Universal quantum phase transition from superconducting to insulating-like states in pressurized Bi2Sr2CaCu2O8+δ superconductors


 Copper oxide superconductors have been continually fascinating the communities of condensed matter physics and material sciences because they host the highest ambient-pressure superconducting transition temperature ( T c ) and mysterious physics 1–3. Searching for the universal correlation between the superconducting state and its normal state or neighboring ground state is believed to be an effective way for finding clues to elucidate the underlying mechanism of the superconductivity. One of the common pictures for the copper oxide superconductors is that a well-behaved metallic phase will present after the superconductivity is entirely suppressed by chemical doping 4–8 or application of the magnetic field 9. Here, we report the first observation of universal quantum phase transition from superconducting state to insulating-like state under pressure in the under-, optimally- and over-doped Bi2Sr2CaCu2O8+δ (Bi2212) superconductors with two CuO2 planes in a unit cell. The same phenomenon has also been found in the Bi2Sr1.63La0.37CuO6+δ (Bi2201) superconductor with one CuO2 plane and the Bi2.1Sr1.9Ca2Cu3O10+δ (Bi2223) superconductor with three CuO2 planes in a unit cell. These results not only provide fresh information on the cuprate superconductors but also pose a new challenge for achieving unified understandings on the mechanism of the high-Tc superconductivity.

understandings on the mechanism of the high-Tc superconductivity.
Although a huge body of experimental investigations has been made for the copper oxide (cuprate) superconductors since they were discovered for more than thirty years 10,11 , the correlation between the superconducting state and its normal state or the neighboring ground state is widely debated 2,6,[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 compound 2 . As the doping level reaches a critical one, superconductivity presents and its transition temperature (Tc) grows to a maximum upon doping to an optimal one, then declines for higher doping, and finally vanishes at a maximum doping level 2,5,7,9,15 . Tc-max are referred to as optimal-doped ones. It is important to recognize that once the superconducting state is completely suppressed by the chemical doping, the material undergoes a quantum phase transition from a superconducting state to a metallic state [16][17][18] . However, the detailed experimental studies on the breakdown of the quantum state in cuprates are still lacking, which may be crucial for understanding how the superconducting state melts into or emerges from its neighboring ground states.
Pressure is an alternative method of tuning superconductivity beyond the chemical doping or external magnetic field, and it can provide significant information on the evolution among 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 the superconductors with higher values of Tc at ambient pressure by the substitution of the smaller ions 19 . A notably successful application of this strategy leads to the discoveries of the important cuprate and Fe-based superconductors 11,20,21 . Therefore, high-pressure studies on superconductivity can benefit not only for searching new superconductors but also for deeper understandings on the correlation between the superconducting and its neighbor normal or ground states [22][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, a combined in-situ high-pressure measurements of the resistance and alternating current (ac) susceptibility for the same sample at the same pressure. The studied samples that have been investigated broadly by variety of methods [26][27][28][29][30][31] are the under-doped (UD), optimally-doped (OP) and over-doped (OD) Bi2Sr2CaCu2O8+ (Bi2212) superconductors with two CuO2 planes in a unit cell. Figure 1 shows the results of temperature versus in-plane resistance for the UD sample with Tc=74 K (Fig.1a), the OP sample with Tc=91 K (Fig.1b) and the OD sample with Tc=82 K (Fig.1c) at different pressures. It is found that the onset Tc of these samples exhibits the same high-pressure behavior: a slight increase initially and then a monotonous decrease upon elevating pressure until not detectable. Subsequently, an unexpected insulating-like state presents at a pressure (Pi) of 34.3 GPa for the UDdoped sample, 39.9 GPa for the OP sample and 42.2 GPa for the OD sample, respectively. And the insulating-like behavior becomes pronounced when the pressure is higher than the Pi, (Fig.1a-1c). It is a grand surprise because naively one expects that by applying pressure the bandwidth should increase and thereby the system should become more metallic, but instead it becomes insulating-like. We repeated the measurements on new samples and found the results are reproducible [see To investigate whether the insulating behavior observed is due to pressure-induced cracks in the material, we performed the experiments for the over-doped Bi2212 sample, and found a reversible transition between the superconducting state and the insulatinglike state (see Supplementary Information). These results rule out the possibility that the transition from a superconducting state to an insulating-like state is caused by cracks.
The combined high-pressure measurements of ac susceptibility and in-plane resistance were performed for the above three kinds of samples. As shown in Fig In order 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+ (Bi2201) superconductor with one CuO2 plane and the Bi2Sr2Ca2Cu3O10+ (Bi2223) superconductor with three CuO2 planes in a unit cell. The same phenomenon is also found in these superconductors (see Supplementary Information), indicating that the observed quantum phase transition is universal in these bismuth-bearing cuprate superconductors, regardless of the doping level and the number of CuO2 planes in a unit cell.
These results impact our knowledge about the cuprate superconductors that, after the superconducting state is destroyed, the sample should show a well-behaved 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 the 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 beamline 4W2 at the Beijing Synchrotron Radiation Facility. Our results indicated that there is no structural phase transition in the range of pressure up to 43.1 GPa, except that the volume of the lattice is apparently compressed (see Supplementary Information). 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 ab-plane of these samples. As shown in Fig.4a-c, the MR of all the samples exhibits a positive effect, the in-plane resistance increases upon elevating magnetic field. Considering that the MR is very weak (~1%) and the appearance of the insulating-like state is close to the superconducting-insulating transition, we presume that the origin of the positive MR may be related to the superconducting fluctuation.
Third, we performed the high-pressure Hall coefficient (RH) measurements for the OD sample (Fig.4d) and find that RH(P) decreases remarkably with increasing pressure up to ~18 GPa. Because the Hall resistance versus magnetic field displays a linear behavior in the pressure range investigated (Supplementary Information), a typical feature of the single band, the decrease of RH(P) below 18 GPa ought to be associated with the enhancement of carrier density. However, RH remains almost unchanged for pressures ranging from ~18 GPa to ~35 GPa and then shows a slow increase from ~35 GPa to 48.3 GPa. No apparent change in RH(P) at Pc =39.5GPa implies that the total density of charge carriers seems to remain in a steady state across the quantum criticality.
The reproducible result is also obtained in the Bi2201 superconductor (see Supplemental 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 fail [see