The search for the nickelate superconductivity was enthused by the idea of mimicking the \(3{d}_{{x}^{2}-{y}^{2}}\,\)orbital of the single-band high-Tc cuprates1. However, the recent results indicate the complex multiband structures in doped infinite-layer nickelates, suggesting a new family of superconductivity1,2. Numerous theoretical works have been conducted based on the bulk pictures;2 however, the superconductivity has only been observed in epitaxial Nd1-xSrxNiO2 and Pr1-xSrxNiO2 ultrathin films (up to ~10 nm) with an infinite-layer structure1,3,4,5,6,7,8,9. In contrast, infinite-layer nickelates prepared in bulk form show only insulating behavior10,11,12. Moreover, the DC diamagnetic response in the superconducting thin films has never been demonstrated1. These beg the question of whether the superconductivity occurs in the whole film or at the interface between the nickelate and SrTiO3 (STO) substrate13,14,15,16. Theoretical calculation further proposed that the interface/surface-induced Fermi surface modification causes the transformation from a d-wave paring in bulk into an s-wave paring at the interface/surface2,17, which might be consistent with the recent observation of two gaps from the tunneling spectrum measurement5. This further adds to the puzzle of whether the observed electronic properties are associated with the bulk or the heterostructure interface. In this work, we comprehensively investigate the Nd0.8Sr0.2NiO2 films of various thicknesses to confirm the bulk nature of the superconductivity and reveal the interfacial effects on the multiband picture of the infinite-layer nickelate thin films and demonstrate their perfect DC diamagnetic response.


Infinite-layer structure

Figure 1a shows the X-ray diffraction (XRD) θ–2θ patterns of the Nd0.8Sr0.2NiO2 thin films of different thicknesses from 4.6 to 15.2 nm. The XRD characterization of the as-grown perovskite Nd0.8Sr0.2NiO3 thin films can be found in Supplementary Fig. 1. The obvious diffraction peak and thickness oscillations (Laue fringes) in the vicinity of the (00l) infinite-layer peak (l is an integer) indicate the high crystallinity of the films. The (00l) peak positions slightly shift towards a higher angle as the thickness increases, indicating a shrinking of the c axis, with the lattice constants c change from ~3.42 Å for the 4.6-nm film to ~3.36 Å for the 15.2-nm film, as plotted in Fig. 1b. It has been shown that Nd1-xSrxNiO2 (x ≤ 0.2) bulks exhibit an in-plane lattice constant (3.914–3.921 Å) slightly larger than that (3.905 Å) of STO substrate10,11, suggesting the presence of compressive strain on the films imposed by the substrate. The extent of compressive strain decreases as the film thickness increases and thus causing the shrinking of c. Figure 1c shows the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of the 10.1-nm film. A clear infinite-layer structure is observed with no obvious defect throughout the layer.

Fig. 1: Thickness dependence of the infinite layer structure.
figure 1

a The XRD θ–2θ scan patterns of the Nd0.8Sr0.2NiO2 thin films with different thicknesses on SrTiO3 substrates. The intensity is vertically displaced for clarity. b The room-temperature c-axis lattice constants, c, as a function of thickness, as calculated from the (001) peak positions. The red dots represent the average c of the two sets of samples and the error bars represent the variance. c The HAADF-STEM image of the 10.1-nm Nd0.8Sr0.2NiO2 on SrTiO3 substrate.

Electronic properties

The resistivity versus temperature (ρ-T) curves for the Nd0.8Sr0.2NiO2 thin films are shown in Fig. 2a, and the zoomed-in ρ-T curves at temperatures from 50 to 2 K are shown in the inset. All the samples behave like a metal at the normal state and are superconducting at low temperatures. The onset superconducting transition temperature Tc,90%R (defined as the temperature at which the resistivity drops to 90% of the value at 15 K) and zero-resistance Tc,zero-R decrease with decreasing thickness (Fig. 2f). Figure 2b shows the corresponding temperature dependence of the normal-state Hall coefficients (RH) of the Nd0.8Sr0.2NiO2 films. The RH for samples with a thickness higher than 6.8 nm shows a negative sign at room temperature and undergoes a smooth transition to a positive sign at a low temperature of ~50 K, consistent with previous observation at the doping level x = 0.21,3,4. However, as the thickness decreases to 6.8 nm, the RH sign-change temperature decreases to 22 K. The RH even remains negative at the whole temperature range below 300 K for the films with thickness lower than 6.8 nm. Figure 2e presents the thickness dependence of the RH at 20 K and 300 K, clearly showing a sign-change from positive to negative with decreasing thickness. This suggests a change of the multiband structures upon reducing thickness.

