Assessing the feasibility of near-ambient conditions superconductivity in the Lu-N-H system

The recent report of near-ambient superconductivity in nitrogen-doped lutetium hydrides (Lu-N-H) has generated a great interest. However, conflicting results have raised doubts regarding superconductivity. Here, we combine high-throughput crystal structure predictions with a fast predictor of the superconducting critical temperature ($T_c$) to shed light on the properties of Lu-N-H at 1 GPa. None of the predicted structures shows the potential to support high-temperature superconductivity and the inclusion of nitrogen favors the appearance of insulating phases. Despite the lack of near-ambient superconductivity, we consider alternative metastable templates and study their $T_c$ and dynamical stability including quantum anharmonic effects. The cubic Lu${}_4$H${}_{11}$N exhibits a high $T_c$ of 100 K at 20 GPa, a large increase compared to 30 K obtained in its parent LuH${}_3$. Interestingly, it has a similar X-ray pattern to the experimentally observed one. The LaH${}_{10}$-like LuH${}_{10}$ and CaH${}_6$-like LuH${}_6$ become high-temperature superconductors at 175 GPa and 100 GPa, with $T_c$ of 286 K and 246 K, respectively. Our findings suggest that high-temperature superconductivity is not possible in stable phases at near-ambient pressure, but metastable high-$T_c$ templates exist at moderate and high pressures.