Formation of a two-dimensional single-component correlated electron system and band engineering in the nickelate superconductor ${\mathrm{NdNiO}}_2$

Motivated by the recent experimental discovery of superconductivity in the infinite-layer nickelate ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$ [Li et al., Nature (London) 572, 624 (2019)], we study how the correlated Ni $3d_{x^2-y^2}$ electrons in the ${\mathrm{NiO}}_2$ layer interact with the electrons in the Nd layer. We show that three orbitals are necessary to represent the electronic structure around the Fermi level: Ni $3d_{x^2-y^2}$, Nd $5d_{3z^2-r^2}$, and a bonding orbital made from an interstitial $s$ orbital in the Nd layer and the Nd $5d_{xy}$ orbital. By constructing a three-orbital model for these states, we find that the hybridization between the Ni $3d_{x^2-y^2}$ state and the states in the Nd layer is tiny. We also find that the metallic screening by the Nd layer is not so effective in that it reduces the Hubbard $U$ between the Ni $3d_{x^2-y^2}$ electrons just by 10%–20%. On the other hand, the electron-phonon coupling is not strong enough to mediate superconductivity of $T_{\mathrm{c}}\sim 10$ K. These results indicate that ${\mathrm{NdNiO}}_2$ hosts an almost isolated correlated $3d_{x^2-y^2}$ orbital system. We further study the possibility of realizing a more ideal single-orbital system in the Mott-Hubbard regime. We find that the Fermi pockets formed by the Nd-layer states dramatically shrink when the hybridization between the interstitial $s$ state and Nd $5d_{xy}$ state becomes small. By an extensive materials search, we find that the Fermi pockets almost disappear in ${\mathrm{NaNd}}_2{\mathrm{NiO}}_4$ and ${\mathrm{NaCa}}_2{\mathrm{NiO}}_3$.

Figure 1

(a) DFT band structure for ${\mathrm{NdNiO}}_2$. The Nd $4f$ orbitals are assumed to be frozen in the core. In ${\mathrm{NdNiO}}_2$, the interstitial $s$ and Nd $5d_{xy}$ orbitals form bonding and antibonding states on the $k_z=\pi /c$ plane. The green open circles at the A point indicate the band bottom of the bonding band (below the Fermi level) and the band top of the antibonding band (above the Fermi level). Electron density of the Kohn-Sham states specified by (b) the blue dot at the $\mathrm{\Gamma }$ point and (c) the blue diamond at ($\pi /a, \pi /2a, \pi /c$) point (drawn by vesta [52]). The positions of the atoms in the crystal coordinate are follows: Ni (0, 0, 0), Nd ($\frac{1}{2}, \frac{1}{2}, \frac{1}{2}$), O ($\frac{1}{2}$, 0, 0), O (0, 0, $\frac{1}{2}$).

Figure 2

Phonon band structure (left panel), atom-projected phonon DOS (middle), and the Eliashberg function $a^{2}F\left(\omega \right)$ (right) of ${\mathrm{NdNiO}}_2$. The dotted line in the right panel shows the accumulated value of $\lambda \left(\omega \right)$ defined as $\lambda \left(\omega \right)=2{\int }_0^{\omega }d{\omega }^{\prime }{\alpha }^{2}F\left({\omega }^{\prime }\right)/{\omega }^{\prime }$.

Figure 3

(a) Dispersion of the three-orbital tight-binding model (blue dashed curves). Red solid curves show the DFT band structure. (b) Isosurfaces (yellow: positive, light blue: negative) of constructed maximally localized Wannier functions (drawn by vesta [52]). (c) Projected density of states (PDOS) and (d) fat bands of the three-orbital tight-binding model. In the fat bands, the size of the symbols is proportional to the weight of the respective orbital components.

Figure 4

DFT band structure of ${\mathrm{NdNiO}}_2$. The black dotted and red solid curves are calculated with the original lattice constant $a$ and $1.05\times a$, respectively. The green open circles indicate the band bottom of the bonding band between the interstitial $s$ and Nd $5d_{xy}$ orbitals (below the Fermi level) and the band top of the antibonding band (above the Fermi level).

Figure 5

(a) Crystal structure and (b) DFT band structure of ${\mathrm{NaNd}}_2{\mathrm{NiO}}_4$. (c) Crystal structure and (d) DFT band structure of ${\mathrm{NaCa}}_2{\mathrm{NiO}}_3$. The green open circles indicate the band bottom of the bonding band between the interstitial $s$ and cation $d_{xy}$ orbital (below the Fermi level) and the band top of the antibonding band (above the Fermi level).

Figure 6

Schematic diagram for screening processes for the $3d_{x^2-y^2}$ orbital at a Ni site (blue circles). Upper-green and lower-gray layers represent Nd and ${\mathrm{NiO}}_2$ layers, respectively. Dashed lines are Coulomb interactions, and solid oval lines with arrows describe the polarization in which the red dots represent the polarization points. In the figure, an RPA diagram (symbolically for the second-order one) for the effective onsite interaction is shown, and three types of screening processes are depicted. (a) Screening process via the intralayer polarization in the ${\mathrm{NiO}}_2$ layer. (b) Screening process via the interlayer polarization. (c) Screening process via the intralayer polarization in Nd layer. The red points and the blue circles in (a) and (b) may share the same Ni site, although they are depicted at difference positions.

Figure 7

(a) Dispersion of three-orbital tight-binding model using Ni $3d_{x^2-y^2}$, Nd $5d_{3z^2-r^2}$, and Nd $5d_{xy}$ orbitals (blue dashed curves). Red solid curves show the DFT band structure. (b) Isosurfaces (yellow: positive, light blue: negative) of constructed maximally localized Wannier function for Nd $5d_{xy}$ orbital (drawn by vesta [52]).