Cuprate-like electronic structures in infinite-layer nickelates with substantial hole dopings

ABSTRACT Superconducting infinite-layer (IL) nickelates offer a new platform for investigating the long-standing problem of high-temperature superconductivity. Many models were proposed to understand the superconducting mechanism of nickelates based on the calculated electronic structure, and the multiple Fermi surfaces and multiple orbitals involved create complications and controversial conclusions. Over the past five years, the lack of direct measurements of the electronic structure has hindered the understanding of nickelate superconductors. Here we fill this gap by directly resolving the electronic structures of the parent compound LaNiO2 and superconducting La0.8Ca0.2NiO2 using angle-resolved photoemission spectroscopy. We find that their Fermi surfaces consist of a quasi-2D hole pocket and a 3D electron pocket at the Brillouin zone corner, whose volumes change upon Ca doping. The Fermi surface topology and band dispersion of the hole pocket closely resemble those observed in hole-doped cuprates. However, the cuprate-like band exhibits significantly higher hole doping in superconducting La0.8Ca0.2NiO2 compared to superconducting cuprates, highlighting the disparities in the electronic states of the superconducting phase. Our observations highlight the novel aspects of the IL nickelates, and pave the way toward the microscopic understanding of the IL nickelate family and its superconductivity.

Various theoretical models on the superconductivity of IL nickelates are based on combinations of different Ni/RE (rare earth) orbitals and Fermi surface topologies.Consequently, distinct superconducting mechanisms could be reached.For instance, Kitatini et.al.propose that RENiO2 can be described by one band Hubbard model with Ni-3dx2-y2 orbital akin to cuprates, based on which superconducting transition temperature can be estimated [18] .However, others suggested that Ni-3dxy or Ni-3d3z2-r2 orbital and Hund's coupling should be included, potentially yielding a high-spin S = 1 state in superconducting nickelates [19,20] .Additionally, the presence of conduction electrons (including various RE-d orbitals and interstitial s orbitals) and their contributions to superconductivity further complicate the understanding [21][22][23][24][25][26][27][28] .Depending on different hybridization and doping levels, various pairing symmetries distinct from hole-doped cuprates were predicted [29][30][31] .
Since accurate knowledge of the low-energy electronic structure is critical for modeling the IL nickelates, many fundamental issues need to be pinned down, such as the Fermi surface topology, hole concentration, the orbital characters of bands, the participation of RE-5d or interstitial s orbitals in the low energy electronic structure, etc. Particularly, a key question is whether the electronic structure resembles those of cuprates.However, due to strong electron correlations, an accurate band calculation for IL nickelates is still challenging, thus direct experimental studies are demanded.

Single-crystalline IL surface
Reliable measurements of the electronic structure of IL nickelates require high-quality stoichiometric RENiO3 perovskite films, sufficient in-situ reduction, and most critically, single crystalline IL surfaces.Especially, achieving single crystalline IL surfaces poses a significant challenge, as it requires a delicate balance in the strength of the reduction conditions: strong enough to facilitate a topotactic transition to the IL phase, yet mild enough to prevent damage to the crystalline surface, which is essential for surface-sensitive techniques like ARPES.To address this challenge, we have performed in-situ reduction and systematically optimized the reducing conditions.We have grown LaNiO3 and La0.8Ca0.2NiO3thin films on SrTiO3 (001) substrates using oxide molecular beam epitaxy with an atomic-layer-by-layer growth method (See Materials and Methods in Supplementary Materials), and then reduced them in-situ with atomic hydrogen.As depicted in Fig. 1A, we have used a shutter to prevent direct H atom bombardment on the sample surface, which effectively avoids disorder formation during the violent topotactic reduction process.In this way, the reflection high energy electron diffraction (RHEED) pattern of the reduced films shows sharp streaks from the surfaces (Fig. 1A), and atomic force microscopy (AFM) shows terraces with unit-cell step height (Supplementary Fig. S4), indicating single-crystalline and atomically flat sample surfaces.Ex-situ X-ray diffraction (XRD) measurements were performed on the same samples after ARPES measurements (Fig. 1B and Fig. S3).The positions of the diffraction peaks shift to higher values compared to those of the perovskite phase (Fig. 1B), and are consistent with those of (La,Ca)NiO2 [10] .The fringes accompanying the diffraction peaks observed in La0.8Ca0.2NiO2(Fig. 1B) and LaNiO2 (Supplementary Fig. S3A) are comparable to, if not more pronounced than, the previous reports [8][9][10]17] . The onversion efficiency from perovskite to IL phase is among the highest as compared to literature [17] (Supplementary Text).These results demonstrate the acquisition of the IL phase with superior surface quality.According to the resistivity measurements (Fig. 1C), 21 unit cell (uc) LaNiO2/SrTiO3 shows a weakly-insulating behavior below 25 K, while 25 uc La0.8Ca0.2NiO2/SrTiO3shows a superconducting transition at 8 K. Thes behaviors are in line with the reported phase diagram of (La,Ca)NiO2 (Fig. 1D, ref. [10] ).ARPES measurements on these samples show clear Fermi surfaces (Figs.1E-1F). .The open circles represent data points reported in Ref. [10] , while the filled stars illustrate the data obtained from our samples.(E, F) Photoemission intensity map of 21 uc LaNiO2/SrTiO3 and 25 uc La0.8Ca0.2NiO2/SrTiO3 at EF.The integration is over the energy window of EF ± 0.1 eV.The red rounded rectangular and the blue small pockets are denoted as α and β pockets, respectively.

