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Linear-in-temperature resistivity for optimally superconducting (Nd,Sr)NiO2


The occurrence of superconductivity in proximity to various strongly correlated phases of matter has drawn extensive focus on their normal state properties, to develop an understanding of the state from which superconductivity emerges1,2,3,4. The recent finding of superconductivity in layered nickelates raises similar interests5,6,7,8. However, transport measurements of doped infinite-layer nickelate thin films have been hampered by materials limitations of these metastable compounds: in particular, a high density of extended defects9,10,11. Here, by moving to a substrate (LaAlO3)0.3(Sr2TaAlO6)0.7 that better stabilizes the growth and reduction conditions, we can synthesize the doping series of Nd1–xSrxNiO2 essentially free from extended defects. In their absence, the normal state resistivity shows a low-temperature upturn in the underdoped regime, linear behaviour near optimal doping and quadratic temperature dependence for overdoping. This is phenomenologically similar to the copper oxides2,12 despite key distinctions—namely, the absence of an insulating parent compound5,6,9,10, multiband electronic structure13,14 and a Mott–Hubbard orbital alignment rather than the charge-transfer insulator of the copper oxides15,16. We further observe an enhancement of superconductivity, both in terms of transition temperature and range of doping. These results indicate a convergence in the electronic properties of both superconducting families as the scale of disorder in the nickelates is reduced.

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Fig. 1: Enhanced crystallinity of Nd1–xSrxNiO2 thin films on LSAT.
Fig. 2: Phase diagram of highly crystalline Nd1–xSrxNiO2.
Fig. 3: Magnetotransport characteristics of the underdoped regime.
Fig. 4: Magnetotransport characteristics of the overdoped regime.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.


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We thank S. Kivelson, T. Devereaux and M. Gabay for useful discussions. This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (contract no. DE-AC02-76SF00515) and the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems Initiative (grant no. GBMF9072, synthesis equipment). C.M. acknowledges support by the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems Initiative (grant no. GBMF8686). B.H.G. and L.F.K. acknowledge support by the Department of Defense Air Force Office of Scientific Research (grant no. FA 9550-16-1-0305) and the Packard Foundation. The XRD reciprocal space map measurements were performed at the Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation (NSF) under award no. ECCS-2026822. This work made use of a Helios FIB supported by the NSF (grant no. DMR-1539918) and the Cornell Center for Materials Research Shared Facilities, which are supported through the NSF MRSEC programme (grant no. DMR-1719875). The Thermo Fisher Spectra 300 X-CFEG was acquired with support from Platform for the Accelerated Realization, Analysis and Discovery of Interface Materials (PARADIM), an NSF MIP (grant no. DMR-2039380), and Cornell University.

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Authors and Affiliations



K.L. and H.Y.H. conceived the project. K.L. and Y.L. fabricated the polycrystalline targets. K.L. fabricated the perovskite thin films. M.O., Y.L. and W.J.K. performed the soft-chemistry reductions. K.L. conducted XRD characterizations. B.Y.W., T.C.W., Y.L., S.H., W.J.K. and Y.Y. performed the transport measurements. B.H.G. and L.F.K. conducted STEM measurements. K.L., B.Y.W., C.M., S.R. and H.Y.H. wrote the manuscript with input from all authors.

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Correspondence to Kyuho Lee.

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Extended data figures and tables

Extended Data Fig. 1 Analytical mapping of Ruddlesden–Popper faults.

a, Raw HAADF-STEM image of the Nd0.85Sr0.15NiO2 film on SrTiO3 substrate shown in Fig. 1a (left) and a magnified view of the region marked by the red dashed box (right). For the magnified view, atomic overlays are shown to illustrate the half-unit-cell displacement induced by the Ruddlesden-Popper-type stacking faults (RP faults), resulting in the reduced cation contrast. b, Composite of the compressive strain measured on the [101] and [\(\bar{1}\)01] pseudocubic lattice fringes for the HAADF-STEM image in a. The infinite-layer film appears as a region of large compressive strain compared to the substrate because of the shortened c-axis lattice constant. Ruddlesden–Popper type faults in the film are highlighted as regions of local expansion (bright lines) within the film. The highlighted boundaries are used to annotate the vertical Ruddlesden–Popper regions, shown as black (yellow) boxes here (in Fig. 1a). c, Identical strain mapping of the [101] and [\(\bar{1}\)01] pseudocubic lattice fringes for the HAADF-STEM image of the Nd0.85Sr0.15NiO2 film on LSAT substrate (Fig. 1b). The circles in b and c illustrate the coarsening length scale of the Fourier-based analysis. Scale bars, 5 nm.

