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 3$d_{x^2-y^2}$ 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 experiment, indicate that the $Γ$ pocket, Nd 4$f$ orbitals, oxygen 2$p$ and {the} other Ni 3$d$ 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 3$d_{x^2-y^2}$ and 3$d_{3z^2-r^2}$ orbitals emerges. Based on our minimal modeling we calculated the superconducting $T_c$ vs. Sr-doping $x$ phase diagram prior to experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as $T_c$, the agreement with 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.
Inspired by a recently proposed superconducting mechanism for a new cuprate superconductor Ba$_2$CuO$_{3+δ}$, we theoretically design an unconventional nickelate superconductor with $d^8$ electron configuration. Our strategy is to enlarge the on-site energy difference between $3d_{x^2-y^2}$ and other $3d$ orbitals by adopting halogens or hydrogen as out-of-plane anions, so that the $3d$ bands other than $d_{x^-y^2}$ lie just below the Fermi level for the $d^8$ configuration, acting as incipient bands that enhance superconductivity. We also discuss a possible relevance of the present proposal t…
Superconducting nickelates appear to be difficult to synthesize. Since the chemical reduction of ABO3 (A: rare earth; B transition metal) with CaH2 may result in both, ABO2 and ABO2H, we calculate the topotactic H binding energy by density functional theory (DFT). We find intercalating H is energetically favorable for LaNiO2 but not for Sr-doped NdNiO2. This has dramatic consequences for the electronic structure as determined by DFT+dynamical mean field theory: that of 3d9 LaNiO2 is similar to (doped) cuprates, 3d8 LaNiO2H is a two-orbital Mott insulator. Topotactical H might hence explain why…
Motivated by the recent realization of the infinite-layer nickelate superconductivity (SC), we quantitatively investigate a two-orbital $d$-$s$ model by dynamic cluster quantum Monte Carlo calculations. Focusing on the impact of inter-orbital hybridization on the superconducting properties, our simulations indicate that the $d$-$s$ hybridization strength has a decisive role in the suppression of the $d$-wave pairing in the doping regime relevant to infinite-layer nickelates. Although we confirm on the single-orbital description at weak hybridization, at relatively large hybridization, there ex…
The recently discovered infinite-layer nickelates show great promise in helping to disentangle the various cooperative mechanisms responsible for high-temperature superconductivity. However, lack of antiferromagnetic order in the pristine nickelates presents a challenge for connecting the physics of the cuprates and nickelates. Here, by using a quantum many-body Green's function-based approach to treat the electronic and magnetic structures, we unveil the presence of many two- and three-dimensional magnetic stripe instabilities that are shown to persist across the phase diagram of LaNiO$_2$. O…
Superconductivity has entered the nickel age marked by enormous experimental and theoretical efforts. Notwithstanding, synthesizing nickelate superconductors remains extremely challenging, not least due to incomplete oxygen reduction and topotactic hydrogen. Here, we present density-functional theory calculations, identify a phonon mode as a possible indication for topotactic hydrogen and discuss the charge redistribution patterns around oxygen and hydrogen impurities.
Following the discovery of superconductivity in the cuprates and the seminal work by Anderson, the theoretical efforts to understand high-temperature superconductivity have been focusing to a large extent on a simple model: the one-band Hubbard model. However, superconducting cuprates need to be doped, and the doped holes go into the oxygen orbitals. This requires a more elaborate multi-band model such as the three-orbital Emery model. The recently discovered nickelate superconductors appear, at first glance, to be even more complicated multi-orbital systems. Here, we analyse this multi-orbita…
After decades of fundamental research, unconventional superconductivity has recently been demonstrated in rare-earth infinite-layer nickelates. The current view depicts these systems as a new category of superconducting materials, as they appear to be correlated metals with distinct multiband features in their phase diagram. Here, we provide an overview of the state of the art in this rapidly evolving topic.