Cuprate-like band dispersion
Figure 2 shows the detailed electronic structure of LaNiO2 measured by ARPES.The α band resembles the low-energy Zhang-Rice singlet of cuprates in terms of both Fermi surface shape and band dispersion [32] .It forms a large rounded square pocket centered at (π, π) with parallel sectors around (π, 0) (Fig. 2A).Note that the spectral weight intensity is higher in the second Brillouin zone (BZ) (Figs.1E,1F,2A), a phenomenon commonly observed in ARPES studies of cuprates and consistent with the photoemission matrix-element of 3dx2-y2 orbitals, and our polarization dependent ARPES measurements also support its dx2-y2 character (as shown in the Fig. S5 of Supplementary Materials).The dispersion of α band exhibits a shallow electron-like dispersion along cut #1 in Figs.2B and 2C.Along cut #2, the dispersion of the α band is steep near the zone center (Fig. 2E) and it flattens towards lower binding energy near (0, π) (Fig. 2D).These demonstrate a saddlepoint dispersion in the (0, π) region (Fig. 2F), akin to the dispersion in the anti-nodal region of cuprates [32] .The saddle-point dispersion is also observed in La0.8Ca0.2NiO2(Supplementary Fig. S6), highlighting its similarity to cuprates.On the other hand, there is an electron-like band centered at (π, π) (Figs.2G-2H), which is absent in cuprates.Note that the quasiparticle weight is weak but discernible here, manifested by the sharper peaks in the momentum distribution curves near Fermi level (Fig. 2H) and reduced band velocity as the energy approaches the Fermi energy (Fig. 2G).The spectral width of the α band broadens as the energy moves away from the Fermi level, and the dispersion of the α band becomes steeper at binding energies beyond 0.2 eV, similar to the steep "water-fall" dispersion observed in the cuprates [33] .

Distinct hole doping phase diagram
To reveal the three-dimensional electronic structure of IL nickelates, we further conducted photon energy-dependent ARPES measurements on the films.As shown in Figs.3A and 3F, the α band shows weak dispersion along kz, demonstrating its quasi-two-dimensional character, whereas the β band is three-dimensional and only appears at the A point.In the Γ-M-X plane, the α Fermi surface forms a large hole pocket centered at M (Figs.3B, 3G), consistent with theoretical calculations [34][35][36] (Fig. S8).The electron pocket with dominant La-5d3z2-r2 character predicted at Γ is absent in the experiment (Figs.3B, 3G).In Figs.3C and 3H, the circular pocket formed by the β band is identified around the A point.It's noteworthy that the Fermi surface of the α band in the Z-A-R plane roughly matches that in the Γ-M-X plane, consistent with its quasi-two-dimensional character.This is different from the prediction by DFT calculations, where the hole pockets of the α band around A expand and transform into an electron pocket around Z in the Z-A-R plane [34] .
As a function of the hole doping in the Zhang-Rice singlet band, cuprate superconductors show a generic phase diagram across various families of materials [37] .Here we compare the doping of the cuprate-like α band of Ni-3dx2-y2 character in IL nickelates with the general phase diagram of cuprates.According to the Luttinger theorem and the measured Fermi surface volume, the quasitwo-dimensional Fermi surface of the dx2-y2 band possesses 1.09 holes in LaNiO2 (see Supplementary Text for details), indicating an excess of 0.09 holes relative to the 3d 9 electronic configuration, far from the half-filled Mott insulator.Upon Ca substitution, the β pocket also shrinks (Fig. S7), and the Fermi crossings of the α band shift away from M point along both the M-Γ-M direction (Figs.3D,3I) and M-X-M direction (Figs.3E,3J), indicating an increase of the hole pocket size.The estimated hole concentration is 1.28 for the α pocket of La0.8Ca0.2NiO2.Therefore, despite the resemblance in the band dispersion, the cuprate-like α band in optimally doped La0.8Ca0.2NiO2possesses an ultra-high doping level of 28%, placing it in the over-doped and non-superconducting regime of the cuprates [37] .As illustrated in the phase diagram (Fig. 4A), the superconducting dome of IL nickelates shows up at a higher doping regime of the dx2-y2 band than that of cuprates, which highlights the intriguing differences between the nickelate and cuprates.

