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We report the electric transport and thermodynamic properties of theskutterudite-related La$_3$Co$_4$Sn$_{13}$ and La$_3$Rh$_4$Sn$_{13}$superconductors. Applying an external pressure to La$_3$Rh$_4$Sn$_{13}$, theresistive superconducting critical temperature Tc decreases, while the criticaltemperature of La$_3$Co$_4$Sn$_{13}$ is enhanced with increasing pressure. Thepositive pressure coefficient dTc/dP correlates with a subtle structuraltransition in La$_3$Co$_4$Sn$_{13}$ and is discussed in the context of latticeinstabilities. Specific-heat data show that both compounds are typical BCSsuperconductors. However, La$_3$Rh$_4$Sn$_{13}$ also exhibits a secondsuperconducting phase at higher temperatures, which is characteristic ofinhomogeneous superconductors. We calculate the specific heat for aninhomogeneous superconducting phase, which agrees well with experimental C(T)data for La$_3$Rh$_4$Sn$_{13}$. We also found that an applied pressure reducesthis second superconducting phase.

Superconductivity of La$_3$Co$_4$Sn$_{13}$ and La$_3$Rh$_4$Sn$_{13}$: A comparative study