Bilayer Two-Orbital Model of La_{3}Ni_{2}O_{7} under Pressure

Electronic and magnetic excitations in La3Ni2O7

High-temperature superconductivity was discovered in the pressurized nickelate La3Ni2O7 which has a unique bilayer structure and mixed valence state of nickel. The properties at ambient pressure contain crucial information of the fundamental interactions and bosons mediating superconducting pairing. Here, using X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we identified that Ni 3d x 2 - y 2 , Ni 3d z 2 , and ligand oxygen 2p orbitals dominate the low-energy physics with a small charge-transfer energy. Well-defined optical-like magnetic excitations soften into quasi-static spin-density-wave ordering, evidencing the strong electronic correlation and rich magnetic properties. Based on an effective Heisenberg spin model, we extract a much stronger inter-layer effective magnetic superexchange than the intra-layer ones and propose two viable magnetic structures. Our findings emphasize that the Ni 3d z 2 orbital bonding within the bilayer induces novel electronic and magnetic excitations, setting the stage for further exploration of La3Ni2O7 superconductor.

Strong interlayer magnetic exchange coupling in La3Ni2O7-δ revealed by inelastic neutron scattering

After several decades of studies of high-temperature superconductivity, there is no compelling theory for the mechanism yet; however, the spin fluctuations have been widely believed to play a crucial role in forming the superconducting Cooper pairs. The recent discovery of high-temperature superconductivity near 80 K in the bilayer nickelate La3Ni2O7 under pressure provides a new platform to elucidate the origins of high-temperature superconductivity. We perform elastic and inelastic neutron scattering studies on a polycrystalline sample of La3Ni2O7-δ at ambient pressure. No magnetic order can be identified down to 10 K. The absence of long-range magnetic order in neutron diffraction measurements may be ascribed to the smallness of the magnetic moment. However, we observe a weak flat spin-fluctuation signal in the inelastic scattering spectra at ∼ 45 meV. The observed spin excitations could be interpreted as a result of strong interlayer and weak intralayer magnetic couplings for stripe-type antiferromagnetic orders. Our results provide crucial information on the spin dynamics and are thus important for understanding the superconductivity in La3Ni2O7.

Unconventional Crystal Structure of the High-Pressure Superconductor La_{3}Ni_{2}O_{7}

The discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} at pressures above 14 GPa has spurred extensive research efforts. Yet, fundamental aspects of the superconducting phase, including the possibility of a filamentary character, are currently subjects of controversial debates. Conversely, a crystal structure with NiO_{6} octahedral bilayers stacked along the c-axis direction was consistently posited in initial studies on La_{3}Ni_{2}O_{7}. Here, we reassess this structure in optical floating zone-grown La_{3}Ni_{2}O_{7} single crystals that show signs of filamentary superconductivity. Employing scanning transmission electron microscopy and single-crystal x-ray diffraction under high pressures, we observe multiple crystallographic phases in these crystals, with the majority phase exhibiting alternating monolayers and trilayers of NiO_{6} octahedra, signifying a profound deviation from the previously suggested bilayer structure. Using density functional theory, we disentangle the individual contributions of the monolayer and trilayer structural units to the electronic band structure of La_{3}Ni_{2}O_{7}, providing a firm basis for advanced theoretical modeling and future evaluations of the potential of the monolayer-trilayer structure for hosting superconductivity.

