In this paper, we investigate the mechanical properties, electronic band structure, lattice dynamics, and electron-phonon interaction in $\delta \text{−}\mathrm{NbN}$, $\varepsilon \text{−}\mathrm{NbN}$, WC-NbN, and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ by performing systematic ab initio calculations based on density functional theory with the generalized gradient approximation. We find that all the four structures are mechanically stable with $\varepsilon \text{−}\mathrm{NbN}$ being the ground-state structure. The calculated elastic constants, which agree well with available experimental data, demonstrate that all four NbN polytypes are hard materials with bulk moduli being close to that of boron nitride. The calculated electronic band structures show that all four polytypes are metallic with the Nb $d$-orbital dominated energy bands near the Fermi level ($E_F$). The calculated phonon dispersion relations of $\delta \text{−}\mathrm{NbN}$ are in good agreement with neutron scattering experiments. The electron-phonon coupling ($\lambda$) in $\delta \text{−}\mathrm{NbN}$ ($\lambda =0.98$) is much stronger than in $\varepsilon \text{−}\mathrm{NbN}$ ($\lambda =0.16$), WC-NbN ($\lambda =0.11$), and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ ($\lambda =0.17$). This results in a much higher superconducting transition temperature ($T_c=18.2\mathrm{K}$) than in $\varepsilon \text{−}\mathrm{NbN}$, WC-NbN, and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ ($T_c\le 1.0\mathrm{K}$). The stronger $\lambda$ and higher $T_c$ in $\delta \text{−}\mathrm{NbN}$ are attributed to its large density of states at $E_F$ and small Debye temperature. The calculated $T_c$ of $\delta \text{−}\mathrm{NbN}$ is in good agreement with the experimental values. However, the predicted $T_c$ of $\varepsilon \text{−}\mathrm{NbN}$ is much smaller than the recent experiment (11.6 K) but agrees well with the earlier experiment, suggesting further experiments on single-phase samples. Finally, the calculated relativistic band structures reveal that all four NbN polytypes are topological metals. Specifically, $\varepsilon \text{−}\mathrm{NbN}$ and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ are type-I Dirac metals whereas $\delta \text{−}\mathrm{NbN}$ is type-II Dirac metal, while WC-NbN is an emergent topological metal that has rare triply degenerate nodes. All these results indicate that all the four NbN polytypes should be hard superconductors with nontrivial band topology that would provide valuable opportunities for studying fascinating phenomena arising from the interplay of band topology and superconductivity.

• Received 8 August 2018
• Revised 28 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.104508