Electronic structure of nitrogen-doped lutetium hydrides

First-principles density functional theory (DFT) calculations of supercell structures based on N-doped $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$ reveal configurations of $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{Lu}}_8{\mathrm{H}}_{23-x}\mathrm{N}$ that exhibit novel electronic properties such as flat bands, sharply peaked densities of states (van Hove singularities, vHs), and intersecting Dirac cones near the Fermi energy (${\mathrm{E}}_F$). These electronic properties are present when N substitutes H in the octahedral interstices of $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$. These structures also exhibit an interconnected metallic hydrogen network, a common feature of high-${\mathrm{T}}_c$ hydride superconductors. Electronic property systematics gives an estimate of ${\mathrm{T}}_c$ for one structure that is well above the critical temperatures predicted for structures considered previously. $\text{DFT}+\text{U}$ has an especially strong effect on one of the structures considered, enhancing the vHs and flat bands near ${\mathrm{E}}_F$. These results provide a basis for understanding the electronic properties observed for nitrogen-doped lutetium hydride.

Figure 1

Top: Unit cell of $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$ followed by depictions of the layers [(100) planes] that form the building blocks of the superlattice structures considered in the present study: ${\mathrm{LuH}}_3$ layer; type 1 ordering, with N in the octahedral site; type 2 ordering, with N in the tetrahedral site; type 3 ordering, with chains of octahedrally coordinated N; and the two types of octahedral H vacancies denoted by open circles (red: type 1, green: type 2), with the tetrahedral hydrogens omitted for clarity. Bottom: the four 2 $\times$ 2 $\times$ 2 superlattice structure types for ${\mathrm{Lu}}_8{\mathrm{H}}_{23-x}\mathrm{N}$ (A, B, C, D) created from the above ordering schemes (see text and Supplemental Material [28]).

Figure 2

The band structures of (top) $\mathrm{Fm}\overline{3}\mathrm{m}{\mathrm{LuH}}_3$, (middle) ${\mathrm{Lu}}_8{\mathrm{H}}_{21}\mathrm{N}$ (${\mathrm{Lu}}_8{\mathrm{H}}_{21}\mathrm{N}$ structure-type B) [6], and (bottom) ${\mathrm{Lu}}_8{\mathrm{H}}_{23}\mathrm{N}$ (structure-type A) using $\text{DFT}+\text{U}$, U=8.2 eV on ${\mathrm{Lu}}_d$, 5.5 eV on ${\mathrm{Lu}}_f$.

Figure 3

Calculated PDOS near ${\mathrm{E}}_F$ of superlattice structure types A-D with DFT-$\text{PBE}+\text{U}$, U=8.2 eV on ${\mathrm{Lu}}_d$ [30] (a)–(d) vs DFT-PBE (e)–(h).

Figure 4

Calculated local bonding and electronic properties for ${\mathrm{Lu}}_8{\mathrm{H}}_{23}\mathrm{N}$ (A), with $\text{DFT}+\text{U}$, U on ${\mathrm{Lu}}_d$ of 8.2 eV. (a) Integrated local density of states (ILDOS), integrated $\pm 5$ meV from ${\mathrm{E}}_F$. (b) The ELF, illustrating the formation of the hydrogen bonding network. (c) Fermi surface (FS).