Doping dependence of electronic structure of infinite-layer ${\mathrm{NdNiO}}_2$

We investigate the electronic structure of nickelate superconductor ${\mathrm{NdNiO}}_2$ upon hole doping, by means of density-functional theory and dynamical mean-field theory. We demonstrate the strong intrinsic hybridization between strongly correlated states formed by Ni-$3d_{x^2-y^2}$ orbital and itinerant electrons due to Nd-$5d$ and Ni-$3d_{z^2}$ orbitals, producing a valence-fluctuating correlated metal as the normal state of hole-doped ${\mathrm{NdNiO}}_2$. The Hund's rule appears to play a dominating role on multiorbital physics in the lightly doped compound, while its effect is gradually reduced by increasing the doping level. Crucially, the hole-doping leads to intricate effects on Ni-$3d$ orbitals, such as a nonmonotonic change of electron occupation in lightly doped level, and a flipping orbital configuration in the overdoped regime. Additionally, we also map out the topology of Fermi surface at different doping levels. These findings render a preferred window to peek into electron pairing and superconductivity.

Figure 1

(a) From left to right: perspective view of ${\mathrm{NdNiO}}_2$ supercell with $\delta$ = 6.25%, 18.75%, and 31.25%. The silver, red, yellow, and green balls represent Ni, O, Nd, and Sr atoms. (b) Lattice constant in $c$ direction and roughness with respect to $\delta$.

Figure 2

[(a)–(d)] Unfolded band structures for different Sr doping concentration. From left to right: $\delta$ = 0.00%, 6.25%, 18.75%, and 31.25%. [(e)–(j)] Projected density of state with different $\delta$ on different subspaces with arbitrary unit (a.u.), from left to right: Nd atoms, O $p_{x+y}$ orbitals, Ni $d_{x^2-y^2}$ orbitals, Ni $d_{z^2}$ orbitals, Ni $d_{xz}+d_{yz}$ orbitals, and Ni $d_{xy}$ orbitals. The weights in panels (e), (i), and (j) have been rescaled by factors of 2, 1/2, and 1/2. From bottom to top, $\delta$ increases from 0.00% to 31.25% in each figure.

Figure 3

$\mathbf{k}$-resolved spectral function from $\mathrm{DFT}+\mathrm{DMFT}$ calculations for (a) pristine, (b) 0.2 hole-doped, and (c) 0.4 hole-doped ${\mathrm{NdNiO}}_2$ at 116 K. $\mathrm{DFT}+\mathrm{DMFT}$ Fermi surfaces of (d) pristine ${\mathrm{NdNiO}}_2$, (e) 0.2 hole-doped ${\mathrm{NdNiO}}_2$, and (f) 0.4 hole-doped ${\mathrm{NdNiO}}_2$ from $V_{dc}=47.4$ eV calculations. For clarity purposes, the dominating $\alpha$ sheet is separated from $\beta$ and $\gamma$ pockets in panel (d).

Figure 4

Evolution of (a) Ni-$3d{e}_g$ orbital occupation, (b) weight of many-body states, and (c) Ni-$3d$ orbital crystal field splitting under hole doping. In panel (a), the occupation of $d_{x^2-y^2}$ is increased by 0.4 to fit in the plot. In panel (b), $d_{x^2-y^2}^9$ indicates $d^9$ state with unpaired $d_{x^2-y^2}$ electron, $d_{S=0}^8$/$d_{S=1}^8$ are $d^8$ spin-singlet/spin-triplet states, respectively. In panel (c), ${\mathrm{\Delta }}_0$ (${\mathrm{\Delta }}_1$) are the energy differences between $d_{x^2-y^2}$ ($d_{zx/zy}$) and $d_{xy}$ orbitals, respectively.

Figure 5

Crystal field splitting of $d$ orbitals with (a) $O_h$ symmetry, (b) $D_{4h}$, (c) $D_{4h}$ plus apical anions, and (d) $D_{4h}$ plus apical anions with interaction. The $d$ orbitals are labeled by different colors: $d_{x^2-y^2}$, $d_{z^2}$, $d_{xz}(d_{yz}$), and $d_{xy}$ orbital corresponds to pink, red, blue, and black. The green filled arrows indicate how orbital order evolves with new effects.

Figure 6

[(a)–(c)] Unfolded band structures for different Sr doping concentration. From left to right: $\delta$ = 0.00%, 6.25%, 18.75%, and 31.25%. [(e)–(j)] Projected density of state with different $\delta$ on different subspaces with arbitrary unit (a.u.), from left to right: Nd atoms, O $p_{x+y}$, Ni $d_{x^2-y^2}$, Ni $d_{z^2}$, Ni $d_{xz}+d_{yz}$, and Ni $d_{xy}$ orbitals. The weights in panels (a), (e), and (f) have been rescaled by factors of 2, 1/2, and 1/2. From bottom to top, $\delta$ increases from 0.00% to 31.25% in each panel.

Figure 7

Doping dependence of hybridization function for (a) Ni-$3d_{x^2-y^2}$, (b) Ni-$3d_{z^2}$, (c) Ni-$3d_{zx/zy}$, and (d) Ni-$3d_{xy}$ orbitals in $V_{dc}=47.4$ eV calculations.

Figure 8

Evolution of (a) Ni-$3d$ orbital occupation and (b) Ni-$3d$ orbital crystal field splitting under hole doping, calculated using $V_{dc}=51.84$ eV.

Figure 9

$\mathbf{k}$-resolved spectral function from $\mathrm{DFT}+\mathrm{DMFT}$ calculations, by including $f$ elections.