The recently discovered nickelate superconductors appear, at first glance, to be even more complicated multi-orbital systems than cuprates. To identify the simplest model describing the nickelates, we analyse the multi-orbital system and find that it is instead the nickelates which can be described by a one-band Hubbard model, albeit with an additional electron reservoir and only around the superconducting regime. Our calculations of the critical temperature T_C are in good agreement with experiment, and show that optimal doping is slightly below 20% Sr-doping. Even more promising than 3d nickelates are 4d palladates.

Superconducting nickelates appear to be difficult to synthesize. Since the chemical reduction of $AB{\mathrm{O}}_3$ [rare earth ($A$), transition metal ($B$)] with ${\mathrm{CaH}}_2$ may result in both $AB{\mathrm{O}}_2$ and $AB{\mathrm{O}}_2\mathrm{H}$, we calculate the topotactic H binding energy by density functional theory (DFT). We find intercalating H to be energetically favorable for ${\mathrm{LaNiO}}_2$ but not for Sr-doped ${\mathrm{NdNiO}}_2$. This has dramatic consequences for the electronic structure as determined by $\mathrm{DFT}+\mathrm{dynamical}$ mean field theory: that of $3d^9$ ${\mathrm{LaNiO}}_2$ is similar to (doped) cuprates, $3d^8$ ${\mathrm{LaNiO}}_2\mathrm{H}$ is a two-orbital Mott insulator. Topotactic H might hence explain why some nickelates are superconducting and others are not.

The discovery of infinite-layer nickelate superconductor marks the new era in the field of superconductivity. In the rare-earth ($R$) nickelates $\mathrm{RNi}{\mathrm{O}}_2$, although the Ni is also of $d^9$ electronic configuration, analogous to Cu $d^9$ in cuprates, whether electronic structures in infinite-layer nickelate are the same as cuprate and possess the single-band feature as well are still open questions. To illustrate the electronic structure of rare-earth infinite-layer nickelate, we perform first-principles calculations of $\mathrm{LaNi}{\mathrm{O}}_2$ and $\mathrm{NdNi}{\mathrm{O}}_2$ compounds and compare them with that of $\mathrm{CaCu}{\mathrm{O}}_2$ using the hybrid functional method together with Wannier projection and group symmetry analysis. Our results indicate that the Ni ${d_{x^2}}_{-y^2}$ in the $\mathrm{LaNi}{\mathrm{O}}_2$ has weak hybridization with other orbitals and exhibits the characteristic single-band feature, whereas in $\mathrm{NdNi}{\mathrm{O}}_2$, the Nd $f$ orbital hybridizes with Ni $d_{x^2-y^2}$ and is a non-negligible ingredient for transport and even high-temperature superconductivity. Given that the Cu $d_{x^2-y^2}$ in cuprate strongly hybridizes with O $2p$, the calculated band structures of nickelate imply some new band characters, which is worthy of more attention.

Identifying a suitable water-soluble sacrificial layer is crucial to fabricating large-scale freestanding oxide membranes, which offer attractive functionalities and integrations with advanced semiconductor technologies. Here, we introduce a water-soluble sacrificial layer, “super-tetragonal” Sr ₄ Al ₂ O ₇ (SAO _T ). The low-symmetric crystal structure enables a superior capability to sustain epitaxial strain, allowing for broad tunability in lattice constants. The resultant structural coherency and defect-free interface in perovskite ABO ₃ /SAO _T heterostructures effectively restrain crack formation during the water release of freestanding oxide membranes. For a variety of nonferroelectric oxide membranes, the crack-free areas can span up to a millimeter in scale. This compelling feature, combined with the inherent high water solubility, makes SAO _T a versatile and feasible sacrificial layer for producing high-quality freestanding oxide membranes, thereby boosting their potential for innovative device applications.

A recent paper [Lee et al., J. Kor. Cryst. Growth Cryst. Technol. 33, 61 (2023)] provides some experimental indications that ${\mathrm{Pb}}_{10-x}{\mathrm{Cu}}_x{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory (DFT) calculations show lattice parameters and a volume contraction with $x$, very similar to experiment. The DFT electronic structure shows ${\mathrm{Cu}}^{2+}$ in a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This puts ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ in an ultracorrelated regime and suggests that, without doping, it is a Mott or charge-transfer insulator. If doped, such an electronic structure might support flat-band superconductivity or a correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.

We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model, we identify the one-band Hubbard model for the Ni 3dx2−y2 orbital plus a pocket around the A-momentum. The latter, however, merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from nominal Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by the experiment, indicate that the Γ pocket, Nd 4f orbitals, oxygen 2p, and the other Ni 3d orbitals are not relevant in the superconducting doping regime. The physics is completely different if topotactic hydrogen is present or the oxygen reduction is incomplete. Then, a two-band physics hosted by the Ni 3dx2−y2 and 3d3z2−r2orbitals emerges. Based on our minimal modeling, we calculated the superconducting T_c vs. Sr-doping x phase diagram prior to the experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as T_c, the agreement with the experiment is astonishingly good. The prediction that T_c is enhanced with pressure or compressive strain has been confirmed experimentally as well. This supports that the one-band Hubbard model plus an electron reservoir is the appropriate minimal model.