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Cuprates are the first family of high-temperature (high-Tc) superconducting materials, characterized by layers of CuO2 interleaved with charge reservoir layers1,2. Despite intensive research on various cuprates, the mechanism responsible for high-Tc superconductivity remains unknown2,3. Consequently, the pursuit of high-Tc superconductors that do not rely on copper oxides has become a focal point of intense experimental and theoretical exploration since the discovery of cuprates nearly four decades ago4,5,6,7,8. This is motivated by the belief that these materials may help to explain the enigmatic mechanisms governing high-Tc superconductivity while providing opportunities for new applications. Nickel, situated immediately to the left of copper on the Periodic Table, offers a playground for materials and chemistry designs aimed at replicating high-Tc unconventional superconductivity8,9,10,11,12. However, despite intensive efforts, achieving superconductivity in nickelates is a formidable challenge. In 2019, a development occurred when superconductivity was observed in infinite-layer nickelate thin films with Tc = 5–20 K (refs. 13,14,15,16). In these materials, Ni1+ (d9) forms square planar NiO2 layers closely resembling Cu2+ (d9) in cuprates13,14,15,16.

More recently, signatures of superconductivity have also been observed in the Ruddlesden–Popper bilayer perovskite La3Ni2O7 under high pressure, achieving a Tc of approximately 80 K above 14 GPa (ref. 17). Subsequent studies have observed zero resistance under improved hydrostatic pressure conditions facilitated by a liquid pressure-transmitting medium18,19,20. However, it has been suggested that the superconductivity in La3Ni2O7 may be filamentary in nature, with a low superconducting volume fraction19,20, underscoring the need for more in-depth research to fully understand the superconducting properties of this class of materials. Unlike infinite-layer nickelates and cuprates with a d9 electron configuration, La3Ni2O7 hosts a bilayer NiO2 square structure featuring Ni2.5+ (d7.5) ions17. Furthermore, the p-orbital of apical oxygen, which connects adjacent NiO2 layers, couples the two nearest-neighbour \(3{d}_{{z}^{2}}\) orbitals, suggesting that interlayer coupling may also play a crucial part in La3Ni2O7 (ref. 17). However, in contrast to cuprate and iron-based superconductors, in which superconductivity typically arises from the suppression of static long-range magnetic order in their parent phases2,3,4,21, infinite-layer and bilayer La3Ni2O7 nickelates have either shown a lack of magnetic order or hinted at the presence of weak magnetism13,17,22,23. This raises a fundamental question about whether magnetism plays the same crucial part in making nickelates into high-Tc superconductors.

Of particular interest, it is well known that the Tc in cuprates depends on the number of CuO2 layers (n) in a non-monotonic way, reaching a maximum for n = 3 in most cases24,25,26. As a result, trilayer cuprates have the highest Tc among all cuprates, reaching up to 135 K at ambient pressure and 164 K under high pressure for mercury-based compounds27,28. The mechanism for this layer dependence of superconductivity remains a subject of intense and ongoing debate26,27,28,29,30. This raises the question of whether trilayer nickelates exhibit superconductivity, and if so, how it might influence Tc.

Theoretical considerations have suggested that trilayer La4Ni3O8, with its Ni1.33+ (d8.67) configuration, closely parallels the cuprates with Cu2+/Cu3+ configurations and thus stands as an ideal candidate for a high-Tc superconductor31,32. However, experimental investigations have thus far failed to observe superconductivity in trilayer La4Ni3O8, both under ambient conditions and at high pressure11,33.

