Quaternary borocarbides: a testbed for DFT for superconductors

TL;DR

This study uses density functional theory for superconductors to analyze quaternary borocarbides, successfully predicting critical temperatures and highlighting the importance of electron-phonon interactions and dynamic screening effects.

Contribution

It demonstrates the effectiveness of SCDFT with RPA in predicting superconducting properties of borocarbides, especially for nonmagnetic compounds, and discusses challenges in magnetic cases.

Findings

Good agreement with experimental $T_c$ for Ni- and Pd-based compounds

Overestimation of $T_c$ in magnetic compounds due to modeling limitations

Trend in $T_c$ across rare-earth series is qualitatively captured

Abstract

Using ab-initio density functional theory for superconductors (SCDFT), we systematically study the quaternary borocarbides $RM_2$B$_2$C. Treating the retarded (frequency-dependent) interaction $W(\omega)$ within the random-phase approximation (RPA), we find good agreement with experiments for the calculated superconducting critical temperature $T_c$ in the nonmagnetic Ni- and Pd-based compounds. We argue that the problem of accurately placing the $f$-bands within DFT, and possibly the lack of an explicit magnetic pair-breaking mechanism, explain the difficulties of SCDFT in reproducing $T_c$ in members of the magnetic $R$Ni$_2$B$_2$C series ($R$ rare-earth with partially filled $4f$). While the calculated $T_c$ is overestimated, SCDFT qualitatively captures the experimentally observed trend along the rare-earth series, which indicates that the electron-phonon couplings and dynamically screened interactions have a significant effect on $T_c$.