The mechanism of high-temperature superconductivity is one of the most challenging problems in condensed matter physics. It has remained unsettled for 35 years ever since Bednorz and Müller discovered high-temperature copper oxide (cuprate) superconductors in 1986. Consensuses are lacking even on some of its fundamental properties, such as the pairing symmetry.
Recently, a joint research team headed by Associate Professor Ding Zhang and Professor Qi-Kun Xue has managed to determine the pairing symmetry of a copper oxide superconductor. By fabricating ultrathin Josephson junctions with atomically flat interfaces, they found clear evidence for dominant s-wave pairing in Bi2Sr2CaCu2O8+x, which overturns the mainstream view of purely d-wave superconductivity in the same compound. It not only constitutes a major breakthrough in the study of copper oxide superconductors but also paves a definitive step toward understanding the mechanism of high-temperature superconductivity. Their study, entitled “Presence of s-wave pairing in Josephson junctions made of twisted ultrathin Bi2Sr2CaCu2O8+x flakes,” was published online in Physical Review X on July 15, 2021.
Superconductivity is one of the macroscopic quantum phenomena. The superconducting state can be described by quantum mechanical wave functions categorized as s-, p-, d-wave, etc., similar to the wave functions of a hydrogen atom. An s-wave is spatially isotropic, and its angular momentum has a quantum number of zero. By contrast, the wave functions of p-wave and d-wave are anisotropic, and their angular momenta are one and two, respectively.
In the case of dx2-y2-wave - the most relevant scenario for high-temperature copper oxide superconductors, for example, the superconducting wave function looks like a flower with four petals. Importantly, the wave function changes signs when changing from one petal to its nearest neighbor due to the variation in its superconducting phase. Conventional superconductors such as tin or aluminum host s-wave pairing symmetry, and although it remains debatable, most researchers believe that copper oxides are d-wave superconductors instead. Still, the scenario of d-wave pairing has been questioned by recent studies.
For instance, the research group of Professor Qi-Kun Xue found that, when measured directly on the superconducting layer of copper oxides by using scanning tunneling microscopy, the superconducting gap exhibits a U-shaped gap, which is typical for an s-wave superconductor. In comparison, a d-wave superconductor is expected to host a V-shaped gap. However, the most critical criterion to distinguish a d-wave from an s-wave is its above-mentioned sign-change property imposed by the superconducting phase.
In the past, phase-sensitive experiments were carried out by merging two or three superconductors in the plane of the “flower petals.” This type of study suffered from the uncertainty brought by the crystalline distortion and faceting at the boundary between the superconductors. By contrast, due to the two-dimensional layered structure of cuprate superconductors, stacking the superconductors vertically may give rise to a Josephson junction with an atomically flat interface. Taking Bi2Sr2CaCu2O8+x (BSCCO) – a typical copper oxide high-temperature superconductor – as an example, the crystal has a layered structure with alternating layers of superconducting copper oxides and non-superconducting bismuth/strontium oxides, as shown in Figure 1. Therefore, this type of junction could be an ideal platform for investigating the pairing symmetry.
Figure 1. Schematic drawing of the atomic structure of a twisted copper oxide Josephson junction. The blue, green, red, yellow, and black spheres represent Bi, Sr, Ca, Cu, and O atoms. The top half of a unit cell is rotated by 45° against the bottom half of a unit cell. The right inset shows that the phase in the s-wave pairing symmetry possesses the same sign in space.
Theoretically, if two d-wave superconductors are stacked vertically, the Josephson coupling strength starts to change once one superconductor is rotated along the vertical axis or in scientific jargon, twisted against the other one. It monotonically drops to zero when the rotation angle increases up to 45 degrees. By contrast, the s-wave superconductors show constant Josephson coupling, irrespective of the rotation angles.
The angular dependence of the Josephson current in the vertically stacked twist junction would therefore be a litmus test of the d-wave pairing symmetry. A few groups pursued this route around the millennium (nearly two-decade ago) without reaching a consensus: two experiments favored s-wave while one seemed to suggest d-wave. The culprit was the possibly reduced quality of such an artificial junction. Moreover, the Josephson coupling involved both the artificial junction and the intrinsic junctions within each constituent superconductor. A definitive study therefore requires the fabrication of atomically flat and macroscopic uniform single Josephson junctions.
The team led by Associate Professor Ding Zhang and Professor Qi-Kun Xue successfully fabricated the required high-quality Josephson junctions with accurate control over the twist angle. They found that these uniform junctions at various twist angles all exhibit a single tunneling branch behavior, suggesting that only the first half of a unit cell on both sides of the twisted flakes is involved in the Josephson tunneling process. Therefore, it avoids the complexity caused by intrinsic Josephson junctions.
Through these artificially and highly accurate controlled phase-sensitive measurements, they found that when one BSCCO flake is rotated by 45° against the other, Josephson coupling still exists, and the coupling strength of 45° and 0° are comparable. This behavior is consistent with s-wave pairing symmetry and questions the applicability of d-wave to BSCCO.
Upon further confirmation and possible extension to other cuprate superconductors, this study can be a turning point in the three-decade study of high-temperature superconductivity and paves a critical step toward nailing down the mechanism of high-temperature superconductivity. To further verify the existence of s-wave pairing, the team is working on pushing down to the atomic limit. They aim at fabricating the thinnest possible junction with just two monolayers of copper oxide superconductors.
The published work is a manifestation of scientific dedication and teamwork. Yuying Zhu, a Researcher at the Beijing Academy of Quantum Information Science (BAQIS) (former postdoctoral fellow at the Department of Physics, Tsinghua University), has been working on this project for four years without publishing a single first-authored paper. She and Dr. Menghan Liao of Tsinghua University are the co-authors of this work. By using the single crystals with the highest quality available worldwide from Prof. Genda Gu’s group at Brookhaven National Laboratory (BNL), Yuying Zhu and Menghan Liao fabricated over 800 samples and tested more than 300 Josephson junctions with different twist angles. To verify the quality of the artificial junctions, it is necessary to characterize the interface down to the atomic scale. This task was completed by Prof. Lin Gu’s group at the Institute of Physics (IOP), Chinese Academy of Sciences (CAS). Dr. Qinghua Zhang, as the co-first author of this work and a member of Prof. Lin Gu’s group, carried out detailed structural characterization with dozens of junctions and revealed the atomically flat nature of the interfaces over a macroscopic scale. Ph.D. candidates Yaowu Liu, Zhonghua Bai, and Jin Zhang of Tsinghua University also contributed to this work. Other collaborators include Prof. Shuaihua Ji (Tsinghua), Prof. Kaili Jiang (Tsinghua), Prof. Xucun Ma (Tsinghua), Prof. Hongyi Xie (BAQIS), Dr. Fanqi Meng (IOP), Dr. Ruidan Zhong (BNL), and Dr. John Schneeloch (BNL).
This work was financially supported by the Ministry of Science and Technology (MOST) of the People’s Republic of China, the National Natural Science Foundation of China (NSFC), the State Key Laboratory of Low Dimensional Quantum Physics at Tsinghua University and the Beijing Advanced Innovation Center for Future Chips (ICFC).
Paper link: https://doi.org/10.1103/PhysRevX.11.031011