Bulk high-temperature superconductivity in pressurized tetragonal La2PrNi2O7

The Ruddlesden-Popper (R-P) bilayer nickelate, La3Ni2O7, was recently found to show signatures of high-temperature superconductivity (HTSC) at pressures above 14 GPa (ref. 1). Subsequent investigations achieved zero resistance in single-crystalline and polycrystalline samples under hydrostatic pressure conditions2-4. Yet, obvious diamagnetic signals, the other hallmark of superconductors, are still lacking owing to the filamentary nature with low superconducting volume fraction2,4,5. The presence of a new 1313 polymorph and competing R-P phases obscured proper identification of the phase for HTSC6-9. Thus, achieving bulk HTSC and identifying the phase at play are the most prominent tasks. Here we address these issues in the praseodymium (Pr)-doped La2PrNi2O7 polycrystalline samples. We find that substitutions of Pr for La effectively inhibit the intergrowth of different R-P phases, resulting in a nearly pure bilayer structure. For La2PrNi2O7, pressure-induced orthorhombic to tetragonal structural transition takes place at Pc ≈ 11 GPa, above which HTSC emerges gradually on further compression. The superconducting transition temperatures at 18-20 GPa reachT c onset = 82.5 K andT c zero = 60 K , which are the highest values, to our knowledge, among known nickelate superconductors. Importantly, bulk HTSC was testified by detecting clear diamagnetic signals below about 75 K with appreciable superconducting shielding volume fractions at a pressure of above 15 GPa. Our results not only resolve the existing controversies but also provide directions for exploring bulk HTSC in the bilayer nickelates.

Prediction of s^{±}-Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates La_{4}Ni_{3}O_{10} under Pressure

Motivated by the recently reported signatures of superconductivity in trilayer La_{4}Ni_{3}O_{10} under pressure, we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni d_{3z^{2}-r^{2}} orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p_{z} orbitals inducing a "trimer" lattice in La_{4}Ni_{3}O_{10}, analogous to the dimers of La_{3}Ni_{2}O_{7}. The Fermi surface consists of three electron sheets with mixed e_{g} orbitals, and a hole and an electron pocket made up of the d_{3z^{2}-r^{2}} orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s^{±}-wave channel due to partial nesting between the M=(π,π) centered pockets and portions of the Fermi surface centered at the Γ=(0,0) point. With changing electronic density n, the s^{±} instability remains leading and its pairing strength shows a domelike behavior with a maximum around n=4.2 (∼6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La_{3}Ni_{2}O_{7}, correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T_{c} superconductivity of La_{3}Ni_{2}O_{7} does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La_{4}Ni_{3}O_{10} with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.

Size and Morphology Dependent Activity of Cu Clusters for CO2 Activation and Reduction: A First Principles Investigation

Various Cu-based materials in diverse forms have been investigated as efficient catalysts for electrochemical reduction of CO2; however, they suffer from issues such as higher over potential and poor selectivity. The activity and selectivity of CO2 electro reduction have been shown to change significantly when the surface morphology (steps, kinks, and edges) of these catalysts is altered. In light of this, size and morphology dependent activity of selected copper clusters, Cun (n=2-20) have been evaluated for the activation and reduction of CO2 molecule. The phase-space of these copper clusters is rich in conformations of distinct morphologies starting from planar, 2D geometries to prolate-shaped geometries and also high-symmetry structures. The binding efficiency and the activation of CO2 are highest for medium sized clusters (n=9-17) with prolate-morphologies as compared to small or larger sized CunCO2 clusters that are existing mainly as planar (triangular, tetragonal etc.) or highly-symmetric geometries (icosahedron, capped-icosahedron etc.), respectively. The best performing (prolate-shaped) CunCO2 conformations are quite fluxional and also they are thermally stable, as demonstrated by the molecular dynamics simulations. Furthermore, on these CunCO2 conformations, the step-by-step hydrogenation pathways of CO2 to produce value-added products like methanol, formic acid, and methane are exceptionally favorable and energy-efficient.

Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7

The discovery of superconductivity with a critical temperature of about 80 K in La3Ni2O7 single crystals under pressure has received enormous attention. La3Ni2O7 is not superconducting under ambient pressure but exhibits a transition at T ∗ ≃ 115 K. Understanding the electronic correlations and charge dynamics is an important step towards the origin of superconductivity and other instabilities. Here, our optical study shows that La3Ni2O7 features strong electronic correlations which significantly reduce the electron's kinetic energy and place this system in the proximity of the Mott phase. The low-frequency optical conductivity reveals two Drude components arising from multiple bands at the Fermi level. The transition at T ∗ removes the Drude component exhibiting non-Fermi liquid behavior, whereas the one with Fermi-liquid behavior is barely affected. These observations in combination with theoretical results suggest that the Fermi surface dominated by the Ni-d 3 z 2 - r 2 orbital is removed due to the transition at T ∗. Our experimental results provide pivotal information for understanding the transition at T ∗ and superconductivity in La3Ni2O7.