DISCUSSION
The quasi-2D α band dominated by Ni-3dx2-y2 orbital and the 3D β band around A qualitatively agree with the previous DFT results, where the orbital characters are predicted to be Ni-3dx2-y2 for α band, and the mixing of La-5dxy, Ni-3dzx/dyz, and interstitial-s for β band, respectively (Ref [34] , Fig. S8).Nonetheless, some discrepancies with the calculated electronic structures are evident.Specifically, there is no electron pocket around Γ in LaNiO2 (Fig. 4B), and the β electron Fermi pocket around the A point shows a slightly smaller size and a shallower band bottom than the calculations (Supplementary Fig. S7j).These observations consistently suggest that the self-doping effect is weaker than calculation prediction.The β and α bands show different EF shifts upon doping (Fig. S7), indicating a non-rigid-band behavior.These discrepancies may be attributed to electron correlation effects overlooked in previous calculations, which potentially alters the dispersion [38] .Our ARPES data thus give a benchmark for further improving theoretical calculations.
In comparison to hole-doped cuprates, although the α band in IL nickelates generally captures the dispersion characteristics of the Zhang-Rice singlet band in cuprates, their superconducting doping ranges are far apart.As shown in Fig. 4A, the doping level of the α band in the parent compound LaNiO2 already falls within the superconducting regime of cuprates, whereas the superconducting La0.8Ca0.2NiO2resides at the highly overdoped and non-superconducting regime of cuprates.The distinct superconducting hole-doping regimes of cuprates and IL nickelates may be rooted in the different nature of their electronic states.In cuprates, holes are predominantly doped into oxygen, and the states near the Fermi level primarily consist of oxygen ligand states.However, due to the large charge transfer gap in IL nickelates [21,39] , the contribution of oxygen p states is significantly less in IL nickelates compared to cuprates, and the α bands are predominantly dominated by the dx2-y2 orbital (Supplementary Fig. S8).Furthermore, the β band persists in the optimally doped superconducting La0.8Ca0.2NiO2,suggesting the multiband nature of nickelate superconductors, distinct from that of cuprate superconductors.
To summarize, by reaching an unprecedented surface quality, we experimentally revealed the low-energy electronic structure of IL nickelates.Our ARPES measurements have revealed a large hole pocket α that bears resemblance to the Zhang-Rice singlet Fermi surface and dispersion in cuprates, and holes could be effectively introduced by Ca doping.The weak but finite self-doping effect, together with the highly hole-doped superconducting state, differs from the electronic structure of cuprates, posing constraints to theories.These findings clarified the fundamental issues on the electronic structure of IL nickelates, which paves the way toward the understanding of the superconductivity mechanism in IL nickelates.The observed large hole doping level in the superconducting La0.8Ca0.2NiO2 is intriguing.It encourages the study of other IL nickelate systems, especially (Nd,Eu)NiO2, which exhibits an additional doping level difference.The method developed for obtaining the single-crystalline surface of IL nickelates opens avenues for further surface-sensitive experimental studies on this family of compounds.

MATERIALS AND METHODS
Thin films growth.Perovskite (La,Ca)NiO3 thin films were grown on TiO2-terminated SrTiO3(001) substrates by oxide molecular beam epita0xy.A layer-by-layer growth mode is used, in which the A site element (La, Ca) and B site element (Ni) were deposited alternatively, while La and Ca were co-deposited to get uniform doping.The flux of each element was measured by quartz crystal microbalance (QCM), and then calibrated by Rutherford backscattering spectrometry (RBS) measurements.X-ray reflection (XRR) measurements were performed to further calibrate the absolute thickness of the films.XRD measurements were performed to optimize the growth conditions.After optimization, LaNiO3 and Ca-doped LaNiO3 were grown at 580℃ under an ozone pressure of 5×10 - 6 mbar and 1.5×10 -5 mbar, respectively.The 2D character of RHEED pattern is maintained during growth, indicating the single-crystalline and two-dimensional sample surface.The doping level calibrated by Rutherford backscattering spectrometry is then further checked by X-ray photoemission on the samples after ARPES studies.
In-situ reduction.After growth, the precursor thin films were transferred in-situ to the pulsed laser deposition (PLD) chamber for reduction.Our PLD system is integrated with an atomic hydrogen gun, which generates atomic hydrogen by dissociating H2 gas through plasma.IL LaNiO2 and La0.8Ca0.2NiO2thin films were obtained by annealing perovskite precursors in an atomic hydrogen environment for 1~2 hours at 340℃, with a ramp rate of 15℃/min.During the reduction process, the H2 gas flow rate was fixed at 3~sccm, and the chamber pressure was around 1.0×10 - 5 mbar.A metal shutter was used to prevent surface crystal structure degradation caused by exposure to H + (Fig. ~1a).Under the optimized conditions, perovskite nickelates were transformed into IL nickelates, as confirmed by the X-ray diffraction pattern (see and Fig S3a).Meanwhile, the fully-strained feature (Fig. ~S3b) and the terraced surfaces were maintained in IL samples (Fig. ~S4).

