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The comprehensive research of the electronic structure, thermodynamic and electrical transport properties reveals the existence of inhomogeneous superconductivity due to structural disorder in Ca$_3$Rh$_4$Sn$_{13}$ doped with La (Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$) or Ce (Ca$_{3-x}$Ce$_x$Rh$_4$Sn$_{13}$) with superconducting critical temperatures $T_c^{star}$ higher than those ($T_c$) observed in the parent compounds. The $T-x$ diagrams and the entropy $S(x)_T$ isotherms well document the relation between degree of an atomic disorder and separation of the {it high-temperature} $T_c^{star}$ and $T_c$-bulk phases. In these dirty superconductors with the mean free path much smaller than the coherence length, the Werthamer-Helfand-Hohenber theoretical model does not well fits the $H_{c2}(T)$ data. We suggest that this can result from two-band superconductivity or from the presence of strong inhomogeneity in these systems. The multiband model very well describes the $H-T$ dependencies, but the present results as well as our previous studies give arguments for the scenario based on the presence of nanoscopic inhomogeneity of the superconducting state. We also revisited the nature of structural phase transition at $T^{star}sim 130-170$ K and documented that there might be another precursor transition at higher temperatures. The impact of the magnetic Ce-Ce correlations on the increase of $T_c$ in respect to the critical temperatures of Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$ is also discussed.
The quasi-skutterudite superconductor Sr$_3$Rh$_4$Sn$_{13}$ features a pronounced anomaly in electrical resistivity at $T^*sim$138 K. We show that the anomaly is caused by a second-order structural transition, which can be tuned to 0 K by applying ph
The nature of the lattice instability connected to the structural transition and superconductivity of (Sr,Ca)$_3$Ir$_4$Sn$_{13}$ is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a f
We perform optical spectroscopy measurement across the charge density wave (CDW) phase transitions on single-crystal samples of Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$. Formation of CDW energy gap was clearly obser
In a superconductor that lacks inversion symmetry, the spatial part of the Cooper pair wave function has a reduced symmetry, allowing for the mixing of spin-singlet and spin-triplet Cooper pairing channels and thus providing a pathway to a non-trivia
The search for non-centrosymmetric superconductors that may exhibit unusual physical properties and unconventional superconductivity has yielded the synthesis of a non-centrosymmetric phosphide Mg$_2$Rh$_3$P with an Al$_2$Mo$_3$C-type structure. Alth