In contrast to many nickelates that exhibit insulating behaviour, including trilayer La4Ni3O8, the trilayer Ruddlesden–Popper compound La4Ni3O10 stands out as a rare oxide compound that maintains its metallic character even at low temperatures under ambient pressure34,35. Trilayer nickelate La4Ni3O10 exhibits a static incommensurate magnetic order accompanied by a charge order36. The nominal valence state of trilayer La4Ni3O10 is Ni2.67+ (d7.33), which is different from the d9 state typically observed in infinite-layer nickelates and cuprates or the d7.5 state found in bilayer La3Ni2O7. Nevertheless, the band structure of La4Ni3O10 shows intriguing features: the \({d}_{{x}^{2}-{y}^{2}}\) hole band bears a striking resemblance to the behaviour observed in hole-doped cuprates, whereas the \({d}_{{z}^{2}}\) band is rather flat and exhibits a 20-meV density wave-like gap opening associated with the spin order transition35,36, reminiscent of the phenomena observed in iron-based superconductors21,37. This distinctive combination of characteristics, coupled with its trilayer structure, positions La4Ni3O10 as an ideal platform for the exploration of the interplay between magnetism, interlayer coupling and potential superconductivity. However, the investigations of La4Ni3O10 were markedly hampered by the scarcity of high-quality single crystals, which necessitated their growth under a high oxygen pressure atmosphere34.

In this study, we report detailed measurements of La4Ni3O10−δ single crystals under both ambient conditions and high pressures, reaching up to 70 GPa. The high-quality La4Ni3O10−δ single crystals were grown using a high-pressure vertical optical-image floating-zone furnace. Our X-ray diffraction (XRD) experiments conducted on powdered La4Ni3O10−δ single crystals at ambient conditions confirm the presence of a pure phase of trilayer La4Ni3O10−δ (Extended Data Fig. 1). Furthermore, we conducted single-crystal neutron-diffraction and single-crystal XRD measurements on La4Ni3O10−δ (Extended Data Fig. 7a and Supplementary Table 1). The combined single-crystal structural refinement analysis using least square fitting by incorporating data from both neutron diffraction and XRD, identified the composition as La4Ni3O9.96(4), pointing to a minor oxygen deficiency. Moreover, the refined crystal structure aligns with the P21/a space group with Z = 2 (Fig. 1e), consistent with previous reports34.

Fig. 1: Pressure-dependent lattice structure and phase diagram of La4Ni3O10-δ.
figure 1

a, Phase diagram of La4Ni3O10−δ under pressure. The red solid triangles and squares represent Tc (onset) of samples S3 and S4 in the helium DAC, respectively. The Tc (onset) is the temperature below which the resistance deviates from its linear dependence at high temperatures. The red solid circles and hexagons represent the Tc (onset) at pressures above 38 GPa of samples S1 and S2, respectively, in which a pronounced sharp drop in resistance below Tc is evident in the KBr DAC. The red open circles and hexagons denote the Tc (onset) at pressures below 25 GPa in the KBr DAC, in which a moderate decrease in resistance below Tc is observed because of filamentary superconductivity (Fig. 3e). The blue diamonds denote the TN determined from resistance measurements in Fig. 3a,b and Supplementary Fig. 7. The purple solid downward triangles and pentagons represent the Tc offset Tczero, in which the resistance equals zero. The bulk superconductivity emerges above around 40 GPa, in which substantial superconducting diamagnetic responses and zero resistance are observed. The shaded area highlights the region of the structural transition. b, HAADF images along the [110] direction at ambient pressure, featuring three layers of NiO2 separated by LaO spacers. c, Lattice constants a, b and c extracted from the synchrotron-based XRD (Extended Data Fig. 3). d, Cell volume V and the refined β angle of P21/a and I4/mmm lattices. The solid lines indicate the Birch–Murnaghan equation fit of cell volume as a function of pressure, with fitted bulk moduli K0 of 152.3 GPa for the low-pressure phase and 147.2 GPa for the high-pressure phase. e, Crystal structure of La4Ni3O10−δ at ambient pressure. f, Crystal structure of La4Ni3O10−δ at 34 GPa. g, Evolution of Ni–O–Ni angle between adjacent NiO2 layers across the structural phase transition. Error bars indicate 1 s.d. DAC, diamond anvil cell; LP, low pressure; HP, high pressure. Scale bar, 2  nm (b).