Quenched Pair Breaking by Interlayer Correlations as a Key to Superconductivity in La_{3}Ni_{2}O_{7}

The recent discovery of superconductivity in La_{3}Ni_{2}O_{7} with T_{c}≃80  K under high pressure opens up a new route to high-T_{c} superconductivity. This material realizes a bilayer square lattice model featuring a strong interlayer hybridization unlike many unconventional superconductors. A key question in this regard concerns how electronic correlations driven by the interlayer hybridization affect the low-energy electronic structure and the concomitant superconductivity. Here, we demonstrate using a cluster dynamical mean-field theory that the interlayer electronic correlations (IECs) induce a Lifshitz transition resulting in a change of Fermi surface topology. By solving an appropriate gap equation, we further show that the leading pairing instability, s± wave, is enhanced by the IECs. The underlying mechanism is the quenching of a strong ferromagnetic channel, resulting from the Lifshitz transition driven by the IECs. Based on this picture, we provide a possible reason of why superconductivity emerges only under high pressure.

A new perspective on ductile high-Tcsuperconductors under ambient pressure: few-hydrogen metal-bonded hydrides

Superconducting materials have garnered widespread attention due to their zero-resistance characteristic and complete diamagnetism. After more than 100 years of exploration, various high-temperature superconducting materials including cuprates, nickelates, iron-based compounds, and ultra-high pressure multi-hydrides have been discovered. However, the practical application of these materials is severely hindered by their poor ductility and/or the need for high-pressure conditions to maintain structural stability. To address these challenges, we first provide a new thought to build high-temperature superconducting materials based on few-hydrogen metal-bonded hydrides under ambient pressure. We then review the related research efforts in this article. Moreover, based on the bonding type of atoms, we classify the existing important superconducting materials and propose the new concepts of pseudo-metal and quasi-metal superconductivity, which are expected to be helpful for the design of new high-temperature superconducting materials in the future.

Evidence of Spin Density Waves in La_{3}Ni_{2}O_{7-δ}

The recently discovered superconductivity with critical temperature T_{c} up to 80 K in the double-layer Nickelate La_{3}Ni_{2}O_{7-δ} under pressure has drawn great attention. Here, we report the positive muon spin relaxation (μ^{+}SR) study of polycrystalline La_{3}Ni_{2}O_{6.92} under ambient pressure. Zero-field μ^{+}SR experiments reveal the existence of magnetic order in La_{3}Ni_{2}O_{6.92} with T_{N}=154  K. The weak transverse field μ^{+}SR measurements reveal the bulk nature of magnetism. In addition, a small quantity of oxygen deficiencies can greatly broaden the internal magnetic field distribution sensed by muons.

Orbital-dependent electron correlation in double-layer nickelate La3Ni2O7

The latest discovery of high temperature superconductivity near 80 K in La3Ni2O7 under high pressure has attracted much attention. Many proposals are put forth to understand the origin of superconductivity. The determination of electronic structures is a prerequisite to establish theories to understand superconductivity in nickelates but is still lacking. Here we report our direct measurement of the electronic structures of La3Ni2O7 by high-resolution angle-resolved photoemission spectroscopy. The Fermi surface and band structures of La3Ni2O7 are observed and compared with the band structure calculations. Strong electron correlations are revealed which are orbital- and momentum-dependent. A flat band is formed from the Ni-3dz 2 orbitals around the zone corner which is ~ 50 meV below the Fermi level and exhibits the strongest electron correlation. In many theoretical proposals, this band is expected to play the dominant role in generating superconductivity in La3Ni2O7. Our observations provide key experimental information to understand the electronic structure and origin of high temperature superconductivity in La3Ni2O7.