Fig. 2: Thickness dependence of the transition temperature, diamagnetic response, and Hall coefficient.
figure 2

a The resistivity versus temperature (ρ-T) curves of the Nd0.8Sr0.2NiO2 thin films with different thicknesses from 4.6 to 15.2 nm. The inset shows the zoomed-in ρ-T curves at temperatures from 50 to 2 K. b The temperature dependence of the normal-state Hall coefficients RH. c The temperature dependence of magnetization (M-T curve) with zero-field cooling (ZFC) for Nd0.8Sr0.2NiO2 thin films with different thicknesses from 5.5 to 15.2 nm. d The zoomed-in M-T curves at temperatures from 20 to 2.1 K with field cooling (FC) and ZFC for the sample with a thickness of 7.5 nm. The measurement and cooling fields are 20 Oe. The magnetic field is applied perpendicularly to the a-b plane. e The RH at T = 300 and 20 K as a function of thickness. f The critical temperature, Tc, as a function of thickness. The Tc,90%R is defined as the temperature at which the resistivity drops to 90% of the value at 15 K (the onset of the superconductivity). The Tc,zero-R, is defined as the temperature at which the resistivity drops to be zero and Tc,dia is defined as the temperature at the onset of the diamagnetic response. The solid and open square for Tc,90%R and Tc,zero-R are the average value of two sets of samples shown in the main text and Supplementary Information, and the error bars represent the variation. The dash lines in (b) and (e) show the position where the RH is zero.

Diamagnetic response

Figure 2c shows the temperature dependence of magnetization (M-T curves) under zero-field cooling (ZFC) mode for Nd0.8Sr0.2NiO2 thin films with thickness varying from 5.5 to 15.2 nm. The normal-state magnetization shows temperature independence. Upon cooling down, the magnetization drops steeply to negative values, confirming the occurrence of superconducting transition in the thin films. Figure 2d shows the zoomed-in M-T curves from 20 down to 2.1 K with ZFC and field cooling (FC) for a representative sample with a thickness of 7.5 nm. Similar to the behavior of typical bulk superconductors, a clear diamagnetic transition is seen, and the onset transitions are the same under ZFC and FC modes, unambiguously confirming the existence of the superconducting phase. The ZFC and FC M-T curves for other thin films are shown in Supplementary Fig. 2. Supplementary Fig. 3 shows the magnetization measured with the applied magnetic field parallel to the ab plane H || ab (in-plane). Compared to H || c, the change of in-plane magnetization is negligible upon cooling. This is because the film is ultrathin (the maximum thickness of the infinite layer is around 11 nm) and is thinner than the out-of-plane London penetration depth. As the magnetic field is applied parallel to the ab plane, the magnetic field fully penetrates the film, and therefore, the absence of Meissner effect is observed. In certain cases, a small diamagnetic response is observed when H || ab with transition temperature similar to that of measured in H || c, which is likely due to imperfect in-plane alignment of the sample during measurement. The Tc,dia, defined as the onset transition temperature in diamagnetic response, is shown in Fig. 2f. It is found that Tc,dia is slightly lower than Tc,zero-R, possibly due to filament superconducting domains or presence of inhomogeneity of the superconducting phase in the thin films. Only well below the zero-resistance temperature, the phase coherence occurs in the entire films, and therefore, the Meissner effect is observed. Supplementary Fig. 4a shows the volume susceptibility as a function of temperature, which accounts for the demagnetizing field Hd = −NM. A large χv(T = 2K) < −0.9 can be observed (for 7.5 nm ZFC MT) which indicates a superconducting volume fraction of >90%, suggesting very few non-superconducting unreduced phases or impurities in the sample. In addition, Meissner effect is observed as the negative slope in M-H curve below superconducting temperature, as shown in Supplementary Fig. 4b.

