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Oxide based electrides are materials in which topotactic removal of loosely bound oxygens leaves behind voids with a landscape of attractive potentials for electrons. We find that this is also what happens in the recently discovered infinite-layer nickelates where one of the two extra electrons needed for charge neutrality when the apical oxygen is removed from the cubic perovskite precursor compound is to a large degree located in the oxygen vacancy position rather than both mainly used to convert Ni from 3+ to 1+. This is shown to be the main reason for the theoretical difficulty in determining the much debated elusive Fermi surface of these novel superconductors.

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature $T_{\rm c}$ as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high $T_{\rm c}$ to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr$_2$PdO$_3$ and $A^{\prime}_2$PdO$_2$Cl$_2$ ($A^{\prime}$=Ba$_{0.5}$La$_{0.5}$), to be virtually optimal, while others, such as NdPdO$_2$, are too weakly correlated., Comment: 8+16 pages, 5+18 figures

The discovery of superconductivity in hole-doped infinite layer nickelates, RNiO2 (R = Nd, Pr, La) has garnered sustained interest in the field. A definitive picture of low-energy many-body states has not yet emerged. We provide new insights into the low-energy physics, based on our embedded dynamical mean-field theory calculations, and propose a correlation (U)-temperature (T) phase diagram. The key features are a low-T Fermi liquid (FL) phase, a high-T Curie-Weiss regime, and an antiferromagnetic phase in a narrow U-T region. We associate the onset of the FL phase with partial screening of Ni-d moments; however, full screening occurs at lower temperatures. This may be related to insufficiency of conduction electrons to effectively screen the Ni-d moments, suggestive of Nozieres Exhaustion Principle. Our results suggest that RNiO2 are in the paramagnetic state, close to an antiferromagnetic dome, making magnetic fluctuations feasible. This may be consequential for superconductivity., Comment: 19 pages, 18 figures

We answer in affirmative the absence of superconductivity in bulk prepared samples of doped infinite-layer Nickelates through a simple magnetostatic model. In an independent approach we also employ Density Functional Theory (DFT) calculations for the same investigation. Our investigations reveal that it is the formation of Nickel clusters and Nickel deficient regions in bulk prepared samples (as opposed to thin films) that leads to the absence of superconductivity in bulk prepared samples.

The interplay between superconductivity and charge density waves (CDWs) under hole doping in cuprates is one of the central phenomena in condensed matter physics. Recently, CDWs are also observed in CaCuO$_2$-analogous nickelates RNiO$_2$ (R = La, Nd) but exhibit fundamentally different hole-doping-dependent behaviors compared to that in cuprates, raising a challenging question on its origin. In this article, we propose that electronic instability (EI) and moment-dependent electron-phonon coupling (MEPC), mainly contributed by Ni 3dx2-y2 and R 5dz2, respectively, may be the possible reasons for CDW formation in RNiO$_2$. Without hole doping, a strong Fermi surface nesting (FSN) induced by the unique feature of van Hove singularity (VHS) across Fermi level exists in RNiO$_2$ but not in CaCuO$_2$, and the unusual temperature-insensitive feature of EI and MEPC could result in rather high temperature CDWs in RNiO$_2$. Under hole doping, the reduced FSN of Ni 3dx2-y2 by the shift of VHS and decreased occupation of R 5dz2 largely weaken EI and MEPC in RNiO$_2$, respectively, suppressing the CDW formation. Our theory not only offers possible explanations to some puzzling experimental observations, but also establishes a unified understanding on the hole-doping-dependent EI and MEPC in nickelates and cuprates.

