equation $H_{c2}(T)=H_{c2}(0)\frac{1-t^2}{1+t^2}$, where $t=\frac{T}{T_c}$. (b) $H_{c2}^{\ast}$ at $T=0.4$ K as a function of $T_c^{\ast}$ at $H=0$ for the series of Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$ superconductors with various level of disorder due to doping.