Electronic structure

The unoccupied states of energy bands are crucial to determine the transport properties and could be detected by X-ray absorption spectroscopy (XAS) on oxygen and transition metal edges. To carefully characterize the electronic structures of samples with pure perovskite phase and the resultant infinite-layer phase, we restrict our XAS measurements on thin films with thickness no >10.1 nm, as confirmed by XRD measurements. Figure 3a shows the O K edge XAS of 10.1-nm perovskite Nd0.8Sr0.2NiO3 and infinite-layer Nd0.8Sr0.2NiO2 thin films. A prominent pre-peak at ~528.9 eV is observed near the O K-edge XAS in Nd0.8Sr0.2NiO3 film, which is attributed to the presence of a ligand hole in oxygen18,19,20. In perovskite nickelates, the oxygen p to nickel d band charge-transfer energy is negative, the electrons spontaneously transfer from oxygen ligands to Ni cations, leaving the holes on the oxygen side even without chemical doping18. Excitation of oxygen 1 s core electrons to such unoccupied states (holes) give rise to the pre-peak in O K-edge XAS. The ligand holes in perovskite Nd0.8Sr0.2NiO3 can also be suggested from the Ni L2,3 edge XAS (Fig. 3b), in which a shoulder is visible at ~856 eV corresponding to the electron transition from the Ni core-level 2p to 3d8L state (L is ligand hole), beside the main sharp peak at ~854.5 eV corresponding to the electron transition from the core-level 2p to 3d7 state18. As the film is reduced from perovskite to infinite-layer structure, the prominent pre-peak in Nd0.8Sr0.2NiO2 film disappears, which is consistent with the previous study in underdoped RNiO2 (R = La, Nd)19,20. Instead, another pre-peak with less intensity at a higher energy of ~530.5 eV is observed, suggesting that the oxygen ligand hole is still present in the infinite-layer film. In the Ni L2,3 edge XAS (Fig. 3b), the main absorption peaks in both films are observed with a position shift to a lower energy for infinite-layer film, consistent with the reduced Ni valence state as the structures evolve from perovskite to infinite layer21. The shoulder is still observed in the infinite-layer Nd0.8Sr0.2NiO2 beside the main peak, even though it shifts to a higher energy position and its intensity is lower compared with that of the perovskite film. This further suggests the presence of oxygen ligand hole state in infinite-layer nickelates.

Fig. 3: Thickness dependence of the X-ray absorption spectroscopy.
figure 3

a The O K edge and (b) Ni L2,3 edge XAS of 10.1 nm perovskite Nd0.8Sr0.2NiO3 and infinite-layer Nd0.8Sr0.2NiO2 thin films. c The O K and (d) Ni L2,3 edge of infinite-layer Nd0.8Sr0.2NiO2 films with different thicknesses.

The parent compound of the canonical cuprate superconductor is a charge-transfer insulator according to the Zaanen-Sawatzky-Allen scheme22. The doped holes reside at the oxygen sites due to the strong hybridization of Cu-\(3{d}_{{x}^{2}-{y}^{2}}\) and O-2p orbitals forming the 3d9L states, and therefore, the pre-peak of O K edge emerges upon doping23. The spin of the doped holes in oxygen sites and spin in Cu site form the Zhang-Rice singlet state, reducing the cuprate to be an effective single-band system24. Whether a similar situation occurs in infinite-layer nickelate, however, is far from clear. The theoretical model suggests that the parent compound NdNiO2 is a Mott-Hubbard insulator, in which the O 2p band is below Ni 3d lower Hubbard Band25,26. This has been suggested by the EELS and XAS measurements that the pre-peak near the O K edge is completely suppressed in undoped NdNiO2 and LaNiO219,20. The pre-peak nature in doped Nd1-xSrxNiO2 has not been fully explored by XAS since the STO capping layer obscures the absorption from the underlying nickelate films27. Our observation of the obvious pre-peak in O K edge and shoulder in Ni L2,3 edge in Nd0.8Sr0.2NiO2 films, which is similar to the cuprate28, suggests the Ni-O orbital hybridization in infinite-layer nickelate. Note that the EELS measurements have also shown the pre-peak feature in Nd1-xSrxNiO2 with increasing doping, although the intensity is weak20. Moreover, a prominent pre-peak has also been seen in trilayer nickelates R4Ni3O8 (R = La and Pr), which possess the same NiO2 square plane as in the infinite-layer nickelates and an effective 1/3 hole doping21,29.

Figure 3c, d show O K edge and Ni L2,3 edge XAS of infinite-layer Nd0.8Sr0.2NiO2 films with different thicknesses. The intensity of pre-peak in O K edge generally increases with decreasing thickness due to the decreasing occupancy (more empty states), suggesting the increase of Ni-O hybridization. The Ni L2,3 peak intensity increases and peak position shifts systematically to higher energies as the thickness decreases. This indicates that with decreasing thickness, the Ni 2p core-level electrons have enhanced binding energy, implying a gradual increase of the oxidation state of Ni. The evolution of XAS may be due to the interface and strain effects with decreasing thickness and could be related to the transport properties as shown above. We note here that the observed XAS signal might contain minute contribution from the presence of local secondary phases in thick films and/or a parasitic surface layer. Nevertheless, all XAS features are similar to those for the ultrathin single-phase film, suggesting that the contribution from the secondary phase is negligible.