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Figure 1b shows the atomic-resolution high-angle annular dark-field (HAADF) images, which show the detailed positions of atoms within the trilayer structure of La4Ni3O10−δ. We also used integrated differential phase contrast (iDPC) imaging techniques to accurately visualize the lighter oxygen atoms (Extended Data Fig. 6). The simultaneous acquisition of HAADF and iDPC images, seamlessly aligns with our neutron diffraction and XRD refinements, reinforcing the accuracy of our structural analysis. The HAADF images in large-area overviews further confirm the phase purity and exceptional quality of our crystals (Extended Data Fig. 6).

To assess the influence of pressure on the crystal structure, we conducted synchrotron-based XRD measurements on powdered La4Ni3O10−δ single crystals (Extended Data Fig. 3). It is shown that the diffraction peaks within the range of 12.5° < 2θ < 14° exhibit a noticeable evolution with increasing pressure, indicative of a structural phase transition. The refinement analyses show a subtle structural transition associated with the tilting of the NiO6 octahedra, shifting from monoclinic P21/a to tetragonal I4/mmm at pressures exceeding approximately 13–15 GPa (Extended Data Fig. 3). Concurrently, the Ni–O–Ni angle between adjacent NiO2 layers changes from around 165.6(6)° to 180° during this phase transition (Fig. 1g), potentially enhancing interlayer coupling. The lattice constants and cell volume also exhibited a progressive decrease under pressure, with an anomaly observed near the structural phase transition (Fig. 1c,d), consistent with a recent independent measurement on polycrystalline samples38. To ascertain if such a phase transition also occurs in single-crystal samples, single-crystal XRD measurements were conducted, with the structural phase transition being further confirmed by single-crystal refinements (Extended Data Fig. 7b and Supplementary Table 2).

To further characterize the material, we conducted magnetic susceptibility measurements, which showed a distinct kink in the data at TN ≈ 136 K (Fig. 2a), suggesting the emergence of the static spin–charge order, as previously shown in neutron diffraction experiments36. This phase transition was corroborated by heat capacity measurements, which exhibited a pronounced peak at a similar temperature (Fig. 2c). These results are consistent with the monoclinic P21/a structure of the material at ambient pressure34,39.

Fig. 2: Magnetic susceptibility, resistivity and specific heat of La4Ni3O10−δ single crystal at ambient pressure.
figure 2

a, Magnetic susceptibility of La4Ni3O10−δ measured from 2 K to 300 K with an applied field of 0.4 T, parallel and perpendicular to the ab plane. The spin and charge order transition characterized by a kink in the χ(T) curve occurs at TN ≈ 136 K. b, Resistivity profile of La4Ni3O10−δ in the ab plane at ambient pressure, using a current of 100 μA. c, Specific heat of La4Ni3O10−δ near TN.

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The electrical resistance R(T) of La4Ni3O10−δ single crystals under various pressure conditions is presented in Fig. 2b and Fig. 3a–e. At ambient pressure, La4Ni3O10−δ exhibits a characteristic metallic behaviour, with resistivity exhibiting a decrease as the temperature descends below 300 K. A distinctive, steplike kink in the resistivity curve manifests at the spin–charge ordering temperature TN (Fig. 2b). The spin and charge order phase transition observed in our measurements shows a marked sharpness, which is notable in comparison with previous studies. This indicates the high quality of our La4Ni3O10−δ single crystals, setting the stage for precise investigations into its physical properties under pressure.

