Strong-coupling superconductivity of the Heusler-type compound ScAu2Al: Ab initio studies

The ${\mathrm{ScAu}}_{2}\mathrm{Al}$ superconducting Heusler-type compound was recently characterized to have the highest critical temperature of ${T}_{c}=5.12$ K and the strongest electron-phonon coupling among the Heusler family. In this work, the electronic structure, phonons, electron-phonon coupling, and superconductivity of ${\mathrm{ScAu}}_{2}\mathrm{Al}$ are studied using ab initio calculations. The spin-orbit coupling significantly changes the electronic structure removing the van Hove singularity from the vicinity of the Fermi level. In the phonon spectrum, low-frequency acoustic modes, additionally softened by the spin-orbit interaction, strongly couple with electrons, leading to the electron-phonon coupling constant $\ensuremath{\lambda}=1.25$, a record high among Heuslers. The density functional theory for superconductors is then used to analyze superconducting state in this two-band superconductor. The effect of spin fluctuations (SF) on superconductivity is also analyzed. The calculated critical temperatures of ${T}_{c}=5.16$ K (4.79 K with SF) agree very well with the experiment, confirming the electron-phonon mechanism of superconductivity and showing a weak spin-fluctuation effect. The superconducting gaps formed on two Fermi surface sheets exhibit moderate anisotropy. Their magnitudes confirm the strong coupling regime, as the reduced average values are $2{\mathrm{\ensuremath{\Delta}}}_{{b}_{1}}/{k}_{B}{T}_{c}\ensuremath{\simeq}4.1$ and $2{\mathrm{\ensuremath{\Delta}}}_{{b}_{2}}/{k}_{B}{T}_{c}\ensuremath{\simeq}4.3$. Anisotropy of the gaps and large spread in their values significantly affect the calculated quasiparticle density of states.