Optical properties and electronic structure of ZrB$_{12}$

TL;DR

This study investigates the optical and electronic properties of ZrB$_{12}$, a boride superconductor, revealing detailed insights into its optical conductivity, electron-phonon coupling, and possible ion delocalization effects.

Contribution

It provides a comprehensive analysis combining experimental optical measurements with theoretical calculations, identifying key phonon modes and electron-phonon coupling characteristics in ZrB$_{12}$.

Findings

Optical spectra match theoretical calculations of plasma frequency and interband conductivity.

Two peaks in the Eliashberg function indicate specific phonon modes involved in superconductivity.

Observed spectral weight transfer suggests metal ion delocalization within the crystal structure.

Abstract

We report optical (6 meV - 4 eV) properties of a boride superconductor ZrB$_{12}$ ($T_c$ = 6 K) in the normal state from 20 to 300 K measured on high-quality single crystals by a combination of reflectivity and ellipsometry. The Drude plasma frequency and interband optical conductivity calculated by self-consistent full-potential LMTO method agree well with experimental data. The Eliashberg function $\alpha_{tr}^2F(\omega)$ extracted from optical spectra features two peaks at about 25 and 80 meV, in agreement with specific heat data. The total coupling constant is $\lambda_{tr}=1.0\pm0.35$. The low energy peak presumably corresponds to the displacement mode of Zr inside $B_{24}$ cages, while the second one involves largely boron atoms. In addition to the usual narrowing of the Drude peak with cooling down, we observe an unexpected removal of about 10 % of the Drude spectral weight which is partially transferred to the region of the lowest-energy interband transition ($\sim$ 1 eV). This effect may be caused by the delocalization of the metal ion from the center of the $B_{24}$ cluster.