Fig. 3: Temperature-dependent resistances and d.c. susceptibilities of La4Ni3O10−δ single crystals under various pressures.
figure 3

a, Resistivity at pressures spanning 0.24 GPa to 1.82 GPa in the piston-cylinder cell, using a current of 2 mA. The spin and charge order transition at TN is progressively suppressed with increasing pressure. b, Resistances at pressures ranging from 3.0 GPa to 63.0 GPa in the helium DAC for sample S3, using a current of 500 μA. The diamond broke on warming to around 250 K at 63.0 GPa. The black dashed lines depict the linear fit of the normal state resistances. c, Resistances in the helium DAC near the superconducting transition for S3. Zero resistances are observed above 43.0 GPa. d, An enlarged view of the resistance curve below Tc within the helium DAC, providing a demonstration of zero resistance for S3. e, Resistances at pressures ranging from 2.2 GPa to 57.3 GPa in the KBr DAC for sample S1, using a current of 100 μA. The black dashed lines depict the linear fit of the normal state resistances. f, Temperature-dependent magnetization curves of La4Ni3O10−δ under a magnetic field of 20 Oe applied perpendicular to the ab plane using the ZFC and FC modes at 40.0 GPa for sample S6. g–i, A distinct superconducting diamagnetic response at Tc is observed in the ZFC curve for 47.0 GPa (g), 50.0 GPa (h) and 55.0 GPa (i). The black arrows indicate the superconducting transition temperatures.

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When external pressure is exerted on the piston-cylinder cell, the characteristic kink related to the spin–charge ordering in the resistivity curve is rapidly suppressed (Fig. 3a), which is consistent with previous measurements on a powder sample below 1.28 GPa (ref. 40).

Resistances above 2.5 GPa were measured in a Be–Cu alloy diamond anvil cell (DAC). To ensure the best hydrostatic condition inside the DAC, we use helium as the pressure-transmitting medium. The resistance initially exhibits weak insulating behaviour, accompanied by a peak anomaly associated with the spin order transition at 3.0 GPa (Fig. 3b). As pressure increases, metallic behaviour is restored and the peak anomaly is progressively suppressed and, eventually, a sharp drop in resistance below a critical temperature Tc of 4.5 K is observed at 15.5 GPa (Fig. 3b). With further increments in pressure, Tc continues to rise, ultimately reaching a point at which zero resistance is observed at pressures exceeding 43.0 GPa (Fig. 3b–d). This signifies the emergence of superconductivity, with the onset superconducting transition temperature ranging from 4.5 K to around 30 K.

We also conducted temperature-dependent resistance measurements in a DAC using KBr as the pressure-transmitting medium. Across the pressure range spanning from 2.2 GPa to 24.6 GPa, a moderate decrease of resistance below a critical temperature of 2–20 K is observed (Fig. 3e). This together with the weak upturn in resistance in the normal state, indicates a limited superconducting volume, probably because of the filamentary nature of the superconductivity in this pressure range. As the pressure is raised further, a notable sharp reduction in resistance becomes evident at approximately 20–30 K, observed at pressures of 38.0 GPa and beyond (Fig. 3e) and the onset Tc reaches 30.1 K at 69.0 GPa (Fig. 3e and Extended Data Fig. 5). However, small residue resistance below Tc was observed in this configuration, probably attributed to the less hydrostatic conditions resulting from the pressure-transmitting medium KBr.

To provide further confirmation of the pressure-induced superconductivity, we conducted ultrasensitive d.c. magnetic susceptibility measurements under high pressures within a custom-built miniature Be–Cu alloy DAC, using nitrogen as the pressure-transmitting medium to provide a hydrostatic pressure environment. A distinctive diamagnetic response at Tc is evident in the zero-field-cooled (ZFC) curve at 40.0 GPa, and as pressure increases, Tc also rises, consistent with the resistance measurements, further confirming the emergence of superconductivity (Fig. 3f–i and Extended Data Fig. 8). We have estimated the maximum superconducting volume fraction to be around 86% across the pressures applied, suggesting the development of bulk superconductivity (Extended Data Fig. 9). Conversely, below 30 GPa, no prominent superconducting diamagnetic responses were detected, suggesting that the superconducting volume fraction is relatively limited at low pressures (Extended Data Fig. 10). The difference of susceptibilities between ZFC and field-cooled (FC) curves in the normal states is because of the magnetic background of the pressure cell with residual magnetic impurities (Supplementary Fig. 5).

