First-principles density functional theory (DFT) calculations of supercell structures based on N-doped $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$ reveal configurations of $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{Lu}}_8{\mathrm{H}}_{23-x}\mathrm{N}$ that exhibit novel electronic properties such as flat bands, sharply peaked densities of states (van Hove singularities, vHs), and intersecting Dirac cones near the Fermi energy (${\mathrm{E}}_F$). These electronic properties are present when N substitutes H in the octahedral interstices of $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$. These structures also exhibit an interconnected metallic hydrogen network, a common feature of high-${\mathrm{T}}_c$ hydride superconductors. Electronic property systematics gives an estimate of ${\mathrm{T}}_c$ for one structure that is well above the critical temperatures predicted for structures considered previously. $\text{DFT}+\text{U}$ has an especially strong effect on one of the structures considered, enhancing the vHs and flat bands near ${\mathrm{E}}_F$. These results provide a basis for understanding the electronic properties observed for nitrogen-doped lutetium hydride.

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• Composition
• Density of states
• Doping effects
• Electronic structure
• Fermi surface
• Flat bands
• Pressure effects
• Superconducting phase transition
• High-temperature superconductors
• Hydrides
• DFT+U
• Density functional theory