Using ab initio density functional theory for superconductors (SCDFT), we systematically study the quaternary borocarbides $R{M}_2{\mathrm{B}}_2\mathrm{C}$. Treating the retarded (frequency-dependent) interaction $W\left(\omega \right)$ within the random-phase approximation, we find good agreement with experiments for the calculated superconducting critical temperature $T_c$ in the nonmagnetic Ni- and Pd-based compounds. Replacing the density functional theory (DFT) bands with a one-shot $GW$-derived quasiparticle band structure in the SCDFT calculations further improves the agreement with experiment for several of the tested systems. We argue that the problem of accurately placing the $f$ bands within DFT, and possibly the lack of an explicit magnetic pair-breaking mechanism, explains the difficulties of SCDFT in reproducing $T_c$ in members of the magnetic $R{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ series ($R$ rare-earth elements with partially filled $4f$ states). 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 $T_c$.

中文翻译：

---

四元硼碳化物：超导体 DFT 的测试平台

利用超导体从头算密度泛函理论（SCDFT），我们系统地研究了四元硼碳化物$右{\mathrm{中号}}_2{\mathrm{乙}}_2\mathrm{C}$。治疗延迟（频率相关）相互作用$瓦（\omega ）$在随机相位近似中，我们发现计算的超导临界温度与实验吻合良好${\mathrm{时间}}_C$在非磁性镍基和钯基化合物中。用一次性替代密度泛函理论 (DFT) 能带$G瓦$SCDFT 计算中导出的准粒子能带结构进一步提高了几个测试系统与实验的一致性。我们认为准确放置的问题$F$DFT 中的能带，以及可能缺乏明确的磁对断裂机制，解释了 SCDFT 在再现方面的困难${\mathrm{时间}}_C$在磁力成员中$右{你}_2{\mathrm{乙}}_2\mathrm{C}$系列 （$右$部分填充稀土元素$4F$状态）。虽然计算出的${\mathrm{时间}}_C$被高估了，SCDFT 定性地捕获了沿稀土系列实验观察到的趋势，这表明电子-声子耦合和动态筛选相互作用对${\mathrm{时间}}_C$。