Electronic properties of hydrogen-doped square-planar nickelates

The layered square-planar nickelates $R_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}$ (R: rare-earth element) hold great promise in realizing cupratelike superconductors. While the appearance of zero resistivity is extremely sensitive to the concentration of hydrogen($x$) in infinite-layer $\mathrm{S}{\mathrm{r}}_{0.2}\mathrm{N}{\mathrm{d}}_{0.8}\mathrm{Ni}{\mathrm{O}}_2{\mathrm{H}}_x$, the configurations of many other $\mathrm{N}{\mathrm{d}}_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}{\mathrm{H}}_x$ and the general roles of H in these systems are still unknown. Using first-principles calculations, we find that H atoms prefer to form staggered one-dimensional chains along the $c$ axis, which are obstructed by the fluorite layer of $\mathrm{N}{\mathrm{d}}_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}$. Importantly, the charge-transfer energy between O $2p$ and Ni $3d$, one of the key factors determining the superconducting temperature in cuprates, is largely and continuously tunable by $n$ and $x$ in nickelates. Further, from the perspective of orbital hybridization and orbital polarization, the quasi-two-dimensional electronic properties are more pronounced for nickelates with smaller $n$, potentially facilitating superconductivity. These findings shed light on the general roles of H in controlling electronic properties in nickelates and provide valuable guidance for the experimental preparation of superconducting $R_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}$ materials.

Figure 1

(a) Crystal structure of $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$. The Ni atoms neighboring FL are labeled as $\mathrm{N}{\mathrm{i}}_{\mathrm{out}}$, and others are labeled as $\mathrm{N}{\mathrm{i}}_{\mathrm{in}}$. (b) PDOS for $\mathrm{N}{\mathrm{d}}_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}$ ($n=3-6$ and $\infty$). The Fermi level is set to the optimal $3d^{8.8}$ filling of Ni. PDOS for the IIS state is amplified by 2. (c) Schematic illustration of orbital hybridization $L_{3d-\mathrm{IIS}}$ and orbital polarization $I_{\mathrm{OP}}$ as functions of H concentration $x$ based on experimental measurements for the $n=\infty$ case [47]. The maximum $L_{3d-\mathrm{IIS}}$ ($L_{\max }$) and minimum $I_{\mathrm{OP}}$ ($I_{\min }$) are determined by the experimental superconducting critical $x$, namely, $x_{\min }$ (minimum $x$) and $x_{\max }$ (maximum $x$), respectively.

Figure 2

Side views (upper panels) and top views (lower panels) of the lowest-energy configurations for (a) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_1$, (b) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_2$, (c) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_3$, and (d) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_4$. Polyhedra highlight the local $\mathrm{N}{\mathrm{i}}_{\mathrm{out}}{\mathrm{O}}_4\mathrm{H}$ or $\mathrm{N}{\mathrm{i}}_{\mathrm{in}}{\mathrm{O}}_4{\mathrm{H}}_2$ environment. Green and pink colors distinguish the existence of H atoms in different blocks.

Figure 3

Projected band structures for (a) $\mathrm{N}{\mathrm{d}}_4\mathrm{N}{\mathrm{i}}_3{\mathrm{O}}_8$, (b) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$, and (c) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_2$ in the $k_z=0$ plane. IIS state is amplified by a factor of 2. The Fermi level is set to zero. (d) Charge-transfer energy ${\mathrm{\Delta }}_{d-p}$ versus $n$ and $x$.

