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Electrical resistivity, magnetic susceptibility, and specific heatmeasurements on single crystals of La$Tr_{2}$Al$_{20}$ ($Tr$ = Ti, V, Nb, andTa) revealed that these four compounds exhibit weak-coupling superconductivitywith transition temperatures $T_{\rm c}$ = 0.46, 0.15, 1.05, and 1.03 K,respectively. LaTi$_{2}$Al$_{20}$ is most probably a type-I superconductor,which is quite rare among intermetallic compounds. Single-crystal X-raydiffraction suggests "rattling" anharmonic large-amplitude oscillations of Alions (16$c$ site) on the Al$_{16}$ cage, while no such feature is suggested forthe cage-center La ion. Using a parameter $d_{\rm GFS}$ quantifying the "guestfree space" of the cage-center ion, we demonstrate that nonmagnetic$RTr_{2}$Al$_{20}$ superconductors are classified into two groups, i.e., (A)$d_{\rm GFS} \ne 0$ and $T_{\rm c}$ correlates with $d_{\rm GFS}$, and (B)$d_{\rm GFS} \simeq 0$ and $T_{\rm c}$ seems to be governed by other factors.

Superconductivity in Cage Compounds La$Tr_{2}$Al$_{20}$ with $Tr$ = Ti, V, Nb, and Ta