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Although a huge body of experimental work has been reported for copper oxide (cuprate) superconductors since they were discovered more than thirty years ago10,11, the correlation between the superconducting state and its normal state or the neighbouring ground state is still widely debated2,6,12,13,14. By changing the chemical makeup of interleaved charge-reservoir layers, electrons can be added to or removed from the CuO2 planes, resulting in the suppression of the antiferromagnetic insulating state of the parent compound2. As the doping level reaches a critical value, superconductivity appears and its transition temperature (Tc) grows to a maximum on doping to an optimal one, then declines for higher doping and finally vanishes at the maximum doping level2,4,7,9,15. It is important to recognize that once the superconducting state is completely suppressed by chemical doping, the material undergoes a quantum phase transition from a superconducting state to a metallic state16,17,18. However, detailed experimental studies of the breakdown of the superconducting state in cuprates are still lacking, and they may be crucial for understanding how the superconducting state melts into or emerges from its neighbouring ground states.

Pressure is an alternative method of tuning the superconductivity beyond the chemical doping or external magnetic field, and it can provide significant information on the evolution of superconductivity, electronic state and crystal structure without changing the chemical composition. On the other hand, it can also provide valuable assistance in the search for superconductors with higher values of Tc at ambient pressure by the substitution of smaller ions19. A notably successful application of this strategy leads to the discoveries of important cuprate- and Fe-based superconductors10,20,21. Therefore, high-pressure studies on superconductivity can not only help the search for new superconductors but also provide a deeper understanding of the correlation between the superconducting state and its neighbouring normal or ground state22,23,24,25,26. To reveal how the superconducting state or non-superconducting state develops—a central issue for understanding the high-Tc superconductivity in cuprates, we performed a series of high-pressure investigations by employing our newly developed state-of-the-art technique—combined in situ high-pressure measurements of the resistance and alternating current (a.c.) susceptibility for the same sample at the same pressure. We studied samples that have been investigated broadly by a variety of methods24,27,28,29,30,31, namely, the under-doped (UD), optimally doped (OP) and over-doped (OD) Bi2Sr2CaCu2O8+δ (Bi2212) superconductors with two CuO2 planes in a unit cell.

Figure 1 shows the results of temperature versus in-plane resistance at different pressures for the UD sample with Tc = 74 K (Fig. 1a,d), the OP sample with Tc = 91 K (Fig. 1b,e) and the OD sample with Tc = 82 K (Fig. 1c,f). It is found that the onset Tc of these samples exhibits the same high-pressure behaviour: a slight increase initially and then a monotonous decrease on elevating pressure until it is not detectable. Subsequently, an unexpected insulating-like state appears at pressure (Pi) of 34.3 GPa for the UD sample, 39.9 GPa for the OP sample and 42.2 GPa for the OD sample. Further, the insulating-like behaviour appears when the pressure is higher than Pi (Fig. 1a–f), which is a grand surprise because one naively expects that by increasing pressure, the bandwidth should widen and the system should become more metallic. We repeated the measurements on new samples and proved that the results are reproducible (Supplementary Fig. 2). Moreover, we found that the transition from the superconducting state to an insulating-like state is reversible when the pressure is released. As shown in Supplementary Fig. 5, the superconductivity with a zero-resistance state reappears in the sample released from the insulating-like state and a metallic normal state appears. In addition, our careful inspection on the sample recovered from 41.6 GPa, by a scanning electronic microscope, demonstrates that no crack is found (Supplementary Fig. 4). These results not only exclude the possibility that the insulating-like state is associated with some pressure-induced cracks but also provides a reasonable explanation on the reversible superconducting transition with a zero-resistance state.

Fig. 1: Temperature dependence of in-plane resistance for Bi2Sr2CaCu2O8+δ (Bi2212) at different pressures.
figure 1

a,d, Plots of temperature versus resistance with linear (a) and log (d) scales for the UD superconductor in the pressure range of 1.5–36.2 GPa. b,e, OP sample with linear (b) and log (e) scales in the pressure range of 0.7–41.2 GPa; the two-step superconducting transition demonstrates a crossover from two-dimensional to three-dimensional superconducting phases in the pressure range of 4.9–23.1 GPa, which is in good agreement with previous studies26. c,f, OD sample with linear (c) and log (f) scales in the pressure range of 1.0–49.0 GPa. The three kinds of samples display the same behaviour of an insulating-like state above pressure Pi.

