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_4H_11N 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.