Concomitant with the emergence of zero resistance at 43.0 GPa, the normal state resistance follows a linear temperature dependence up to 300 K (Fig. 3b). This behaviour is a hallmark of the so-called strange metal state, a characteristic phenomenon observed in optimal doped cuprates, certain iron-based materials and nickelate superconductors2,17,18,41,42,43,44,45, implying the existence of strong correlations and underscores the unconventional nature of superconductivity. Similar strange metal behaviour was also confirmed in the measurements conducted within the KBr DAC above 38.0 GPa (Fig. 3e).

Figure 4a–d shows the temperature-dependent magnetoresistance measured in magnetic fields perpendicular to the ab plane under various pressures. As the magnetic field is increased, superconductivity is progressively suppressed, providing further confirmation that the transition in resistance is because of the onset of superconductivity. We use the 90% resistance transition to the normal state near Tc and fit it to the Ginzburg–Landau form Hc2(T) = Hc2(0)[(1 − t2)/(1 + t2)], where t = T/Tc. This analysis yields an estimation of the upper critical field, with values reaching 44 T at 63.0 GPa when using the helium DAC, and 48 T at 69.0 GPa with the KBr DAC (Fig. 4e and Extended Data Fig. 5). These values of upper critical field exceed those observed in infinite-layer nickelates13 but fall below La3Ni2O7 (ref. 17).

Fig. 4: Magnetic field effects on the superconducting transition in La4Ni3O10−δ.
figure 4

a–d, Field dependences of electrical resistance for sample S3 at 48.0 GPa (a), 53.0 GPa (b), 57.0 GPa (c) and 63.0 GPa (d). e, The Ginzburg–Landau fittings of the upper critical fields at 53.0 GPa and 63.0 GPa. The magnetic fields are applied perpendicular to the ab plane. Inset, a photograph of the electrodes used for high-pressure resistance measurements. Scale bar, 100 μm (e, inset).

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Figure 1a summarizes the pressure-dependent spin–charge order and superconductivity phase diagram in trilayer La4Ni3O10-δ. This phase diagram bears some analogy to those found in cuprate and iron-based superconductors2,21, in which high-Tc superconductivity arises on suppression of a static magnetic order. From the electronic structure perspective, it suggests that the \({d}_{{z}^{2}}\) band could play an important part in shaping the pressure-dependent phase diagram of La4Ni3O10-δ. The \({d}_{{z}^{2}}\) band is notably flat and shows a 20-meV spin-density wave-like gap35. This unique electronic structure feature, coupled with its propensity to interact with the p-orbital of apical oxygen, renders the \({d}_{{z}^{2}}\) band highly susceptible to external pressure, with the potential to alter nesting conditions and influence the spin-density wave (SDW)–charge-density wave (CDW) order.

Therefore, the concurrent emergence of bulk superconductivity and strange metal behaviour could be attributed to the pressure effect that suppresses the density wave gap, brings the flat \({d}_{{z}^{2}}\) band into proximity with the Fermi surface and consequently induces strong correlations and fosters the emergence of the strange metal behaviour. Simultaneously, the closing of the density wave gap dampens the static spin order and promotes dynamic spin fluctuations, paving the way for superconductivity to emerge, in which the hole Fermi surface associated with the \({d}_{{x}^{2}-{y}^{2}}\) orbital may also come into play.

If this analysis were extended to the bilayer system, it suggests that the absence of (or weak) static magnetic order in La3Ni2O7 may be attributed to the fact that the \({d}_{{z}^{2}}\) band lies considerably further below the Fermi level compared with La4Ni3O10 (refs. 35,46). However, even the flat bands located away from the Fermi level have the potential to generate high-energy spin fluctuations, which could exert a noteworthy influence on the phase diagram or serve as a mediator of electron pairing47. Further investigations in this direction are warranted to fully explain the role of magnetism in nickelate superconductors.