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The combined high-pressure measurements of a.c. susceptibility and in-plane resistance were performed for the three kinds of samples mentioned above. The superconducting transitions of the samples detected by a.c. susceptibility can be clearly identified by the onset signal of the deviation from the almost-constant background on the high-temperature side (Fig. 2, blue plots) and the plunge of resistance to zero (Fig. 2, red plots). On compression to 34.3 GPa for the UD sample, 39.9 GPa for the OP sample and 42.2 GPa for the OD sample, all their resistances show an insulating-like behaviour (Fig. 2d,h,l, red plots) and also no diamagnetic signal is captured by the a.c. susceptibility measurements (Fig. 2d,h,l, blue plots). These results reveal that the pressure induces a quantum phase transition from a superconducting state to an insulating-like state in all these superconductors.

Fig. 2: In-plane resistance (R) and a.c. susceptibility (Δχ′) as a function of temperature (T).
figure 2

a–d, Plots of the UD superconductor. e–h, Plots of the OP superconductor. i–l, Plots of the OD superconductor. The blue lines in the figures are the data for Δχ′(T), whereas the red lines are the data for R(T). The red and blue arrows indicate the temperatures of the onset of superconducting transition detected by the resistance (Tc(R)) and a.c. susceptibility (Tc(a.c.)) measurements, respectively.

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We summarize the experimental results in the normalized pressure–Tc phase diagram (Fig. 3, left), which is established on the basis of the pressure–Tc phase diagrams of the UD, OP and OD Bi2212 samples (Fig. 3, right). The phase diagram for the three kinds of samples shows two distinct regions: the superconducting state (SC) and the insulating-like state (I), and demonstrates a universal quantum phase transition from the superconducting to the insulating-like states. It is shown that Tc displays a slight increase initially within a small pressure range, and then a continuous decrease with elevating pressure, in good agreement with the results reported previously32. At a critical pressure Pc and above (determination of Pc is shown in Fig. 3, inset), an insulating-like state emerges (Fig. 3, left) (details of the normalizing analysis are provided in Supplementary Fig. 11). It is worth noting that Pc for the superconductor–insulator transition increases with the increase in the doping level but does not follow the change in Tc (Fig. 3, top). These results demonstrate that the factors determining thermal stability (Tc) and quantum stability (Pc) of the superconducting ground state are not the same. These results raise two important questions: what is the factor that determines the value of Tc and what is the factor that controls the Pc value of the superconducting ground state? Further, how do they connect with each other? These questions are still open and call for further investigations from a broader perspective.

Fig. 3: Pressure–Tc phase diagrams for Bi2Sr2CaCu2O8+δ superconductors.
figure 3

Left, a normalized phase diagram that is built on the basis of the experimental phase diagrams (right). Right: phase diagrams established by the experimental results from the UD, OP and OD samples, together with the mapping information of temperature- and pressure-dependent R (shown in the colour scale). PTc-max and Pc stand for the pressures where Tc reaches the maximum and zero, respectively. Tc-atm stands for the superconducting transition temperature at ambient pressure. In the normalizing analysis, we define the pressure as PTc-max when (P – PTc-max)/(Pc – PTc-max) = 0 and define the pressure as Pc when (P – PTc-max)/(Pc – PTc-max) = 1. The results of the normalizing analysis for Tc/Tc-max versus (P – PTc-max)/(Pc – PTc-max) and Tins/Tc-max versus (P – PTc-max)/(Pc – PTc-max) show that the three kinds of samples display a universal quantum phase transition from the superconducting state to an insulating-like state. SC, M and I stand for superconducting state, metallic state and insulating-like state, respectively. The region of the M phase is determined by the critical value of R/R290 K, where the quantum phase transition occurs. Tc-R-onset and Tc-Δχ′-onset denote the onset temperatures of the superconducting transition detected by the resistance and a.c. susceptibility measurements, respectively. Tc-max and Tins are the maximum value of Tc and the characteristic temperature of the insulating-like transition, respectively. Pc represents the critical pressure from the superconducting state to insulating-like state (methods for determining Tins and Pc are shown in Supplementary Fig. 11). The details about determining error bars can be found in SI.

