Superconductivity enhancement and quantum critical point of chiral structure induced by atomic substitutions in La$3T_4$Sn${13}$ ($T$ = Co and Rh)

Unconventional Cooper-paring mechanisms of superconductivity in inversion-broken materials is an attractive topic. Theoretical investigations suggested that superconductivity is enhanced near quantum critical points of structural transformation associated with an inversion breaking order, and the enhanced superconductivity is characterized by the parity mixing $(s + p)$ electronic state [1, 2]. There is need to establish materials that exhibit both superconductivity and structural transformations to inversion breaking crystal structures.

Previous studies reported that La$_3$Co$_4$Sn$_{13}$ and La$_3$Rh$_4$Sn$_{13}$ are superconductors below $T_{\rm C}$ = 2.7 and 2.9 K, respectively [3, 4]. Detailed crystal structure analyses revealed that these compounds undergo chiral structural phase transitions at $T_{\rm D}$ = 160 and 350 K, respectively, from the high-temperature phase of space group $Pm{\bar 3}n$ to the low-temperature chiral lattice phase of space group $I2_13$ [5, 6]. In contrast, La$_3$Ru$_4$Sn$_{13}$ is a superconductor below $T_{\rm C}$ = 3.9 K without any structural transformation [7]. In this study, we report atomic substitution effects on the chiral structure transformations and the superconductivity of La$_3$(Co$_{1-x}$Fe$_x$)$_4$Sn$_{13}$, La$_3$(Co$_{1-x}$Ru$_x$)$_4$Sn$_{13}$, and La$_3$(Rh$_{1-x}$Ru$_x$)$_4$Sn$_{13}$ synthesized by the Sn-flux method. Synchrotron X-ray diffraction measurements were conducted at BL-4C, 8A, and 8B of the Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK). The superconductivity was confirmed by SQUID magnetometer measurements. The atomic substitution magnitude $x$ was determined using X-ray fluorescence measurement and X-ray diffraction structural refinement.

The combined phase diagram of $T_{\rm C}$ and $T_{\rm D}$ of the Fe- and Ru-substituted materials is shown in the figure. With an increase in x of La$_3$(Co$_{1-x}$Fe$_x$)$_4$Sn$_{13}$, the chiral phase transition temperature becomes lower than $T_{\rm D}$ = 160 K of La$_3$(Co$_{1-x}$Fe$_x$)$_4$Sn$_{13}$ (black hexagons with the right ordinate). In contrast, $T_{\rm C}$ is independent of the atomic substitution (blue diamonds with the left ordinate). La$_3$(Co$_{1-x}$Ru$_x$)$_4$Sn$_{13}$ ($x \simeq 0.5$) does not exhibit the chiral structural phase transition, and $T_{\rm C}$ increases to 5.7 K (red diamonds), which is approximately twice of $T_{\rm C}$ of La$_3$Co$_4$Sn$_{13}$ and La$_3$Ru$_4$Sn$_{13}$. La$_3$(Rh$_{1-x}$Ru$_x$)$_4$Sn$_{13}$ ($x$ = 0.33 and 0.37) also shows $T_{\rm C} \simeq$ 6 K, which is approximately twice of $T_{\rm C}$ of La$_3$Rh$_4$Sn$_{13}$, and $T_{\rm D}$ decreases to lower than 300 K. These experimental results indicate that the superconductivity is enhanced with the suppression of the chiral structure phase. The phenomenon is consistent with the predicted enhancement of superconductivity near the quantum critical points of the inversion breaking structure phase. It is attractive to investigate in the future whether the parity-mixing superconductivity is induced in these higher-$T_{\rm C}$ materials.

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