Superconductivity in Ban+2Ir4nGe12n+4 (n=1,2) with cage structure and softening of low-lying localized mode

We report on new superconductors Ban+2Ir4nGe12n+4 (n = 1, 2) with critical temperatures T-c = 6.1 and 3.2 K, respectively, along with their crystal structures, electron transport, and specific heat. The compounds are composed of alternating Ba@Ir8Ge16 and Ba@Ir2Ge16 cages, both of which are larger in the n = 1 sample than in the n = 2 sample. The normal-state heat capacity reveals two low-lying vibration modes associated with guest Ba cations, and both characteristic temperatures in Ba3Ir4Ge16 are smaller than those in Ba4Ir8Ge28. Meanwhile, the density functional theory calculations reveal that the Ge-4p bands dominated the Fermi level in both samples. We propose that the softening of localized phonons due to expansion of the cage strengthens the electron-phonon coupling between Ba cations and Ge anions, leading to the higher T-c in Ba3Ir4Ge16.