Second-order Structural Transition in Superconductor La$_3$Co$_4$Sn$_{13}$

The family of the superconducting quasiskutterudite with general chemical formula R$_3$T$_4$Sn$_{13}$ (R = Ca, Sr; T = Rh, Ir) was recently found to feature a structural transition at $T*$. The structural transition can be tuned to a structural quantum critical point by chemical and/or physical pressure, around which a dome-shaped variation of the superconducting transition temperature $T_c$ is found. Similar behavior was found in the isostructural compound La$_3$Co$_4$Sn$_{13}$, although there is currently a dispute in the literature regarding the nature of $T*$ transition. To shed light on the interplay of structural instability and superconductivity, we performed resistivity, specific heat and X-ray diffraction measurements on La$_3$Co$_4$Sn$_{13}$, focusing particularly on their temperature dependence around $T*$. Our results, in combination with lattice dynamics calculations, are more consistent with the second-order nature of the phase transition at $T*$.