Extended Data Fig. 2 High-resolution HAADF- and ABF-STEM imaging of Nd0.85Sr0.15NiO2 film on LSAT.

a, High-resolution HAADF- (left) and annular bright-field (ABF)- (right) STEM images of the Nd0.85Sr0.15NiO2 film on LSAT shown in Fig. 1b. Both the lattice size and oxygen column structure visible in the ABF image are consistent with the infinite-layer structure. Atomic model overlays show columns of Nd/Sr (orange), Ni (purple), La/Sr (green), Al/Ta (blue), and O (red). b, HAADF-STEM image of the same Nd0.85Sr0.15NiO2 film on LSAT. c. Quantitative tracking of the local c-axis lattice constant measured between consecutive A-site planes (e.g., Nd to Nd). The lattice constant within the film shows good agreement with the expected value for the infinite-layer structure and the measurements of a fully reduced film by XRD. Scale bars, 5 Å.

Extended Data Fig. 3 X-Ray diffraction of Nd1–xSrxNiO2 on LSAT substrates.

a, Representative XRD θ–2θ symmetric scans of optimized Nd1–xSrxNiO2 (x = 0.05–0.325). The curves are vertically offset for clarity. b, XRD θ–2θ symmetric scan of Nd0.85Sr0.15NiO2 (solid curve) and the corresponding symmetric scan fit (dashed curve). The close agreement in the positions of the main film peak and the Laue fringes indicates a good fit. The asymmetry in the Laue fringes of the film peaks arises from the asymmetric background intensity and the resolution limit of the instrument. The extracted out-of-plane lattice constant c from the fit is labelled. c, c-axis lattice constant versus x for Nd1–xSrxNiO2 films on LSAT (green filled triangles, extracted from a) and on SrTiO3 (red filled circles) using the same growth conditions (Extended Data Table 1). Error bars are the larger of the error in the fit and standard deviation in the values from multiple samples. c increases linearly with x, consistent with systematic doping of Sr in the films. Previous experimental data9,10 on SrTiO3 are also shown as open circles. The substantial elimination of Ruddlesden–Popper-type faults, which locally expand the in-plane lattice11, results in the overall decrease in c compared to previous experimental data. In their absence, the larger c-axis lattice constant in LSAT with respect to SrTiO3 is due to larger compressive strain. Dotted lines are linear fits to the experimental data. dg, Reciprocal space maps of Nd1–xSrxNiO2 films on LSAT for x = 0.075 (d), x = 0.15 (e), x = 0.225 (f), and x = 0.3 (g), showing that the films are fully strained to the LSAT substrate across doping.

Extended Data Fig. 4 Atomic-scale structural characterization by HAADF-STEM of the Nd0.7Sr0.3NiO2 film on LSAT with SrTiO3 capping layer.

HAADF-STEM image of the Nd0.7Sr0.3NiO2 film on LSAT. Scale bar, 5 nm.

Extended Data Fig. 5 Individual resistivity curves of Nd1–xSrxNiO2 on LSAT.

ρ versus T curves of optimized Nd1–xSrxNiO2 films (x = 0.05–0.325). Curves for additional samples at x = 0.075, 0.15, and 0.275 are also shown.

Extended Data Fig. 6 Comparing the Nd1–xSrxNiO2 and the La2–xSrxCuO4 phase diagrams.

