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Recently it was claimed that nitrogen-doped lutetium hydride exhibited anear-ambient superconducting transition with a temperature of 294 K at apressure of only 10 kbar, this pressure being several orders of magnitude lowerthan previously demonstrated for hydrides under pressure. In this paper, weinvestigate within DFT+U the electronic structure of both parent lutetiumhydride LuH$_3$ and nitrogen doped lutetium hydride LuH$_{2.75}$N$_{0.25}$. Wecalculated corresponding bands, density of states and Fermi surfaces. It isshown that in the stoichiometric system the Lu-5d states cross the Fermi levelwhile the H-1s states make almost no contribution at the Fermi level. However,with nitrogen doping, the N-2p states enter the Fermi level in large quantitiesand bring together a significant contribution from the H-1s states. Thepresence of N-2p and H-1s states at the Fermi level in a doped compound canfacilitate the emergence of superconductivity. For instance, nitrogen dopingalmost doubles the value of DOS at the Fermi level. Simple BCS analysis showsthat the nitrogen doping of LuH$_3$ can provide T$_c$ more than 100K and evenincrease it with further hole doping.

Anatomy of the band structure of the newest apparent near-ambient superconductor LuH$_{3-x}$N$_x$