Figure 4

(a) Schematic intercell hopping between Ni $3d_{x2-y2}$ orbital and IIS orbital ($t_{3d-\mathrm{IIS}}$) via O pσ orbital for $\mathrm{N}{\mathrm{i}}_{\mathrm{out}}$ and $\mathrm{N}{\mathrm{i}}_{\mathrm{in}}$ atoms. Only intercell hopping along the (1 0 0) direction is plotted as an example. Nd atoms are not displayed. (b) Averaged hopping strength ${\overline{t}}_{3d-\mathrm{IIS}}$ and $I_{\mathrm{OP}}$ changing as $n$ and $x$. For a given $n$, five $x$ ($x=0$, 0.25, 0.5, 0.75, 1) are given and the symbols become darker for larger $x$. The experimentally determined $x_{\min }$ ($\sim 0.22$) and $x_{\max }$ ($\sim 0.28$) for the superconducting dome in (Nd,Sr)$\mathrm{Ni}{\mathrm{O}}_2$ are labeled, along with the corresponding maximum ${\overline{t}}_{3d-\mathrm{IIS}}$ (${\overline{t}}_{max}$) and $I_{\min }$.

Figure 5

(a) Crystal structures for $\mathrm{N}{\mathrm{d}}_{n+1}\mathrm{N}{\mathrm{i}}_n{\mathrm{O}}_{2n+2}$ ($n=3-6$ and $\infty$). Nonequivalent Ni atoms ($\mathrm{N}{\mathrm{i}}_{\mathrm{in}}$ and $\mathrm{N}{\mathrm{i}}_{\mathrm{out}}$) are labeled. (b) IIS orbital (blue) located at the AOV site.

Figure 6

(a) Four possible high-symmetry H configurations in $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$, i.e., AOV site, the center of the $xy$ plane, the center of the $yz$ plane, and the site in the FL layer. (b) Relaxed crystal structure of the oxyhydride configuration. Energy differences for these configurations are listed below each configuration. The total energy of the H occupying the AOV site is set to zero.

Figure 7

(a) Local environment of one H chain in $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$. (b) The local environment of H-inserted Ni atoms.

Figure 8

Phonon spectra of $\surd 2\times \surd 2\times 1 \mathrm{N}{\mathrm{d}}_4\mathrm{N}{\mathrm{i}}_3{\mathrm{O}}_8$ supercell doped with (a) $x=0$, (b) $x=0.5$, (c) $x=1$.

Figure 9

Fully projected band structures (left panel) and DOS (right panel) for (a) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$ and (b) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_4$. DOS for nonequivalent $\mathrm{N}{\mathrm{i}}_{\mathrm{out}}$ and $\mathrm{N}{\mathrm{i}}_{\mathrm{in}}$ are given separately.

Figure 10

Band structure for ${\mathrm{Nd}}_6{\mathrm{Ni}}_5{\mathrm{O}}_{12}$ with Ni ${3d}_{x2-y2}$ and O $p\sigma$ orbitals projected.

Figure 11

The band structure of ${\mathrm{Nd}}_6{\mathrm{Ni}}_5{\mathrm{O}}_{12}{\mathrm{H}}_{0.5}$, with ${3d}_{x2-y2}$ orbital projected onto the ${\mathrm{Ni}}_{\mathrm{Ni}}$ and ${\mathrm{Ni}}_{\mathrm{out}}$ atoms.

Figure 12

Fermi Surfaces for (a) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}$ (left panel) and (b) $\mathrm{N}{\mathrm{d}}_6\mathrm{N}{\mathrm{i}}_5{\mathrm{O}}_{12}{\mathrm{H}}_4$ (right panel) in the $k_z=0$ section. Panel (c) is the same as (b) but for the $k_z=\pi$ section.

Figure 13

Charge-transfer energy ${\mathrm{\Delta }}_{d-p}$ versus $n$ for $x=0.0$. The black and orange lines are results obtained by DFT+$U$ and DFT methods, respectively.

Figure 14

The hopping paths and the corresponding strength (in units of eV) for interlayer coupling between $d_{z2}$ orbitals. (a) Local environment of $\mathrm{Ni}{\mathrm{O}}_4$. (b) Local environment of $\mathrm{Ni}{\mathrm{O}}_4\mathrm{H}$. The direct hopping paths ($t_{d-\mathrm{IIS}}, t_{d-s}$, and $t_{d-d}$) are labeled by gray lines, and the indirect hopping paths (${t^{\prime }}_{d-d}$) are labeled as dashed pink lines.