The discovery of superconductivity in infinite-layer nickelates has added a new family of materials to the fascinating growing class of unconventional superconductors. By incorporating the strongly correlated multi-orbital nature of the low-energy electronic degrees of freedom, we compute the leading superconducting instability from magnetic fluctuations relevant for infinite-layer nickelates. Specifically, by properly including the doping dependence of the Ni $d_{x^2-y^2}$ and $d_{z^2}$ orbitals as well as the self-doping band, we uncover a transition from $d$-wave pairing symmetry to nodal $s_\pm$ superconductivity, driven by strong fluctuations in the $d_{z^2}$-dominated orbital states. We discuss the properties of the resulting superconducting condensates in light of recent tunneling and penetration depth experiments probing the detailed superconducting gap structure of these materials., Comment: 7 pages, 4 figures, supplement included

Infinite-layer nickelates present a new family of potential unconventional superconductors. A key open question is the superconducting pairing symmetry. We present low-temperature measurements of the London penetration depth in optimally doped La_{0.8}Sr_{0.2}NiO_{2}, Pr_{0.8}Sr_{0.2}NiO_{2}, and Nd_{0.8}Sr_{0.2}NiO_{2}. For La and Pr-nickelates, the superfluid density shows a quadratic temperature dependence, indicating nodal superconductivity in the presence of disorder. Nd-nickelate exhibits complex low-temperature behavior, which we attribute to magnetic impurities. These results are consistent with d-wave pairing., Comment: 5 pages, 4 figures, 1 table, 1 supplementary material

The discovery of superconductivity in infinite-layer nickelates has attracted much attention due to their association to the high-$T_c$ cuprates. Cuprate superconductivity was first demonstrated in bulk samples and subsequently in thin films. In the nickelates, however, the situation has been reversed: although surging as a bulk phenomenon, nickelate superconductivity has only been reported in thin films so far. At the same time, the specifics of infinite-layer nickelates yield distinct interface and surface effects that determine their bulk vs thin-film behavior. In this paper, we provide an overview on these important aspects., Comment: 6 pages, 2 figures. Front. Phys.

Recent experiments have shown that the reduced multilayer rare-earth (RE) nickel oxides of form RE$_{p+1}$Ni$_p$O$_{2p+2}$ may belong to the novel family of superconducting lanthanide nickelates. Here, the correlated electronic structure of Pr$_{4}$Ni$_3$O$_{8}$ and Nd$_{6}$Ni$_5$O$_{12}$ is studied by means of an advanced realistic many-body framework. It is revealed that the low-energy physics of both systems is dominated by an interplay of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ degrees of freedom. Whilst the Ni-$d_{x^2-y^2}$ orbitals are always highly correlated near an (orbital-selective) Mott-insulating regime, the Ni-$d_{z^2}$ orbitals give rise to intriguing non-dispersive features. At low temperature, the Pr compound still displays QP-like Ni-$d_{x^2-y^2}$-derived states at the Fermi level, but the interacting fermiology of the Nd compound is outshined by an emergent Ni-$d_{z^2}$-controlling flat band. These findings translate well to the previous characterization of doped infinite-layer nickelates, and hence further make the case for a mechanism of unconventional superconductivity which is distinct from the one in high-$T_{\rm c}$ cuprates., Comment: 10 pages, 6 figures

This article summarizes recent work on the many-body (beyond density functional theory) electronic structure of layered rare-earth nickelates, both in the context of the materials themselves and in comparison to the high-temperature superconducting (high-$T_c$) layered copper-oxide compounds. It aims to outline the current state of our understanding of layered nickelates and to show how the analysis of these fascinating materials can shed light on fundamental questions in modern electronic structure theory. A prime focus is determining how the interacting physics defined over a wide energy range can be estimated and "downfolded" into a low energy theory that would describe the relevant degrees of freedom on the $\sim 0.5$ eV scale and that could be solved to determine superconducting and spin and charge density wave phase boundaries, temperature-dependent resistivities, and dynamical susceptibilities., Comment: 34 pages, 10 figuress and 2 tables. An invited review by Frontiers in Physics as part of a collection on nickelate superconductors

Infinite-layer (IL) nickelates are an emerging class of superconductors, where the Ni$^{1+}$ valence state in a square planar NiO$_2$ coordination can only be reached via topotactic reduction of the perovskite phase. However, this topotactic soft chemistry with hydrogenous reagents is still at a stage of rapid development, and there is a number of open issues, especially considering the possibility of hydrogen incorporation. Here we study the time dependence of the topotactic transformation of LaNiO$_3$ to LaNiO$_2$ for powder samples with x-ray diffraction and gas extraction techniques. While the hydrogen content of the powder increases with time, neutron diffraction shows no negative scattering of hydrogen in the LaNiO$_2$ crystal lattice. The extra hydrogen appears to be confined to grain boundaries or secondary-phase precipitates. The average crystal structure, and possibly also the physical properties, of the primary LaNiO$_2$ phase are therefore not noticeably affected by hydrogen residues created by the topotactic transformation.

