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

The quasi-skutterudite superconductor La$_3$Co$_4$Sn$_{13}$ undergoes a phase transition at $T^*=152$ K. By measuring the temperature dependence of heat capacity, electrical resistivity, and the superlattice reflection intensity using X-ray, we explore the character of the phase transition at $T^*$. Our lattice dynamic calculations found imaginary phonon frequencies around the ${\bf M}$ point, when the high temperature structure is used in the calculations, indicating that the structure is unstable at the zero temperature limit. The combined experimental and computational results establish that $T^*$ is associated with a second-order structural transition with $\bf{q}$=(0.5, 0.5, 0) (or the ${\bf M}$ point). Further electronic bandstructure calculations reveal Fermi surface sheets with low curvature segments, which allow us to draw qualitative comparison with both Sr$_3$Ir$_4$Sn$_{13}$ and Sr$_3$Rh$_4$Sn$_{13}$ in which similar physics has been discussed recently.