Effect of electron-phonon coupling on the superconducting transition temperature in dodecaboride superconductors: A comparison ofLuB12withZrB12

Abstract

We report a detailed study of specific heat, electrical resistivity, and optical spectroscopy in the superconducting boride ${\text{LuB}}_{12}$ $({T}_{c}=0.4\text{ }\text{K})$, and compare it to the higher ${T}_{c}$ compound ${\text{ZrB}}_{12}$ $({T}_{c}=6\text{ }\text{K})$. Both compounds have the same structure based on enclosed metallic Lu or Zr ions in oversized boron cages. The infrared reflectivity and ellipsometry in the visible range allow us to extract the optical conductivity from 6 meV to 4 eV in the normal state from 20 to 280 K. By extracting the superconducting properties, phonon density of states, and electron-phonon coupling function from these measurements, we discuss the important factors governing ${T}_{c}$ and explain the difference between the two compounds. The phonon density of states seems to be insignificantly modified by substitution of Zr with Lu. However, the soft vibrations of the metal ions in boron cages, responsible for the relatively high ${T}_{c}$ in ${\text{ZrB}}_{12}$, have almost no contribution to the electron-phonon coupling in ${\text{LuB}}_{12}$.