I show the infinite-layer rare-earth nickelates are near a structural quantum critical point by mapping the energetics of their structural instabilities using first priniciples calculations. I first confirm previous results that show a phonon instability in the $P4/mmm$ phase leading to the $I4/mcm$ structure for $R$NiO$_2$ with $R$ = Sm--Lu. I then study the non-spin-polarized phonon dispersions of the $I4/mcm$ phase and find that they exhibit rare-earth size dependent instabilities at the $X$ and $M$ points for materials with $R$ = Eu--Lu. Group-theoretical analysis was used to enumerate all the isotropy subroups due to these instablities, and the distorted structures corresponding to their order parameters were generated using the eigenvectors of the unstable phonons. These structures were then fully relaxed by minimizing both the atomic forces and lattice stresses. I was able to stabilize only five out of the twelve possible distortions. The $Pbcn$ isotropy subgroup with the $M_5^+(a,a)$ order parameter shows noticeable energy gain relative to other distortions for the compounds with late rare-earth ions. However, the order parameter of the lowest-energy phase switches first to $X_2^- (0,a) + M_5^+ (b,0)$ and then to $X_2^- (0,a)$ as the size of the rare-earth ion is progressively increased. Additionally, several distorted structures lie close in energy for the early members of this series. These features of the structural energetics persist even when antiferromagnetism is allowed. Such a competition between different order parameters that can be tuned by rare-earth ion substitution suggests that any structural transition that could arise from the phonon instabilities present in these materials can be suppressed to 0 K.

We analyze the electronic structure of the recently synthesized higher-order nickelate Ruddlesden-Popper phases La$_{n+1}$Ni$_n$O$_{3n+1}$ ($n=4-6$) using first-principles calculations. For all materials, our results show large holelike Fermi surfaces with $d_{x^2-y^2}$ character that closely resemble those of optimally hole-doped cuprates. For higher values of $n$, extra non-cuprate-like bands of $d_{z^2}$ orbital character appear. These aspects highlight that this Ruddlesden-Popper series can provide a means to modify the electronic ground states of nickelates by tuning their dimensionality. With their similarities and differences to the cuprates, this new family of materials can potentially shed light on the physics of copper-based oxides., Comment: 12 pages, 11 figures

Building upon the recent progress on the intriguing underlying physics for the newly discovered infinite-layer nickelates, in this article we review an examination of valence charge and spin excitations via multi-orbital Hubbard models as way to determine the fundamental building blocks for Hamiltonians that can describe the low energy properties of infinite-layer nickelates. We summarize key results from density-functional approaches, and apply them to the study of x-ray absorption to determine the valence ground states of infinite-layer nickelates in their parent form, and show that a fundamental $d^9$ configuration as in the cuprates is incompatible with a self-doped ground state having holes in both $d_{x^2-y^2}$ and a rare-earth-derived axial orbital. When doped, we determine that the rare-earth-derived orbitals empty and additional holes form low spin $(S=0)$ $d^8$ Ni states, which can be well-described as a doped single-band Hubbard model. Using exact diagonalization for a 2-orbital model involving Ni and rare earth orbitals, we find clear magnons at 1/2 filling that persist when doped, albeit with larger damping, and with a dependence on the precise orbital energy separation between the Ni- and rare-earth-derived orbitals. Taken together, a full two-band model for infinite-layer nickelates can well describe the valence charge and spin excitations observed experimentally.