Furthermore, it is important to consider the impact of the interlayer coupling, a factor that could potentially promote superconductivity and has been intensively discussed in multilayer cuprates and bilayer La3Ni2O7 (refs. 2,17,29,30,48). The observation of pressure-induced superconductivity accompanied by a structural transition from monoclinic to tetragonal phases also suggests a potential role of interlayer coupling in trilayer La4Ni3O10−δ. However, unlike cuprate superconductors for which the highest Tc is achieved in trilayer systems, in the case of trilayer La4Ni3O10−δ, the Tc is lower than that of bilayer La3Ni2O7. This discrepancy suggests the presence of distinct interlayer interaction mechanisms between these two systems. Further investigations are needed to explain these coupling mechanisms, particularly focusing on differences in carrier concentrations and magnetic structures between the inner and outer NiO2 layers, as well as the interlayer coupling between the two outer NiO2 layers. These factors are crucial for understanding the evolution of Tc in multilayer superconductors2,29,30,48.

In summary, we present evidence of bulk superconductivity in trilayer nickelate La4Ni3O10−δ single crystals under pressure. Our experiments also show strange metal behaviour in the normal state, characterized by the linear temperature dependence of resistance up to 300 K, which may be linked to the enhanced spin fluctuations and strong correlations induced by the flat \({d}_{{z}^{2}}\) band positioned near the Fermi level. Furthermore, the layer-dependent Tc in nickelates is distinct from that observed in cuprates, suggesting unique interlayer coupling and charge transfer mechanisms specific to nickelates. Further research is required to fully understand the precise role of interlayer coupling in the pairing, especially considering the differences in carrier concentrations and magnetism between the inner and outer NiO2 layers, as well as the interlayer coupling between the two outer NiO2 layers, which are absent in the bilayer system. Furthermore, a comprehensive exploration of the role of the \({d}_{{x}^{2}-{y}^{2}}\) orbital and pairing symmetry is necessary for a complete understanding. In essence, our findings establish a promising new material platform, inviting deeper exploration into the intricate interplay between spin–charge order, flat band structure, interlayer coupling, strange metal behaviour and high-Tc superconductivity. This avenue of research holds great potential for uncovering new phenomena and advancing our understanding of high-Tc superconductors.

Methods

Growth of La4Ni3O10−δ single crystals

The precursor powder for the La4Ni3O10−δ compound was prepared using the conventional solid-state reaction method. Chemically stoichiometric raw materials, La2O3 and NiO (Aladdin, 99.99%), were meticulously ground and mixed using a Vibratory Micro Mill (FRITSCH PULVERISETTE 0). An additional 0.5% of NiO was included to compensate for potential NiO volatilization during the crystal growth process. The resulting mixture underwent calcination at 1,373 K for 24 h, with two repeated calcination cycles to ensure complete and homogeneous reactions.

Subsequently, the resulting precursor material was pressed into a cylindrical rod, approximately 13 cm in length and 6 mm in diameter, using a hydrostatic pressure of 300 MPa. The shaped rod then underwent once sintering at 1,673 K for 12 h in air. Single crystals were grown using a vertical optical-image floating-zone furnace (Model HKZ, SciDre) at Fudan University. During the crystal growth process, we carefully maintained an oxygen pressure of 18–22 bar, and used a 5-kW Xenon arc lamp as the light source. The rod was rapidly traversed through the growth zone at a speed of 15 mm h−1 to enhance the density, after which a growth rate of 3 mm h−1 was maintained.

STEM measurements

The scanning transmission electron microscopy (STEM) experiments were performed on a double aberration-corrected S/TEM (Themis Z, Thermo Fisher Scientific) operated at 300 kV. For STEM-HAADF imaging, the probe semi-convergent angle is 21.4 mrad, and the HAADF collection angle is from 79 mrad to 200 mrad. The atomic-resolution EDX imaging was recorded with a Super-X detector.