We give a brief review of the Mott-Kondo scenario and its consequence in the recently-discovered infinite-layer nickelate superconductors. We argue that the parent state is a self-doped Mott insulator and propose an effective $t$-$J$-$K$ model to account for its low-energy properties. At small doping, the model describes a low carrier density Kondo system with incoherent Kondo scattering at finite temperatures, in good agreement with experimental observation of the logarithmic temperature dependence of electric resistivity. Upon increasing Sr doping, the model predicts a breakdown of the Kondo…
We study theoretically spin excitations in the newly discovered nickelate superconductors based on a single-band model and the random phase approximation. The spin excitations are found to be incommensurate in a low energy region. A spin resonance phenomena is revealed as the excitation energy increases. The maximum intensity may be at the incommensurate momentum or the commensurate momentum, depending on the out-of-plane momentum. The spin excitations become incommensurate again at higher energies. The similarities and differences of the spin excitations between nickelate and cuprate supercon…
We propose the parent compound of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ as a self-doped Mott insulator, in which the low-density Nd-$5d$ conduction electrons couple to localized Ni-3$% d_{x^{2}-y^{2}}$ electrons to form Kondo spin singlets at low temperatures. This proposal is motivated with our analyses of the reported resistivity and Hall coefficient data in the normal state, showing logarithmic temperature dependence at low temperatures. In the strong Kondo coupling limit, we derive a generalized $t$-$J$ model with both Kondo singlets and nickel holons m…
Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are significantly larger than in the cuprates. A fluctuation exchange study for the model indicates that dx2-y2-wave superconductivity is likely to occur as in the cuprates, where the transition temperatu…
Motivated by recent experimental studies on superconductivity found in nickelate-based materials, we study the temperature dependence of the spin correlation and the superconducting pairing interaction within an effective two-band Hubbard model by the quantum Monte Carlo method. Based on parameters extracted from first-principles calculations, our intensive numerical results reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over other pairings at low temperature, which is mainly determined by the Ni 3$d$ orbital. It is also found that the effective pairing interaction is e…
After the reward of more than two decades of pursuit on the high-Tc cuprate analog with the hope to obtain a better understanding of the mechanism of high-Tc superconductivity, the discovery of superconductivity in the infinite-layer nickelate brings more mystery to the picture than expected. Tops in the list of questions are perhaps (1) absence of superconductivity in the bulk nickelate and limited thickness of the infinite-layer phase in thin film, (2) absence of superconductivity in the La-nickelate despite it being the earliest studied rare-earth nickelate, and the role of 4f orbital in th…
Recently Li et al (2019 Nature 572 624) discovered a new type of oxide superconductor Nd0.8Sr0.2NiO2 with T$_c$ = 14 K. To classify superconductivity in this infinite-layer nickelate experimental upper critical field, B$_{c2}$(T), and the self-field critical current densities, J$_c$(sf,T), reported by Li et al (2019 Nature 572 624), are analysed in assumption of s-, d-, and p-wave pairing symmetries and single- and multiple-band superconductivity. Based on deduced the ground-state superconducting energy gap, $Δ$(0), the London penetration depth, $λ$(0), the relative jump in electronic specific…
Heterostructuring as Gateway to Electron Doping of Nickelate Superconductors
Northwest University（西北大学）；University of Hyogo（兵库大学）；Kyushu Institute of Technology（九州工业大学）；Soochow University（苏州大学）；Universität Würzburg（维尔茨堡大学）；Southeast University（东南大学）；University of Science and Technology of China（中国科学技术大学）；TU Wien（维也纳工业大学）
Electronic structures across superconductor-insulator transition in Ruddlesden-Popper bilayer nickelate films
University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）；Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（微观尺度物理科学合肥国家研究中心，中国科学技术大学）；Southern University of Science and Technology（南方科技大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Nanjing University（南京大学）；Shanghai Jiao Tong University（上海交通大学）；Tsinghua University（清华大学）
Bosonic phases across the superconductor-insulator transition in infinite-layer samarium nickelate
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Southern University of Science and Technology（南方科技大学）；City University of Hong Kong（香港城市大学）；Shenzhen Research Institute of City University of Hong Kong（香港城市大学深圳研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Hefei National Laboratory（合肥国家实验室）；Peking University（北京大学）；Tsinghua University（清华大学）