In materials science, much effort has been devoted to reproduce superconductivity in chemical compositions analogous to cuprate superconductors since their discovery over thirty years ago. This approach was recently successful in realising superconductivity in infinite-layer nickelates. Although differing from cuprates in electronic and magnetic properties, strong Coulomb interactions suggest infinite-layer nickelates have a propensity to various symmetry-breaking orders that populate the cuprates. Here we report the observation of charge density waves (CDWs) in infinite-layer NdNiO$_2$ films using Ni-$L_3$ resonant x-ray scattering. Remarkably, CDWs form in Nd 5$d$ and Ni 3$d$ orbitals at the same commensurate wavevector $(0.333, 0)\;r.l.u.$, with non-negligible out-of-plane dependence, and an in-plane correlation length up to $\sim$ 60 Angstrom. Spectroscopic studies reveal a strong connection between CDWs and the Nd 5$d$ - Ni 3$d$ orbital hybridisation. Upon entering the superconducting state at 20\% Sr doping, the CDWs disappear. Our work demonstrates the existence of CDWs in infinite-layer nickelates with a multi-orbital character distinct from cuprates, which establishes their low-energy physics., Comment: 9 pages, 4 figures, and Supplementary Information

Rare-earth nickelates RNiO$_2$ adopting an infinite-layer phase show superconductivity once La, Pr or Nd are substituted by a divalent cation. Either in the pristine or doped form, these materials are reported to adopt a high symmetry, perfectly symmetric, P4/mmm tetragonal cell. Nevertheless, bulk compounds are scarce, hindering a full understanding of the role of chemical pressure or strain on lattice distortions that in turn could alter magnetic and electronic properties of the 2D nickelates. Here, by performing a full analysis of the prototypical YNiO$_2$ compound with first-principles simulations, we identify that these materials are prone to exhibit O$_4$ group rotations whose type and amplitude are governed by the usual R-to-Ni cation size mismatch. We further show that these rotations can be easily tuned by external stimuli modifying lattice parameters such as pressure or strain. Finally, we reveal that H intercalation is favored for any infinite-layer nickelate member and pushes the propensity of the compounds to exhibit octahedra rotations.

Since the discovery of superconductivity in infinite-layer nickelates RNiO$_2$ (R=La, Pr, Nd), great research efforts have been paid to unveil its underlying superconducting mechanism. However, the physical origin of the intriguing hole-doped superconductivity phase diagram, characterized by a superconductivity dome sandwiched between two weak insulators, is still unclear. Here, we present a microscopic theory for electronic structure of nickelates from a fundamental model-based perspective. We found that the appearance of weak insulator phase in lightly and heavily hole-doped regime is dominated by Mottness and Hundness, respectively, exhibiting a unique orbital-selective doping originated from the competition of Hund interaction and crystal field splitting. Moreover, the superconducting phase can also be created in the "mixed" transition regime between Mott-insulator and Hund-induced insulator, exactly reproducing the experimentally observed superconducting phase diagram. Our findings not only demonstrate the orbital-dependent strong-correlation physics in Ni 3$d$ states, but also provide a unified understanding of superconducting phase diagram in hole-doped infinite-layer nickelates, which are distinct from the well-established paradigms in cuprates and iron pnictides., Comment: 17 pages, 11 figures, 4 Tables; comments are welcome

We derive an effective three-orbital model for the infinite-layer nickelates based on the band structure obtained by the GW approximation (GWA), where we consider the Ni 3$d_{x^2-y^2}$ and O 2$p$ orbitals forming the $\sigma$-bond. In the GWA, the self-energy correction to the local density approximation (LDA) increases the energy difference between Ni $3d_{x^2-y^2}$ and O $2p$, which reduces the bandwidth of the antibonding 3$d_{x^2-y^2}$ orbitals. The isolation of the Ni $3d_{x^2-y^2}$ around the Fermi level suppresses the screening effect. As a result, the correlation effect becomes more significant than that in the model constructed by the LDA-based downfolding. Furthermore, the Mott-Hubbard type character is enhanced in the GWA-based effective model, because the charge-transfer energy increases more rapidly compared to the increase in the interaction parameters., Comment: 13 pages, 5 figures