Measurements under high pressure

We conducted electrical resistance measurements on La4Ni3O10−δ single crystals under pressure in a physical property measurement system by Quantum Design. The temperature range covered was from 1.8 K to 300 K, and magnetic fields of up to 9 T were applied. The electrical resistivity measurements at low pressures (below 2.5 GPa) were performed in a piston-cylinder cell using the standard four-probe method (Fig. 3a). The pressure-transmitting medium used in this setup was liquid Daphne 7373. The pressure was calibrated from the superconducting transition temperature of Pb. The electrical resistance measurements at high pressures (above 2.2 GPa) were performed in a DAC with 200–300 μm culets using the standard van der Pauw four-probe method (Figs. 3b–d and 4 and Extended Data Fig. 4). The sample chamber was constructed using a mixture of cubic boron nitride and epoxy, with a diameter ranging from 140 μm to 280 μm. The single crystal was loaded under helium as the pressure-transmitting medium. KBr powders were also used as a different pressure-transmitting medium (Fig. 3e and Extended Data Fig. 5). Pressure calibration was carried out using ruby fluorescence peak shift at room temperature.

Ultrasensitive magnetic susceptibility measurements under pressure were conducted using a custom-built beryllium-copper alloy miniature DAC equipped with a rhenium gasket, using a design similar to that in refs. 49,50. The mini-DAC has dimensions of approximately 8.5 mm in diameter and 30 mm in length. The measurements were performed using a Magnetic Property Measurement System (MPMS3, Quantum Design). The DAC includes a pair of diamond anvils with a diameter of 300 μm and a sample chamber with a diameter of 210 μm. The sample chamber was filled with a single crystal of La4Ni3O10−δ and liquid nitrogen as the pressure-transmitting medium to provide a hydrostatic pressure environment. The samples had a diameter of approximately 150–200 μm and a thickness of roughly 25 μm.

The single-crystal neutron-diffraction experiments were performed using the HB-3A four-circle single-crystal neutron diffractometer at the High Flux Isotope Reactor at Oak Ridge National Laboratory. An Si (220) monochromatic neutron beam with a wavelength of 1.533 Å was used for the measurements. In situ lab-based high-pressure XRD measurements on powder and single crystals were carried out using a Bruker D8 Venture diffractometer, using Mo Kα radiation (λ = 0.7107 Å) in a DAC with 300-μm-diameter culets and stainless steel gaskets (Extended Data Figs. 2 and 7, Supplementary Fig. 9 and Supplementary Tables 1 and 2). A methanol:ethanol:water mixture in the ratio of 16:3:1 was used as the pressure-transmitting medium for these measurements. For the powder measurements, we captured two-dimensional patterns of powder diffraction rings, which were subsequently processed to yield one-dimensional profiles (Extended Data Fig. 2). We included a small ruby ball within the chamber to facilitate pressure calibration by monitoring the fluorescence peak shift of ruby. In situ synchrotron-based high-pressure XRD measurements were performed at the beamline 15U1 at Shanghai Synchrotron Radiation Facility, using an X-ray beam with a wavelength of 0.6199 Å (Extended Data Figs. 1b and 3 and Supplementary Table 3). A symmetric DAC with anvil culet sizes of 300 μm and rhenium gaskets were used. Helium was used as the pressure-transmitting medium to maintain optimal hydrostatic pressure conditions, with pressure calibration again based on the shift in the fluorescence peak of a ruby indicator.

Calculation of superconducting volume fraction

The susceptibility χm of a superconductor can be decomposed into

$${\chi }_{{\rm{m}}}=(1-f){\chi }_{{\rm{p}}}+f{\chi }_{{\rm{d}}},$$
(1)

where f is the superconducting volume fraction, χp denotes the paramagnetic susceptibility and χd denotes the diamagnetic susceptibility.