ARPES measurements.
All the ARPES experiments were performed at the Shanghai Synchrotron Radiation Facility (SSRF).All samples were reduced in-situ and then transferred to beamline by vacuum suitcases and measured under an ultra-high vacuum better than 7×10 -11 mbar.The SX-ARPES data and the complementary VUV-ARPES data were collected at beamline 09U and beamline 03U, respectively.In VUV ARPES experiments, we set the energy resolution power to 3000 for higher photon flux, which gives a typical energy resolution of 40~meV at 145eV photon energy.The estimated energy resolution of SX-ARPES is 100~meV at 250~eV, and 200~meV at 400~eV.The angle resolution is 0.1°.

Fig. 1 .
Fig. 1.In-situ reduction and optimization to get atomically flat and clean surfaces for ARPES measurements.(A) Evolution of RHEED image along the [110] azimuth after in-situ reduction.The RHEED pattern is single-crystalline (poly-crystalline) when the shutter is on (off) after reduction.The shutter was designed to screen the by-product H + generated with atomic H. (B) XRD θ-2θ scans of the perovskite 25 uc La0.8Ca0.2NiO3/SrTiO3and in-situ reduced IL La0.8Ca0.2NiO2/SrTiO3.(C) Temperature-dependent resistivity curves of the LaNiO2/SrTiO3 and La0.8Ca0.2NiO2/SrTiO3samples in this study.(D) Superconducting Tc vs. Ca doping level plot in the phase diagram of (La,Ca)NiO2 adapted from Ref.10.The open circles represent data points reported in Ref.[10] , while the filled stars illustrate the data obtained from our samples.(E, F) Photoemission intensity map of 21 uc LaNiO2/SrTiO3 and 25 uc La0.8Ca0.2NiO2/SrTiO3 at EF.The integration is over the energy window of EF ± 0.1 eV.The red rounded rectangular and the blue small pockets are denoted as α and β pockets, respectively.

Fig. 2 .
Fig. 2. Cuprate-like low-energy electronic structure of LaNiO2.(A) Photoemission intensity map of 21uc LaNiO2/SrTiO3 at EF.The integration is over the energy window of EF ± 0.1 eV.The Fermi surfaces of a cuprate-like hole pocket α and an electron pocket β are illustrated.(B) Energy distribution curves (EDCs) along the momentum cut #1.(C) Momentum distribution curves (MDCs) along the momentum cut #1.(D) the same as panel B, but along cut #2.(E) the same as panel C, but along cut #2.(F) Schematic dispersion of α and β bands.The saddle point of the α band is indicated.(G) Photoemission intensity along cut #3.(H) MDCs along cut #3.The circle markers track the local maxima/shoulders to demonstrate the dispersion of α band (red circles) and β band (blue circles).

Fig. 3 .
Fig. 3. Doping dependence of the three-dimensional electronic structure.(A) Photon-energy dependent photoemission intensity map of LaNiO2/SrTiO3 at EF in the Γ-M-A-Z plane.(B) Photoemission intensity map at EF measured at Γ-M-X plane (kz=0).(C) Same as panel B but measured at the Z-A-R plane (kz=π).The linear horizontal (LH) and linear vertical (LV) polarizations of photons are indicated, corresponding to the photoemission geometry of πpolarization and σ-polarization, respectively.(D-E) Photoemission spectra along the M-Γ-M direction (D) and M-X-M direction (E) of LaNiO2/SrTiO3 measured using 107 eV photons (kz=0).The MDCs at EF were overlaid to show the Fermi crossings.(F-J) Same as panels A-E but measured on La0.8Ca0.2NiO2/SrTiO3.
2023YFA1406300), the New Cornerstone Science Foundation, the Innovation Program for Quantum Science and Technology (2021ZD0302803), and Shanghai Municipal Science and Technology Major Project (2019SHZDZX01), the China National Postdoctoral Program for Innovative Talents (BX20230078).Part of this research used Beamline 03U of the Shanghai Synchrotron Radiation Facility, which is supported by ME2 project (11227902) from National Natural Science Foundation of China.