Low-valent nickelates R$_{n+1}$Ni$_n$O$_{2n+2}$ (R = rare earth) containing Ni$^{1+}$ (d$^{9}$) with a quasi-two-dimensional (quasi-2D) square planar coordination geometry possess structural and electronic properties that are similar to those of high-Tc cuprates, including superconductivity itself in the doped infinite layer ($n = \infty$) RNiO$_2$ system. Within this R$_{n+1}$Ni$_n$O$_{2n+2}$ nickelate family, the crystallographic isomorphs Pr$_4$Ni$_3$O$_8$ and La$_4$Ni$_3$O$_8$ exhibit singularly different ground states: Pr$_4$Ni$_3$O$_8$ is metallic and La$_4$Ni$_3$O$_8$ is a charge- and spin-stripe ordered insulator. To explore and understand the ground state evolution from metallic Pr$_4$Ni$_3$O$_8$ to stripe-ordered La$_4$Ni$_3$O$_8$ in the R$_4$Ni$_3$O$_8$ family, we have grown a series of isovalent-substituted single crystals (Pr$_{1-x}$La$_x$)$_4$Ni$_3$O$_8$. Combining thermodynamic, transport, magnetic, and synchrotron X-ray single crystal diffraction measurements, we reveal a transition between metallic and stripe-insulator phase regions, with a putative quantum phase transition at x = 0.4. We propose two possible models for (Pr$_{1-x}$La$_x$)$_4$Ni$_3$O$_8$: an electronically inhomogeneous system that could serve as a candidate for exploring quantum Griffiths phase physics and a homogeneous system with a putative quantum critical point at the phase boundary.

The discovery of superconductivity in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ [1] introduced a new family of layered nickelate superconductors that has now been extended to include a range of Sr-doping [2, 3], Pr or La in place of Nd [4-6], and the 5-layer Nd$_6$Ni$_5$O$_{12}$ [7]. A number of studies indicate that electron correlations are strong in these materials [8-14], and hence a central question is whether or not magnetism is present as a consequence of these interactions. Here we report muon spin rotation/relaxation studies of a series of superconducting infinite-layer nickelates. In all cases we observe an intrinsic magnetic ground state, regardless of the rare earth ion or doping, arising from local moments on the nickel sublattice. The coexistence of magnetism - which is likely to be antiferromagnetic and short-range ordered - with superconductivity is reminiscent of some iron pnictides [15] and heavy fermion compounds [16], and qualitatively distinct from the doped cuprates [17].

Low-valence nickelates $-$ including infinite-layer (IL) and trilayer (TL) compounds $-$ are longstanding candidates for mimicking the high-temperature superconductivity of cuprates. A recent breakthrough in the field came with the discovery of superconductivity in hole-doped IL nickelates. Yet, the degree of similarity between low-valence nickelates and cuprates is the subject of a profound debate for which soft x-ray spectroscopy experiments at the Ni $L$- and O $K$-edge provided critical input. In this review, we will discuss the essential elements of the electronic structure of low-valance nickelates revealed by x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS). Furthermore, we will review magnetic excitations observed in the RIXS spectra of IL and TL nickelates, which exhibit characteristics that are partly reminiscent of those of cuprates., Comment: 11 pages, 2 figures, submitted to the Condensed Matter Physics section in Frontiers in Physics for the research topic "Advances in Superconducting Infinite-Layer and Related Nickelates"

Geometric effects in the infinite-layer nickelates $R$NiO$_2$ associated with the relative size of the $R$-site atom are investigated via first-principles calculations. We consider, in particular, the prospective YNiO$_2$ material to illustrate the impact of these effects. Compared to LaNiO$_2$, we find that the La $\to$ Y substitution is equivalent to a pressure of 19 GPa and that the presence of topotactic hydrogen can be precluded. However, the electronic structure of YNiO$_2$ departs from the cuprate-like picture due to an increase in both self-doping effect and $e_g$ hybridization. Furthermore, we find that geometric effects introduce a quantum critical point in the $R$NiO$_2$ series. This implies a $P4/mmm \leftrightarrow I4/mcm$ structural transformation associated to a $A_3^+$ normal mode, according to which the oxygen squares undergo an in-plane rotation around Ni that alternates along $c$. We find that such a $A_3^+$-mode instability has a generic character in the infinite-layer nickelates and can be tuned via either the effective $R$-site atom size or epitaxial strain., Comment: 6 pages, 4 figures, 4 tables