Magnetism and superconductivity are closely entangled, elucidating the magnetic interactions in nickelate superconductors is at the heart of understanding the pairing mechanism. Our first-principles and spin-wave theory calculations highlight that NdNiO$_2$ is in the vicinity of a transition between a quasi-two-dimensional (2D) antiferromagnetic (AFM) state and a three-dimensional (3D) C-AFM state. Both states could accurately reproduce the experimentally measured magnetic excitation spectra, which was previously explained in terms of a 2D model. We further reveal that hole doping stabilizes a…
Charge order is a central feature of the physics of cuprate superconductors and is known to arise from a modulation of holes with primarily oxygen character. Low-valence nickelate superconductors also host charge order, but the electronic character of this symmetry breaking is unsettled. Here, using resonant inelastic x-ray scattering at the Ni $L_2$-edge, we identify intertwined involvements of Ni $3d_{x^2-y^2}$, $3d_{3z^2-r^2}$, and O $2p_σ$ orbitals in the formation of diagonal charge order in an overdoped low-valence nickelate La$_{4}$Ni$_{3}$O$_{8}$. The Ni $3d_{x^2-y^2}$ orbitals, strong…
Emergent quantum phenomena via phase-coherence engineering in infinite-layer nickelate superconductors
Peking University（北京大学）；University of Electronic Science and Technology of China（电子科技大学）；Renmin University of China（中国人民大学）；ShanghaiTech University（上海科技大学）；Tsinghua University（清华大学）；Institute of Physics Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Beijing Normal University（北京师范大学）；Fudan University（复旦大学）；Hefei National Laboratory（合肥国家实验室）
The recent discovery of superconductivity in hole-doped planar nickelates R1-xSrNiO2 (R=Pr,Nd) raises the foundational question of how the electronic structure and electronic correlations of these Ni1+ compounds compare to those of the Cu2+ cuprate superconductors. Here, we present an Angle-Resolved Photoemission Spectroscopy (ARPES) study of the trilayer nickelate Pr4Ni3O8, revealing an electronic structure and Fermi surface very similar to that of the hole-doped cuprates but with a few critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of…
Multiorbital character of the density wave in trilayer nickelate superconductors
Max-Planck-Institute for Solid State Research（马克斯·普朗克固体研究所）；Facultad de Ciencias Exactas, Ingeniería y Agrimensura and Instituto de Física Rosario (UNR-CONICET)（罗萨里奥大学精确科学、工程与测量学院及罗萨里奥物理研究所（UNR-CONICET））；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心 (iTHEMS)）
Recent scanning tunneling microscopy (STM) observation of U-shaped and V-shaped spectra (and their mixture) in superconducting Nd$_{1-x}$Sr$_x$NiO$_2$ thin films has been interpreted as presence of two distinct gap symmetries in this nickelate superconductor [Gu et al., Nat. Comm. 11, 6027 (2020)]. Here, using a two-band model of nickelates capturing dominant contributions from Ni-$3d_{x^2-y^2}$ and rare-earth (R)-$5d_{3z^2 - r^2}$ orbitals, we show that the experimental observation can be simply explained within a pairing scenario characterized by a conventional $d_{x^2-y^2}$-wave gap structu…
Controlling the Band Filling and the Band Width in Nickelate Superconductors
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 emergent matter science 中心）；RIKEN Pioneering Research Institute（理化学研究所 先锋研究院）；The University of Tokyo（东京大学）；Department of Applied Physics, The University of Tokyo（东京大学 应用物理系）；Institute of Engineering Innovation, The University of Tokyo（东京大学 工程创新研究所）；Nanostructures Research Laboratory, Japan Fine Ceramics Center（日本精细陶瓷中心 纳米结构研究实验室）
$d$-wave superconductivity in quintuple-layer bulk superconductor La$_6$Ni$_5$O$_{12}$
Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学卡尔丹理论科学研究所）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学理学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；New Cornerstone Science Laboratory（新Cornerstone科学实验室）
Motivated by the recent X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) experiments, we use a detailed impurity model to explore the nature of the parent compound and hole doped states of (La, Nd, Pr)NiO$_2$ by including the crystal field splitting, the Ni-$3d$ multiplet structure, and the hybridization between Ni-$3d$, O-$2p$, and Nd-$5d$ orbitals. For simplicity and stimulated by the recent electronic structure calculations, the latter are formally replaced with symmetric orbitals centered at the missing O sites in the Nd layer, forming a two-dimensional (2…
Superconductivity can be destroyed by a magnetic field with an upper bound known as the Pauli-limit in spin-singlet superconductors. Almost all the discovered superconductors are spin-singlet, with the highest transition temperature $T_c$ at ambient pressure achieved in the cuprate family. The closest cuprate analogue is the recently discovered infinite-layer nickelate, which hosts substantial structural and electronic similarity to the cuprate. A previous magnetotransport study on Nd$_{0.775}$Sr$_{0.225}$NiO$_2$ has observed an isotropic Pauli-limited upper critical field. Here, we report a l…
Bulk superconductivity in quintuple-layer square-planar nickelate La6Ni5O12
University of Science and Technology of China（中国科学技术大学）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
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 $…