In SI units, χd = −1, and χp → 0, equation (1) can be then expressed as

$$f=| {\chi }_{{\rm{m}}}| ,$$
(2)

On converting between unit systems, the susceptibility equation becomes

$${\chi }_{{\rm{SI}}}=4{\rm{\pi }}{\chi }_{{\rm{CGS}}}=4{\rm{\pi }}M/H=4{\rm{\pi }}\sum {\mu }_{i}/\sum {V}_{i}=(4{\rm{\pi }}\mu {m}_{{\rm{a}}})/(HV{N}_{{\rm{a}}}m),$$
(3)

where μ ≈ 1.69 × 10−6 emu represents the measured magnetic moment at 5 K after subtracting the constant background signal at the onset of Tc for sample S6 at 20 Oe and 50 GPa. m ≈ 3.16 μg is the sample mass that was calculated based on the refined density ρ = 7.16 g cm−3 and the sample volume at ambient condition; ma is the molar mass, Na is the Avogadro constant and V = 342.837 Å3 is the cell volume for an I4/mmm primitive cell with Z = 2 at 50 GPa (Fig. 1d and Supplementary Table 3).

The demagnetizing factor N of a finite cylinder with an axial magnetic field can be approximated using51

$${N}^{-1}\approx 1+1.6(C/A),$$
(4)

where A is the diameter and C is the thickness of the sample. For sample S6, A = 160 μm and C = 22 μm at ambient conditions, yielding a demagnetizing factor of N = 0.82. This factor remains largely unchanged under hydrostatic pressure because of the proportional contraction of the lattice dimensions of the crystal structure (Supplementary Table 3). The susceptibility χ can be calculated as

$$N=1/{\chi }_{0}-1/\chi ,$$
(5)

where χ0 is the measured value and χ is the adjusted susceptibility for the sample geometry. Implementing the above procedure, χ calculates to approximately −0.86 at 5 K for S6, indicating a superconducting volume fraction of 86% as shown in Extended Data Fig. 9. This substantiates pressure-induced bulk superconductivity in La4Ni3O10-δ.

Extended analysis and discussion

The upper critical fields of nickelates are comparable with those observed in hole-doped cuprate and iron-pnictide superconductors exhibiting similar Tc values52,53,54 but surpass those of simple conventional superconductors49,55. Furthermore, our estimation of the in-plane superconducting coherence length of La4Ni3O10−δ approximates to 26 Å at 69.0 GPa, close to values of 122 iron pnictide and La2−xSrxCuO4 (refs. 52,53,54). The high upper critical fields and the correspondingly shorter superconducting coherence lengths point to tightly bound Cooper pairs, hinting at an unconventional pairing mechanism possibly driven by spin fluctuations and strong electronic correlations. Theoretical calculations on both infinite-layered and bilayer nickelates suggest that electron–phonon coupling alone is insufficient to account for the observed high critical temperatures56,57. We anticipate that the scenario for La4Ni3O10 is similar, although specific calculations for this material have not yet been published in the literature.

Recently, several theoretical preprints on La4Ni3O10 have appeared, examining its intricate electronic structure, the unique layer-dependent magnetism of its trilayer configuration and its superconductivity. These analyses underscore the impact of electronic correlations, spin fluctuations and interlayer coupling on the strange metal behaviour of the material and its unconventional superconducting pairing mechanism, with an emphasis on the s±-wave pairing symmetry58,59,60,61,62,63,64. It has been suggested that the magnetic structures in La4Ni3O10 vary substantially between the inner and outer NiO2 layers, in which the inner layer is non-magnetic and the outer layers are antiferromagnetic61,62,63. There are also likely variations in carrier concentrations and electron correlations across these layers58,59,60,61,62,63,64. These distinctions in magnetic structure and electron dynamics potentially introduce a unique phenomenon not present in bilayer and infinite-layer nickelates, warranting further exploration.

While preparing this paper, we found three related studies that reported resistance measurements on La4Ni3O10 polycrystalline samples65,66,67. In refs. 66,67, a reduction in resistance—ranging from 4% to 7% below the 15–20 K temperature range—under pressures exceeding roughly 30 GPa is observed, whereas in ref. 65 this phenomenon is not observed below 50 GPa.