We use first-principles calculations to find that in infinite-layer nickelates $R$NiO$_2$, the widely studied tetragonal $P4/mmm$ structure is only dynamically stable for early lanthanide elements $R$ = La-Sm. For late lanthanide elements $R$ = Eu-Lu, an imaginary phonon frequency appears at $A=(\pi,\pi,\pi)$ point. For those infinite-layer nickelates, condensation of this phonon mode into the $P4/mmm$ structure leads to a more energetically favorable $I4/mcm$ structure that is characterized by an out-of-phase rotation of "NiO$_4$ square". Special attention is given to two borderline cases: PmNiO$_2$ and SmNiO$_2$, in which both the $P4/mmm$ structure and the $I4/mcm$ structure are local minima and the energy difference between the two structures can be fine-tuned by epitaxial strain. Compared to the $P4/mmm$ structure, $R$NiO$_2$ in the $I4/mcm$ structure has a substantially reduced Ni $d_{x^2-y^2}$ bandwidth, a smaller Ni $d$ occupancy, a "cleaner" Fermi surface with a lanthanide-$d$-derived electron pocket suppressed at $\Gamma$ point, and a decreased critical $U_{\textrm{Ni}}$ to stabilize long-range antiferromagnetic ordering. All these features imply enhanced correlation effects and favor Mott physics. Our work reveals the importance of structure-property relation in infinite-layer nickelates, in particular, the spontaneous "NiO$_4$ square" rotation provides a tuning knob to render $R$NiO$_2$ in the $I4/mcm$ structure a closer analogy to superconducting infinite-layer cuprates., Comment: 26 pages and 6 figures

The recent discovery of superconductivity in Sr-doped NdNiO$_2$, with a critical temperature of $10-15$ K suggests the possibility of a new family of nickel-based high-temperature superconductors (HTS). NdNiO$_{2}$ is the $n=\infty$ member of a larger series of layered nickelates with chemical formula R$_{n+1}$Ni$_{n}$O$_{2n+2}$ (R $=$ La, Nd, Pr; $n = 2, 3, \dots, \infty$). The $n=3$ member has been experimentally and theoretically shown to be cuprate-like and a promising HTS candidate if electron doping could be achieved. The higher-order $n=4,5,$ and $6$ members of the series fall directly into the cuprate dome area of filling without the need of doping, thus making them promising materials to study, but have not been synthesized yet. Here, we perform first-principles calculations on hypothetical $n=4,5,$ and $6$ structures to study their electronic and magnetic properties and compare them with the known $n=\infty$ and $n=3$ materials. From our calculations, we find that the cuprate-like character of layered nickelates increases from the $n=\infty$ to the $n=3$ members as the charge transfer energy and the self-doping effect due to R-$d$ bands around the Fermi level gradually decrease., Comment: 11 pages, 6 figures

We study the magnetic and spectral properties of a single-band Hubbard model for the infinite-layer nickelate compound LaNiO$_2$. As spatial correlations turn out to be the key ingredient for understanding its physics, we use two complementary extensions of the dynamical mean-field theory to take them into account: the cellular dynamical mean-field theory and the dynamical vertex approximation. Additionally to the systematic analysis of the doping dependence of the non-Curie-Weiss behavior of the uniform magnetic susceptibility, we provide insight into its relation to the formation of a pseudogap regime by the calculation of the one-particle spectral function and the magnetic correlation length. The latter is of the order of a few lattice spacings when the pseudogap opens, indicating a strong-coupling pseudogap formation in analogy to cuprates., Comment: 8 pages, 5 figures, submitted to the Condensed Matter Physics section in Frontiers in Physics for the research topic "Advances in Superconducting Infinite-Layer and Related Nickelates"

