Recently, nitrogen-doped lutetium hydride was found to be a near-ambient superconductor with a $T_c=294$K at a pressure of only 10 kbar. In this paper, within DFT+U, we investigate the electronic structure of both parent lutetium hydride LuH$_{\boldsymbol{3}}$ and the nitrogen doped lutetium hydride LuH$_{\boldsymbol{2.75}}$N$_{\boldsymbol{0.25}}$. It is shown that with nitrogen doping, the N-2p states enter the Fermi level in large quantities and bring together a significant contribution from the H-1s states. The presence of N-2p and H-1s states at the Fermi level in a doped compound might facilitate the emergence of superconductivity. For instance, nitrogen doping almost doubles the value of DOS at the Fermi level for LuH$_{2.75}$N$_{0.25}$. A  simple BCS analysis shows that for the nitrogen doped LuH$_{2.75}$N$_{0.25}$ compound,   $T_c$ value might be more than 100 K and may even increase with further hole doping.

(Left) Crystal structure of LuH2.75N0.25 with two types of H atom surroundings. (Right) The bands projected on Wannier function with linewidth showing contributions of H-1s octahedral and N-2p states

 

                                 N. S.Pavlov, I.R. Shein, K. S.Pervakov, V.M.Pudalov, I.A.Nekrasov

                        JETP Letters 118, issue 9 (2023)