It has been constructed by the bulk electronic structure calculations that the infinite-layer nickelate possesses multiband structures which show the hole pocket originating from a Ni-\(3{d}_{{x}^{2}-{y}^{2}}\) orbital and the electron pockets from the rare-earth element 5dxy and \(5{d}_{3{z}^{2}-{r}^{2}}\) orbitals2. Such multiband pictures are consistent with the observed change of RH in Sr-doped NdNiO2 and PrNiO21,3,4,6. Our observation is that the RH of Nd0.8Sr0.2NiO2 also changes with the thickness (Fig. 2b), possibly related to the alteration of band structure due to the interface and strain effects.


Theoretical calculations suggested the presence of electronic and atomic reconstructions at NdNiO2/SrTiO3 interfaces and the resultant alteration of band structure at the interface13,14,15,16. At the surface and interface, the NiO2 layer bends and Ni is displaced vertically due to atomic reconstruction and/or the presence of residual apical oxygen at the NdO plane. It is expected that as the thickness decreases, the interface and/or strain effects are more pronounced. Likely, the bending of the NiO2 layer causes the overall increase of the c-axis lattice constant, as indicated by the XRD measurement (Fig. 1b). The bending of the NiO2 layer and the resultant tilt of Ni-O bonding causes the extra extraction of the electron from Ni to O. This is consistent with our XAS measurement that the oxidation state of Ni increases as the thickness decreases (Fig. 3b, d). Moreover, it has been revealed that the multiband structures become more pronounced at the interface, for example, the mixture of \({d}_{{x}^{2}-{y}^{2}}\) and \({d}_{{z}^{2}}\) states are present near Fermi level at the interface, causing extra electron pockets13,14,15,16. Therefore, as the thickness decreases, the RH remains negative below 300 K (Fig. 2b). It was proposed that the pairing state of Nd1-xSrxNiO2 changes from (d + is)-wave to d-wave paring as the doping increases30, in line with the crossover of RH from negative to positive sign3,4. Interestingly, the interface/surface effect, which caused the negative RH sign in our result, also induced dominant s-wave paring17 as opposed to d-wave symmetry for the bulk2,31. Overall, even though the Meissner effect is confirmed in the nickelate thin films, the interfacial effects due to the atomic reconstruction play an important role in the modification of multiband structures.


Thin film growth and reduction

The perovskite Nd0.8Sr0.2NiO3 thin films with different thicknesses were grown on a TiO2-terminated (001) SrTiO3 (STO) substrate using a pulsed laser deposition (PLD) technique with a 248-nm KrF excimer laser. No capping layer is introduced for all samples. The deposition temperature and oxygen partial pressure PO2 for all samples were 600 °C and 150 mTorr, respectively. The laser energy density on the target surface was set to be 1.8 Jcm−2. After deposition, the samples were annealed for 10 min at 600 °C and 150 mTorr and then cooled down to room temperature at a rate of 8 °C/min. The as-grown samples were cut into pieces with a size of around 2.5 × 5 mm2. The pieces were then embedded with about 0.15 g of CaH2 powder and wrapped in aluminum foil, and then placed into the PLD chamber for reduction. Using the PLD heater, the wrapped samples were heated to 340–360 °C at a rate of 25 °C/min and kept for 80 min, and then cooled down to room temperature at a rate of 25 °C/min.

Electrical and magnetic characterizations

The wire connection for the electrical transport measurement was made by Al ultrasonic wire bonding. The electrical transport and magnetization measurements were performed using a Quantum Design Physical Property Measurement System and Superconducting Quantum Interference Device Magnetometer, respectively.

X-ray diffraction and absorption spectrocopy

The X-ray diffraction (XRD) measurement was done in the X-ray Diffraction and Development (XDD) beamline at Singapore Synchrotron Light Source (SSLS) with an X-ray wavelength of λ = 1.5404 Å. The XAS measurements were performed using linearly polarized X-ray from the Soft X-ray-ultraviolet (SUV) beamline at SSLS, using a total electron yield (TEY) detection method. The incidence angle (90-θ)° of X-rays refers to the normal of the sample surface, which was varied by rotating the polar angle of the sample. The spectra were measured in a grazing-incident alignment (θ = 20°) to obtain better sample signals. The spectra were normalized to the integrated intensity at the tail of the spectra after subtracting an energy-independent background.

Scanning transmission electron microscopy

The high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging was carried out at 200 kV using a JEOL ARM200F microscope, and the cross-sectional TEM specimens were prepared by a focused ion beam machine (FEI Versa 3D). All the data of the same thickness are measured from the exact same sample to ensure consistency in comparing the results of various measurements.