The newly synthesized strontium doped RNiO$_2$ (R=Nd, La) superconductors have stimulated extensive interests in understanding their pairing mechanism and pairing nature. Here we study the pairing mechanism in this family from a two-orbital model comprising the Ni- $3d_{x^2-y^2}$- and $3d_{xy}$- orbitals, equipped with extended Hubbard interactions and induced low-energy effective superexchange interactions. We then study the pairing symmetry in this system by using large scale variational Monte Carlo approach. Our results yield the intraorbital $d_{x^2-y^2}$-wave singlet pairing as the leading pairing symmetry in the nickelates, which is analogous to the cuprates. However, there exist two important differences between the physical properties of the two families due to the fact that at the low Sr-doping regime, while the Ni-$3d_{x^2-y^2}$ orbitals remain half-filled and singly-occupied to form a Mott-insulating background, the Ni-$3d_{xy}$ orbitals accommodate nearly all the extra doped holes, which move freely on this background. The first difference lies in the single-particle aspect: while the $3d_{x^2-y^2}$ degree of freedom remains Mott insulating with spectra weight pinned down at zero at low dopings, the $3d_{xy}$ one behaves as Fermi liquid with spectra weight near 1. The second difference lies in the pairing aspect: while the huge intra-$3d_{x^2-y^2}$-orbital pairing gap is actually a pseudo gap which has nothing to do with the SC, the small intra-$3d_{xy}$-orbital pairing gap serves as the true superconducting pairing gap, which is related to the $T_c$ via the BCS relation. Both differences can be verified by the angle-resolved photo-emission spectrum., Comment: 12 pages, 3 figures, 2 appendixes

The recent discovery of the superconductivity in the doped infinite layer nickelates $R$NiO$_2$ ($R$=La, Pr, Nd) is of great interest since the nickelates are isostructural to doped (Ca,Sr)CuO$_2$ having superconducting transition temperature ($T_{\rm c}$) of about 110 K. Verifying the commonalities and differences between these oxides will certainly give a new insight into the mechanism of high $T_{\rm c}$ superconductivity in correlated electron systems. In this paper, we review experimental and theoretical works on this new superconductor and discuss the future perspectives for the "nickel age" of superconductivity., Comment: Review article, 22 pages, 21 figures, 152 references, accepted for publication in Reports on Progress in Physics (https://iopscience.iop.org/article/10.1088/1361-6633/ac5a60)

A series of Ruddlesden-Popper nickelates, Nd$_{n+1}$Ni$_{n}$O$_{3n+1}$ (${n}$ = 1-5), have been stabilized in thin film form using reactive molecular-beam epitaxy. High crystalline quality has been verified by X-ray diffraction and scanning transmission electron microscopy. X-ray photoelectron spectroscopy indicates the ${n}$-dependent valence states of nickel in these compounds. Metal-insulator transitions show clear ${n}$ dependence for intermediate members (${n}$ = 3-5), and the low-temperature resistivities of which show logarithmic dependence, resembling the Kondo-scattering as observed in the parent compounds of superconducting infinite-layer nickelates., Comment: 12 pages, 4 figures

The discovery of superconductivity in the infinite-layer nickelates has opened new perspectives in the context of quantum materials. We analyze, via first-principles calculations, the electronic properties of La$_2$NiO$_3$F -- the first single-layer T'-type nickelate -- and compare these properties with those of related nickelates and isostructural cuprates. We find that La$_2$NiO$_3$F is essentially a single-band system with a Fermi surface dominated by the Ni-3$d_{x^2-y^2}$ states with an exceptional 2D character. In addition, the hopping ratio is similar to that of the highest $T_c$ cuprates and there is a remarkable $e_g$ splitting together with a charge transfer energy of 3.6~eV. According to these descriptors, along with a comparison to Nd$_2$CuO$_4$, we thus indicate single-layer T'-type nickelates of this class as very promising analogs of cuprate-like physics while keeping distinct Ni$^{1+}$ features., Comment: 5 + epsilon pages, 4 figures, 2 tables