Superconducting phase diagram of Nd1–xSrxNiO2 on LSAT (red) and La2–xSrxCuO4 (green), both plotted against the nominal Sr composition x12,36,37,41. The superconducting onset temperature is shown via circles, while the resistive upturn temperature Tupturn is shown as triangles. For La2–xSrxCuO4, the open triangles are Tupturn obtained by suppressing superconductivity with high magnetic field37. The superconducting dome extends from x ≈ 0.1–0.3 (Δx ≈ 0.2) for Nd1–xSrxNiO2 and x ≈ 0.05–0.26 (Δx ≈ 0.21) for La2–xSrxCuO4.

Extended Data Fig. 7 Suppression of superconductivity by magnetic field.

a, ρ versus T of Nd0.825Sr0.175NiO2 film on LSAT under perpendicular magnetic field (0.2–14 T, indicated by color). b, The real (red, left) and imaginary (blue, right) parts of the inductance Lp as a function of T in the pickup coil on a Nd0.825Sr0.175NiO2 film on LSAT, measured using a two-coil mutual-inductance measurement (see Methods).

Extended Data Fig. 8 Individual RH(T) curves of Nd1–xSrxNiO2 on LSAT.

RH versus T curves of optimized Nd1–xSrxNiO2 films (x = 0.05–0.325) on LSAT substrate. RH = 0 is marked as a black dotted line.

Extended Data Fig. 9 Minimal epitaxial strain dependence of Tupturn.

ρ(T) of Nd0.7Sr0.3NiO2 films on SrTiO3 (blue) and LSAT (red), both synthesized using the growth parameters specified in Extended Data Table 1. Prior data of ρ(T) of Nd0.75Sr0.25NiO2 film on SrTiO3 from ref. 9 (yellow dashed curve, see Fig. 2f) is also plotted for comparison. The films on SrTiO3 show considerable suppression of Tupturn (black arrows) upon enhanced crystallinity, with similar order of suppression as the film on LSAT. This suggests that the suppression of the resistive upturn is primarily due to higher film quality, and epitaxial strain plays a sub-dominant role in the resistive upturn.

Extended Data Fig. 10 Cumulative phase diagram of the infinite-layer nickelate Nd1–xSrxNiO2 on LSAT.

The main features of the phase diagram of Nd1–xSrxNiO2 are summarized here. The onset temperature of the superconducting transition Tc,onset is defined as the temperature at which the second derivative of ρ(T) becomes negative, and the 50% transition temperature Tc,50% is defined as the temperature at which ρ is 50% of ρ(Tc,onset). In the underdoped region, ρ shows a resistive upturn, with Tupturn (dark-blue triangles) decreasing as hole doping is increased and superconductivity emerges. Simultaneously, the local maximum in RH (light-blue diamonds) tracks the doping dependence of the resistive Tupturn. Superconductivity emerges at x ≈ 0.1 and persists up to x ≈ 0.3. In the optimal doping of x ≈ 0.15–0.175, the normal-state resistivity shows a linear T-dependence. As superconductivity is suppressed in the overdoped region, T2 resistivity emerges, with a small resistive upturn at low temperatures (dark-blue triangles) driven by disorder. The open circles at the overdoped region delineate the boundary below which the T2 fit shows good agreement with ρ. As x is increased, RH starts to cross zero into positive values (green squares). This transition occurs near the optimal doping, and the zero-crossing temperature increases into the overdoped region.

Extended Data Fig. 11 Powder XRD of polycrystalline target.

Powder XRD of polycrystalline nickelate target with nominal stoichiometry of Nd0.825Sr0.175Ni1.15O3 (red), along with bulk powder XRD of Nd2NiO4 and NiO44,45. Aside from minor shifts in the peak positions due to chemical substitution of Sr, the observed peaks of the target are a superposition of Nd2NiO4 and NiO11.

Extended Data Table 1 Pulsed-laser deposition growth parameters optimized for perovskite Nd1–xSrxNiO3 thin films on LSAT
Extended Data Table 2 Summary of superconducting transition temperatures of Nd1–xSrxNiO2 thin films on LSAT

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Lee, K., Wang, B.Y., Osada, M. et al. Linear-in-temperature resistivity for optimally superconducting (Nd,Sr)NiO2. Nature 619, 288–292 (2023).

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