Interlayer-Coupling-Driven High-Temperature Superconductivity in La_{3}Ni_{2}O_{7} under Pressure

The newly discovered high-temperature superconductivity in La_{3}Ni_{2}O_{7} under pressure has attracted a great deal of attention. The essential ingredient characterizing the electronic properties is the bilayer NiO_{2} planes coupled by the interlayer bonding of 3d_{z^{2}} orbitals through the intermediate oxygen atoms. In the strong coupling limit, the low-energy physics is described by an intralayer antiferromagnetic spin-exchange interaction J_{∥} between 3d_{x^{2}-y^{2}} orbitals and an interlayer one J_{⊥} between 3d_{z^{2}} orbitals. Taking into account Hund's rule on each site and integrating out the 3d_{z^{2}} spin degree of freedom, the system reduces to a single-orbital bilayer t-J model based on the 3d_{x^{2}-y^{2}} orbital. By employing the slave-boson approach, the self-consistent equations for the bonding and pairing order parameters are solved. Near the physically relevant 1/4-filling regime (doping δ=0.3∼0.5), the interlayer coupling J_{⊥} tunes the conventional single-layer d-wave superconducting state to the s-wave one. A strong J_{⊥} could enhance the interlayer superconducting order, leading to a dramatically increased T_{c}. Interestingly, there could exist a finite regime in which an s+id state emerges.

Pressure Driven Fractionalization of Ionic Spins Results in Cupratelike High-T_{c} Superconductivity in La_{3}Ni_{2}O_{7}

Beyond 14 GPa of pressure, bilayered La_{3}Ni_{2}O_{7} was recently found to develop strong superconductivity above the liquid nitrogen boiling temperature. An immediate essential question is the pressure-induced qualitative change of electronic structure that enables the exciting high-temperature superconductivity. We investigate this timely question via a numerical multiscale derivation of effective many-body physics. At the atomic scale, we first clarify that the system has a strong charge transfer nature with itinerant carriers residing mainly in the in-plane oxygen between spin-1 Ni^{2+} ions. We then elucidate in electron-volt scale and sub-electron-volt scale the key physical effect of the applied pressure: it induces a cupratelike electronic structure via fractionalizing the Ni ionic spin from 1 to 1/2. This suggests a high-temperature superconductivity in La_{3}Ni_{2}O_{7} with microscopic mechanism and (d-wave) symmetry similar to that in the cuprates.

Structure Responsible for the Superconducting State in La3Ni2O7 at High-Pressure and Low-Temperature Conditions

Very recently, a new superconductor with Tc = 80 K has been reported in nickelate (La3Ni2O7) at around 15-40 GPa conditions (Nature, 621, 493, 2023), which is the second type of unconventional superconductor, besides cuprates, with Tc above liquid nitrogen temperature. However, the phase diagram plotted in this report was mostly based on the transport measurement under low-temperature and high-pressure conditions, and the assumed corresponding X-ray diffraction (XRD) results were carried out at room temperature. This encouraged us to carry out in situ high-pressure and low-temperature synchrotron XRD experiments to determine which phase is responsible for the high Tc state. In addition to the phase transition from the orthorhombic Amam structure to the orthorhombic Fmmm structure, a tetragonal phase with the space group of I4/mmm was discovered when the sample was compressed to around 19 GPa at 40 K where the superconductivity takes place in La3Ni2O7. The calculations based on this tetragonal structure reveal that the electronic states that approached the Fermi energy were mainly dominated by the eg orbitals (3dz2 and 3dx2-y2) of Ni atoms, which are located in the oxygen octahedral crystal field. The correlation between Tc and this structural evolution, especially Ni-O octahedra regularity and the in-plane Ni-O-Ni bonding angles, is analyzed. This work sheds new light to identify what is the most likely phase responsible for superconductivity in double-layered nickelate.

Structural phase transition, s±-wave pairing, and magnetic stripe order in bilayered superconductor La3Ni2O7 under pressure

Motivated by the recently discovered high-Tc superconductor La3Ni2O7, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y2- mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y2- mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector (π, 0) was stable at the intermediate region. Pairing is induced in the s±-wave channel due to partial nesting between the M = (π, π) centered pockets and portions of the Fermi surface centered at the X = (π, 0) and Y = (0, π) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La3Ni2O7 is qualitatively different from infinite-layer nickelates and cuprate superconductors.

