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Character of Doped Holes in Nd_{1−x}Sr_{x}NiO_{2}

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## Abstract

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## 1. Introduction: Superconducting Infinite-Layered Nickelates Nd_{1−x}Sr_{x}NiO_{2}

## 2. Charge-Transfer Model Revisited: Charge-Transfer Model for an NiO_{2} Plane

## 3. Electronic Structure Calculations

## 4. Effective Two-Band Hamiltonian

## 5. Results and Discussion

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Doping tendency of NiO${}_{2}$ model as a function of crystal-field splitting $\Delta $: (

**a**) ${U}_{dp}=0$; (

**b**) ${U}_{dp}=1$ eV. (Blue) undoped, ${N}_{\uparrow}=2$ and ${N}_{\downarrow}=2$; (Orange) one hole doped, ${N}_{\uparrow}=3$, ${N}_{\downarrow}=2$; (Green) two holes doped, ${N}_{\uparrow}=3$, ${N}_{\downarrow}=3$ in Ni${}_{4}$O${}_{8}$ (Cu${}_{4}$O${}_{8}$) cluster. The nickelate (cuprate) regime is highlighted in blue (orange). The model parameters are given in Table 1.

**Figure 2.**DFT band structure and DOS of the Wannier Hamiltonian: (

**a**) DFT band structure (black solid lines) compared with Wannier band structure (red dashed lines), and (

**b**) Wannier DOS for the Ni(${x}^{2}-{y}^{2}$) (red) and apical Ni(s) orbital (blue).

**Figure 3.**Orbital-resolved electron densities as obtained for: (

**a**) set A, and (

**b**) set B, see Table 3. Strongly anisotropic electron distribution over the ${d}_{{x}^{2}-{y}^{2}}$ and s orbitals is favored when the interactions are screened by $\alpha >0.5$, as shown for: (

**c**) set A, and (

**d**) set B.

**Figure 5.**Competition between low-spin and high-spin states as obtained for the parameters of: (

**a**,

**c**) set A, and (

**b**,

**d**) set B, see Table 3. Panels (

**a**,

**b**) show local double occupancy ${D}_{\alpha}$ in each $\alpha ={x}^{2}-{y}^{2},s$ orbital, while panels (

**c**,

**d**) show local triplet states T.

${\mathit{t}}_{\mathit{p}\mathit{d}}$ | ${\mathit{t}}_{\mathit{p}\mathit{p}}$ | $\mathbf{\Delta}$ | ${\mathit{U}}_{\mathit{z}}={\mathit{U}}_{\overline{\mathit{z}}}$ | ${\mathit{J}}_{\mathit{H}}$ | ${\mathit{U}}_{\mathit{p}}$ | ${\mathit{J}}_{\mathit{H}}^{\mathit{p}}$ |
---|---|---|---|---|---|---|

1.30 | 0.55 | 7.0 | 8.4 | 1.2 | 4.4 | 0.8 |

(x,y,z) | ${\mathit{t}}_{\mathbf{ijk}}^{\mathit{\alpha}\mathit{\beta}}$ |
---|---|

(0,0,0) | $\left(\begin{array}{cc}0.2& 0\\ 0& 1.2\end{array}\right)$ |

(1,0,0) | $\left(\begin{array}{cc}-0.380& -0.050\\ -0.050& -0.031\end{array}\right)$ |

(0,1,0) | $\left(\begin{array}{cc}-0.380& 0.050\\ 0.050& -0.031\end{array}\right)$ |

(0,0,1) | $\left(\begin{array}{cc}-0.039& 0\\ 0& -0.076\end{array}\right)$ |

(1,1,0) | $\left(\begin{array}{cc}0.088& 0\\ 0& -0.111\end{array}\right)$ |

(1,0,1) | $\left(\begin{array}{cc}0.001& -0.009\\ -0.009& -0.252\end{array}\right)$ |

(0,1,1) | $\left(\begin{array}{cc}0.001& 0.009\\ 0.009& -0.252\end{array}\right)$ |

(1,1,1) | $\left(\begin{array}{cc}0.015& 0\\ 0& 0.056\end{array}\right)$ |

**Table 3.**Parameters of the two-band model (all in eV) used in exact diagonalization calculations. The reference energies for the two bands of ${x}^{2}-{y}^{2}$ and s symmetry are 0 and $\u03f5$, respectively.

Set | $\mathit{\u03f5}$ | t | ${\mathit{U}}_{1}$ | ${\mathit{J}}_{\mathit{H}}$ |
---|---|---|---|---|

A | 1.21 | 0.38 | 8.0 | 1.2 |

B | 1.21 | 0.38 | 4.0 | 0.6 |

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**MDPI and ACS Style**

Plienbumrung, T.; Schmid, M.T.; Daghofer, M.; Oleś, A.M.
Character of Doped Holes in Nd_{1−x}Sr_{x}NiO_{2}. *Condens. Matter* **2021**, *6*, 33.
https://doi.org/10.3390/condmat6030033

**AMA Style**

Plienbumrung T, Schmid MT, Daghofer M, Oleś AM.
Character of Doped Holes in Nd_{1−x}Sr_{x}NiO_{2}. *Condensed Matter*. 2021; 6(3):33.
https://doi.org/10.3390/condmat6030033

**Chicago/Turabian Style**

Plienbumrung, Tharathep, Michael Thobias Schmid, Maria Daghofer, and Andrzej M. Oleś.
2021. "Character of Doped Holes in Nd_{1−x}Sr_{x}NiO_{2}" *Condensed Matter* 6, no. 3: 33.
https://doi.org/10.3390/condmat6030033