Electron-phonon coupling, superconductivity and nontrivial band topology in NbN polytypes

Abstract: In this paper, we investigate the electronic band structure, lattice dynamics and electron-phonon interaction in $\delta$-NbN, $\varepsilon$-NbN and WC-NbN by performing systematic ab initio calculations based on DFT-GGA. The calculated electronic band structures show that all three polytypes are metallic with the Nb $d$-orbital dominated energy bands near the Fermi level ($E_F$). The calculated phonon dispersion relations of $\delta$-NbN are in good agreement with neutron scattering experiments. The electron-phonon coupling ($\lambda$) in $\delta$-NbN ($\lambda=0.98$) is much stronger than in $\varepsilon$-NbN ($\lambda=0.16$) and WC-NbN ($\lambda=0.11$). This results in a much higher superconducting transition temperature ($T_c =18.2$ K) than in $\varepsilon$-NbN and WC-NbN ($T_c \le 1.0$ K). The stronger $\lambda$ and higher $T_c$ in $\delta$-NbN are attributed to its large density of states at $E_F$ and small Debye temperature. The calculated $T_c$ of $\delta$-NbN is in good agreement with the experimental values. However, the predicted $T_c$ of $\varepsilon$-NbN is much smaller than the recent experiment (11.6 K) but agrees well with the earlier experiment. Finally, the calculated relativistic band structures reveal that all three NbN polytypes are topological metals. Specifically, $\varepsilon$-NbN and $\delta$-NbN are, respectively, type-I and type-II Dirac metals, while WC-NbN is an emergent topological metal that has rare triply degenerate nodes. All these results indicate that all the three 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.