Quantum stabilization and flat hydrogen-based bands of nitrogen-doped lutetium hydride

We explore the electronic and structural properties of $Fm\overline{3}m$ Lu-H-N structures with specific N,H ordering due to their remarkably narrow hydrogen-based bands at the Fermi level. Although ${\mathrm{LuH}}_{2.875}{\mathrm{N}}_{0.125}$ exhibits a classical instability persisting up to 17 GPa, it is anharmonically stable near ambient pressure when accounting for quantum nuclear effects. The presence of flat bands near ${E}_{\text{F}}$ is understood to arise from destructive quantum interference between ${\mathrm{N}}_{\mathrm{p}}$ and surrounding ${\mathrm{H}}_{\mathrm{s}}$ orbitals, with certain types of defects leaving the flat bands unaffected. The results suggest that if this system is superconducting, there is an optimal pressure near ambient where the superconducting ${T}_{\text{c}}$ is maximized by anharmonically stabilized low-frequency and nonadiabatically coupled high-frequency hydrogen modes. Despite the metastability of this structure, its dynamical stability when modeled beyond a classical harmonic approach suggests the narrow bands near ${E}_{\text{F}}$ do not cause structural distortions in certain Lu-H-N stoichiometries.