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To know whether the quantum phase transition discovered in this study is a common phenomenon beyond the Bi2212 superconductors investigated, we conducted the same measurements on the Bi2Sr1.63La0.37CuO6+δ (Bi2201) superconductor with one CuO2 plane as well as the Bi2Sr2Ca2Cu3O10+δ (Bi2223) superconductor with three CuO2 planes in a unit cell. The same phenomenon is also found in these superconductors (Supplementary Fig. 3), indicating that the observed quantum phase transition is universal in bismuth-bearing cuprate superconductors, regardless of the doping level and number of CuO2 planes in a unit cell.

These results impact our knowledge about cuprate superconductors that after the superconducting state is destroyed, the sample should show a metallic state because pressure generally increases the bandwidth. To clarify the possible origin that leads to the destruction of the superconducting state and the emergence of an insulating-like state under pressure, we carried out more experiments.

First, we conducted the high-pressure synchrotron X-ray diffraction measurements at 50 K for the OD sample on 4W2 beamline at the Beijing Synchrotron Radiation Facility. Our results indicated that there is no structural phase transition in the range of pressures up to 43.1 GPa, except that the volume of the lattice is apparently compressed (Supplementary Fig. 9). These results ruled out the possibility that the quantum phase transition from superconducting to insulating-like states connects with a pressure-induced structural phase transition.

Second, we measured the magnetoresistance (MR) at 4 K for the compressed UD, OP and OD samples that host the insulating-like state. The magnetic field was applied perpendicular to the a–b plane of these samples. As shown in Fig. 4a–c, the MR values of all the samples exhibit a positive effect. These results are reminiscent of what has been seen in disordered superconducting films. When the film samples move into an insulating state (driven by the magnetic field) from a superconducting state, a positive MR value indicating a superconducting fluctuation state exists on increasing the field33,34,35. These results lead us to consider that the positive MR effect may be a universal feature manifesting the existence of a superconducting fluctuation in the insulating state induced either by a magnetic field in the film samples or pressure in the bulk cuprates. As only a small MR value (of the order of 1%) is observed in the insulating-like state of our bulk cuprate superconductor, it implies that the superconducting fluctuation—if it indeed exists in these samples—should be weak.

Fig. 4: Magnetoresistance (MR) of the UD, OP and OD Bi2Sr2CaCu2O8+δ superconductors, and Hall coefficient of the OP sample under pressure.
figure 4

a–c, Plots of MR versus B for the UD (a), OP (b) and OD (c) samples measured at 4 K and 36.2 GPa for the UD sample, 41.2 GPa for the OP sample and 49 GPa for the OD sample. It is seen that all of them exhibit a positive magnetic effect. The red and beige arrows represent the directions of increasing and decreasing magnetic field, respectively. d, Pressure dependence of the Hall coefficient (RH) for the OD superconductor measured at 100 K.

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Third, we performed the high-pressure Hall coefficient (RH) measurements for the OD sample (Fig. 4d; measurement details can be found in Supplementary Fig. 1) and find that RH(P) decreases remarkably with increasing pressure up to approximately 18 GPa. Because the Hall resistance versus magnetic field displays a linear behaviour in the pressure range investigated (Supplementary Fig. 6), a typical feature of the single-band system—the decrease in RH(P) below 18 GPa—ought to be associated with the enhancement in carrier density. However, RH remains almost unchanged for pressures ranging from approximately 18.0 to 35.0 GPa and then shows a slow increase from approximately 35.0 to 48.3 GPa. No apparent change in RH(P) at Pc = 39.5 GPa implies that the total density of charge carriers seems to remain in a steady state with a very slow change when crossing quantum criticality. The reproducible result is also obtained in the Bi2201 superconductor (Supplementary Information).

It is noted that unlike the usual insulator, the low-temperature resistance in the insulating-like state rises way too slowly to be exponential. We attempted to fit the low-temperature resistance with exponential dependence and power law, but they failed (Supplementary Fig. 12). Slow rises of this kind have been found in low-temperature orthorhombic La2–xSrxCuO4, YiBa2Cu3O7–δ cuprates and La1–xMxOBiS2 (M = Ti or Th), which are perceived as fairly mysterious36,37,38.

There is, in fact, no precedence anywhere else for such a transition from a superconducting state to an insulating-like state, to the best of our knowledge. Therefore, some questions are naturally raised: why do itinerant superconducting electrons become localized after the quantum phase transition and what is the exotic pathway that results in the quantum phase transition? All the above are attractive issues in searching for new physics behind the pressure-induced quantum phase transition from a superconducting state to an insulating-like state, which deserves further investigation with other advanced experimental probes and sophisticated theoretical studies.