We report a comprehensive study of magnetic correlations in LaNiO$_{2}$, a parent compound of the recently discovered family of infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods. Our specific heat, muon-spin rotation ($\mu$SR), and magnetic susceptibility measurements on polycrystalline LaNiO$_{2}$ show that long-range magnetic order remains absent down to 2 K. Nevertheless, we detect residual entropy in the low-temperature specific heat, which is compatible with a model fit that includes paramagnon excitations. The $\mu$SR and low-field static and dynamic magnetic susceptibility measurements indicate the presence of short-range magnetic correlations and glassy spin dynamics, which we attribute to local oxygen non-stoichiometry in the average infinite-layer crystal structure. This glassy behavior can be suppressed in strong external fields, allowing us to extract the intrinsic paramagnetic susceptibility. Remarkably, we find that the intrinsic susceptibility shows non-Curie-Weiss behavior at high temperatures, in analogy to doped cuprates that possess robust non-local spin fluctuations. The distinct temperature dependence of the intrinsic susceptibility of LaNiO$_{2}$ can be theoretically understood by a multi-method study of the single-band Hubbard model in which we apply complementary cutting-edge quantum many-body techniques (dynamical mean-field theory, cellular dynamical mean-field theory and the dynamical vertex approximation) to investigate the influence of both short- and long-ranged correlations. Our results suggest a profound analogy between the magnetic correlations in parent (undoped) IL nickelates and doped cuprates., Comment: 18 pages, 14 figures

Although rare earth nickelates (ReNiO3) exhibit abundant electronic phases and widely adjustable metal to insulator electronic transition properties, their practical electronic applications are largely impeded by their intrinsic meta stability. Apart from elevating oxygen reaction pressures, heterogeneous nucleation is expected as an alternative strategy that enables the crystallization of ReNiO3 at low meta stability. In this work, the respective roles of high oxygen pressure and heterogeneous interface in triggering ReNiO3 thin films growth at metastable state are revealed. The ReNiO3 (Re:Nd, Sm, Eu, Gd, and Dy) heterogeneous thin films growth on LaAlO3 single crystal substrate have an effective crystallization at atmosphere without the necessity to apply high oxygen pressures, suggesting the interfacial bonding between the ReNiO3 and substrates can sufficiently reduce the positive Gibbs formation energy of ReNiO3, which is further verified by the first principles calculations. Nevertheless, the abrupt electronic transitions only appear in ReNiO3 thin films grown at high oxygen pressures, in which cases the oxygen vacancies are effectively eliminated via high oxygen pressure reactions as indicated by near edge X ray absorption fine structure (NEXAFS). This work unveils the synergistic effects of heterogeneous nucleation and high oxygen pressure on the growth of high quality ReNiO3 thin films., Comment: 33 Pages

The series of nickel-oxide compounds LaNiO$_3$ (formal Ni$(d^7)$), La$_2$NiO$_4$ (formal Ni$(d^8)$) and LaNiO$_2$ (formal Ni$(d^9)$) is investigated by first-principles many-body, using a combination of density functional theory, self-interaction correction and dynamical mean-field theory. The characteristics of these different nickelates, in good agreement with available experimental data, is revealed by employing a compound-independent choice for the local Coulomb interactions. The dichotomy within the low-energy dominant Ni-$e_g$ sector of $\{d_{z^2},d_{x^2-y^2}\}$ kind is rising with growing Ni$(3d)$ filling across the series. An intermediate-coupling scheme for spin-polarized calculations is introduced, which leads to very weak Ni ordered moments for the infinite-layer compound LaNiO$_2$ in contrast to the robust-moment system La$_2$NiO$_4$., Comment: 17 pages, 4 figures

The discovery of superconductivity in thin films ($\sim$10 nm) of infinite-layer hole-doped NdNiO$_2$ has invigorated the field of high-temperature superconductivity research, reviving the debate over contrasting views that nickelates that are isostructural with cuprates are either (1) sisters of the high-temperature superconductors, or (2) that differences between nickel and copper at equal band filling should be the focus of attention. Each viewpoint has its merits, and each has its limitations, suggesting that such a simple picture must be superseded by a more holistic comparison of the two classes. Several recent studies have begun this generalization, raising a number of questions without suggesting any consensus. In this paper, we organize the findings of the electronic structures of $n$-layered NiO$_2$ materials ($n$= 1 to $\infty$) to outline (ir)regularities and to make comparisons with cuprates, with the hope that important directions of future research will emerge.