Superconductivity is one of the most exotic quantum phenomena in nature. Superconductors conduct electricity without resistance and tend to expel magnetic fields. Hence, they hold the promise to revolutionize future power transmission and transportation technologies. While the superconductivity in many materials can be understood from the celebrated Bardeen-Schrieffer-Cooper theory that was formulated back in the 1950s, a class of superconductors, commonly referred to as unconventional superconductors, do not fall into the BCS paradigm. The compound Sr₂RuO₄ is an archetypal unconventional superconductor. However, despite nearly thirty years of intense research, the superconductivity in Sr₂RuO₄ remains an outstanding puzzle.

A research team led by Associate Researcher Wen Huang from the Shenzhen Institute for Quantum Science and Engineering (SIQSE) at the Southern University of Science and Technology (SUSTech) has made progress in unveiling the important role played by quantum geometry in Sr₂RuO₄, bringing hope of further narrowing down the symmetry of its superconducting order parameter.

Their study, entitled “Quantum-Geometry-Induced Anomalous Hall Effect in Nonunitary Superconductors and Application to Sr₂RuO₄”, has been published in Physical Review Letters, one of the most prestigious journals in physics.

The researchers aimed to elucidate the origin of the polar Kerr effect, wherein a linearly polarized light shone vertically on Sr₂RuO₄ samples gets reflected with a rotated polarization angle. This novel phenomenon is one of this material’s most distinguishing experimental signatures. Previously proposed mechanisms for this effect need to invoke either extrinsic defect scatterings or an intrinsic condition – the presence of a sizable interband Cooper pairing. However, the actual strength of the interband pairing is unknown for a weak coupling superconductor like Sr₂RuO₄.

This study shows that by virtue of the spin-orbit-coupling-enriched quantum geometry of the superconducting electrons, some special superconducting states can readily generate the intrinsic Kerr effect in the absence of the aforementioned conditions. Such superconducting states are characterized by an unequal pairing strength between spin-up electrons and that between spin-down electrons, and are referred to as nonunitary pairings. Thus, if the reported Kerr effect is of intrinsic origin, the superconductivity of Sr₂RuO₄ is likely limited to nonunitary states, of which there are only two types allowed by its crystallographic symmetry. The present study, therefore, provides an important perspective toward unraveling the decades-old puzzle in Sr₂RuO₄.

Figure 1. Two ingredients for realizing the intrinsic polar Kerr effect in Sr2RuO4 in the absence of interband Cooper pairing: nonunitary pairing and spin-orbit-coupling-enriched quantum geometry. Upper panel: nonunitary superconducting pairing, which is characterized by unequal strength of the pairing between spin-up electrons and that between spin-down electrons. Lower panel: quantum geometry as manifested in the interband velocity of the Bloch electrons in a multiband system.

Jia-Long Zhang, a postdoctoral fellow from the Hong Kong University of Science and Technology and visiting scholar at SIQSE, and Weipeng Chen, a postdoctoral fellow from SIQSE and currently a faculty member at Jinan University, are the co-first authors of the paper. Associated Researcher Wen Huang is the corresponding author, and other contributors include Hao-Tian Liu from SUSTech, Yu Li from the University of Chinese Academy of Sciences, and Zhiqiang Wang from the University of Chicago. 

This work was supported by National Natural Science Foundation of China (NSFC), Guangdong Science and Technology Department, Guangdong Provincial Key Laboratory, and the Shenzhen Science and Technology Program.

Paper link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.136001

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