Rattling induced superconductivity in RV$_{\mathrm{2}}$Al$_{\mathrm{20}}$ (R $=$ Sc, Lu, Y) aluminides -- an experimental and theoretical study*

Polycrystalline samples of four ternary intermetallics RV$_{\mathrm{2}}$Al$_{\mathrm{20}}$ (R $=$ Sc, Y, La, and Lu) were synthesized. Structural studies carried out using powder x-ray diffraction and Rietveld analysis show that all compounds crystallize in CeCr$_{\mathrm{2}}$Al$_{\mathrm{20}}$-type structure composed of icosahedral Al-R cages. Results of physical properties measurements reveal that ScV$_{\mathrm{2}}$Al$_{\mathrm{20}}$, YV$_{\mathrm{2}}$Al$_{\mathrm{20}}$, and LuV$_{\mathrm{2}}$Al$_{\mathrm{20}}$ are weakly-coupled BCS superconductors with critical temperatures T$_{\mathrm{c}}=$ 1.0, 0.57, and 0.60 K, respectively. Electronic and phonon structure calculations reveal the key role of low-frequency anharmonic vibrations of R atoms (rattling effect) for the appearance of superconductivity. A correlation between phonon and crystal structures was observed, allowing to search for new RV$_{\mathrm{2}}$Al$_{\mathrm{20}}$ superconductors.