Possible High T_{c} Superconductivity in La_{3}Ni_{2}O_{7} under High Pressure through Manifestation of a Nearly Half-Filled Bilayer Hubbard Model

Inspired by a recent experiment showing that La_{3}Ni_{2}O_{7} exhibits high T_{c} superconductivity under high pressure, we theoretically revisit the possibility of superconductivity in this material. We find that superconductivity can take place, which is somewhat similar to that of the bilayer Hubbard model consisting of the Ni 3d_{3z^{2}-r^{2}} orbitals. Although the coupling with the 3d_{x^{2}-y^{2}} orbitals degrades superconductivity, T_{c} can still be high enough to understand the experiment thanks to the very high T_{c} reached in the bilayer Hubbard model.

Bilayer t-J-J_{⊥} Model and Magnetically Mediated Pairing in the Pressurized Nickelate La_{3}Ni_{2}O_{7}

The recently discovered nickelate superconductor La_{3}Ni_{2}O_{7} has a high transition temperature near 80 K under pressure, providing an additional avenue for exploring unconventional superconductivity. Here, with state-of-the-art tensor-network methods, we study a bilayer t-J-J_{⊥} model for La_{3}Ni_{2}O_{7} and find a robust s-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter K_{SC}≲1. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength Δ[over ¯]_{z}∼O(0.1). Tangent-space tensor renormalization group simulations elucidate the temperature evolution of SC pairing and further determine a high SC temperature T_{c}^{*}/J∼O(0.1). Because of the intriguing orbital selective behaviors and strong Hund's rule coupling in the compound, t-J-J_{⊥} model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal a robust SC order in the bilayer t-J-J_{⊥} model and shed light on the pairing mechanism of the high-T_{c} nickelate superconductor.

s^{±}-Wave Pairing and the Destructive Role of Apical-Oxygen Deficiencies in La_{3}Ni_{2}O_{7} under Pressure

Recently, the bilayer perovskite nickelate La_{3}Ni_{2}O_{7} has been reported to show evidence of high-temperature superconductivity (SC) under a moderate pressure of about 14 GPa. To investigate the superconducting mechanism, pairing symmetry, and the role of apical-oxygen deficiencies in this material, we perform a random-phase approximation based study on a bilayer model consisting of the d_{x^{2}-y^{2}} and d_{3z^{2}-r^{2}} orbitals of Ni atoms in both the pristine crystal and the crystal with apical-oxygen deficiencies. Our analysis reveals an s^{±}-wave pairing symmetry driven by spin fluctuations. The crucial role of pressure lies in that it induces the emergence of the γ pocket, which is involved in the strongest Fermi-surface nesting. We further found the emergence of local moments in the vicinity of apical-oxygen deficiencies, which significantly suppresses the T_{c}. Therefore, it is possible to significantly enhance the T_{c} by eliminating oxygen deficiencies during the synthesis of the samples.

Correlated Electronic Structure of La_{3}Ni_{2}O_{7} under Pressure

Recently, superconductivity with a T_{c} up to 78 K has been reported in bulk samples of the bilayer nickelate La_{3}Ni_{2}O_{7} at pressures above 14 GPa. Important theoretical tasks are the formulation of relevant low-energy models and the clarification of the normal state properties. Here, we study the correlated electronic structure of the high-pressure phase in a four-orbital low-energy subspace using different many-body approaches: GW, dynamical mean field theory (DMFT), extended DMFT (EDMFT) and GW+EDMFT, with realistic frequency-dependent interaction parameters. The nonlocal correlation and screening effects captured by GW+EDMFT result in an instability toward the formation of charge stripes, with the 3d_{z^{2}} as the main active orbital. We also comment on the potential relevance of the rare-earth self-doping pocket, since hole doping suppresses the ordering tendency.