Fig. 1. Raw data plots of modulated ac susceptibility Δχ′ vs temperature T measured at different pressures for La₃Ni₂O₇ single crystal. (a)–(c) Results obtained at 8.4, 15.7, and 20.7 GPa, respectively. On compression, no superconducting diamagnetic signal is observed. (d)–(f) Results obtained at 22.0, 25.1, and 28.2 GPa, respectively, revealing a superconducting diamagnetic transition at temperatures of 63.4, 62.0, and 61.2 K, respectively. (g)–(i) Results obtained during the pressure release process, at 24.4, 21.2, and 17,2 GPa, respectively, showing loss of superconductivity at 17.2 GPa. The insets depict the corresponding superconducting transition of elemental vanadium, captured through synchronous measurements with the La₃Ni₂O₇ single crystal in the same high-pressure chamber. The onset T_c is indicated by the red arrow. By comparing the jump height of the sample and the vanadium, the relative superconducting volume fraction of La₃Ni₂O₇ is estimated to be 0.68% (∼1%) at 22.0 GPa, suggesting that the superconductivity of the compressed La₃Ni₂O₇ is filamentary-like.

Fig. 2. Temperature dependence of dc susceptibilities for superconducting vanadium and La₃Ni₂O₇ single crystal. No evidence of a superconducting transition is observed in the La₃Ni₂O₇ single crystal at 28.2 and 31 GPa, in the pressure range in which superconductivity of La₃Ni₂O₇ should appear.

Fig. 3. Temperature dependence of resistance measured at different pressures for La₂Ni₃O₇ single crystal. (a) and (b) Results of resistance measurements on sample A within the pressure range 2.5–33.3 GPa, illustrating the evolution from a semiconducting-like state to a superconducting-like state. (c) Resistance–temperature curves at different pressures for sample B, showing a superconducting transition with zero resistance in the pressure range 17.8–31.5 GPa. The inset displays an enlarged view of the low-temperature resistance. (d) Results obtained from pressure release measurements, demonstrating a gradual disruption of the superconducting state.

Fig. 4. Pressure–temperature phase diagram and Hall coefficient R_H as a function of pressure for La₃Ni₂O₇ single crystal. (a) Summary of our results and reported results obtained from high-pressure modulated ac susceptibility and resistance measurements. The filled stars represent the data from our susceptibility measurements. The green balls, purple squares, and pink-filled circles are the data from our resistance measurements. DW and SC indicate density-wave and superconducting phases, respectively. T_D denotes the onset temperature of the DW-like phase transition, and Tconset and TcR=0 denote the onset and zero-resistance temperatures of the superconducting transition, respectively. (b) Plot of pressure vs Hall coefficient R_H measured at 90 K, demonstrating a significant drop in R_H around the boundary between the DW-like phase and the SC phase.

Fig. 5. Scanning transmission electron microscopy (STEM) images of superconducting samples. (a) Low-magnification low-angle annular dark-field (LAADF) image along the [110] direction of La₃Ni₂O_7.07 polycrystalline sample. The extensive gray regions correspond to pure 327 phase with 2222 stacking sequence, and the white line regions indicate the interface structure. (b) Atomic-scale high-angle annular dark-field (HAADF) image along the [110] direction obtained from the area within the red box in (a). This image reveals the layered stacking interface structure. The atoms of La in the 327, 4310, and 124 phases are represented by green, orange, and red dots, respectively. T, B, and S denote trilayer, bilayer, and single-layer arrangements of Ni–O planes. (c)–(e) Low-magnification HAADF image, LAADF image, and annular bright-field (ABF) images, respectively, along the [110] direction of La₃Ni₂O₇ single-crystal sample, revealing the existence of many interface structures (white lines) in the single crystal (the sample size is about 3 μm). (f)–(n) STEM images obtained from the areas in (c)–(e) within the boxes labeled 1, 2, and 3 in (c), again revealing many interfaces within the single crystal. (o)–(q) Atomic-scale images of the 327 and 4310 phases and their mixed phase at the interfaces in the La₃Ni₂O₇ single-crystal sample. (r)–(t) Corresponding fast Fourier transform (FFT) diffraction patterns [with diffuse streaks in (t)] of the 327 and 4310 phases and their mixed phase at the interfaces. (u) Intensity profile corresponding to the FFT diffraction patterns in (r)–(t).

Fig. 6. Lower and upper bounds on the oxygen vacancy δ for the presence of superconductivity. (a) Relationship between δ in La₃Ni₂O_7+δ and the presence of superconductivity. The lower and upper bounds on the oxygen vacancy for the presence of superconductivity are estimated to be about −0.11 and 0.35, respectively, the values of which have been determined from the average oxygen contents for nonsuperconducting and superconducting samples: δ_L = [(7 − 6.88) + (7 − 6.91)]/2 = 0.11 and δ_H = [(7.42 − 7) + (7.28 − 7)]/2 = 0.35. The shaded region represents the range where the low-temperature resistance of the sample exhibits metallic behavior, while outside this region, the low-temperature resistance displays a noticeable upturn. (b)–(e) Temperature–resistance and temperature–susceptibility results for samples with different oxygen content. The combined ac susceptibility and resistance measurements were conducted in two different diamond anvil cells (DAC No. 1 and DAC No. 2). We identified that the backgrounds of these two DACs were not the same. The modulated ac susceptibility measurements for samples No. 1 and No. 4 were conducted in DAC No. 1, as a consequence of which both samples exhibited the same background signal [(b) and (e)], whereas the susceptibility measurements for samples No. 2 and No. 3 were performed in DAC No. 2, leading to both samples exhibiting the same background signal [(c) and (d)].