Physicists Looked Inside a Superconductor's 'Rivers of Charge' and Found the Pairs Are Made of Magnetic Defects Locked Like a Yin-Yang

For four decades, physicists have known that copper-oxide superconductors carry current with zero resistance at temperatures far higher than any conventional theory allows, and for nearly as long they have watched electrons in those materials organize themselves into stripes, which the late theorist Jan Zaanen called "rivers of charge" flowing between insulating banks. What nobody could say was whether the stripes helped or hindered the superconductivity, or what, precisely, was doing the pairing inside them. A team from the Beijing Computational Science Research Center, Beijing Normal University and Chongqing University now says it has an answer, published this week in Physical Review Letters.

"Looking at a stripe and seeing pairing is like hearing an orchestra and knowing the melody is beautiful, without knowing which instrument is playing it," said senior author Xue-Feng Zhang. "Our objective was simple but terrifying: look inside the stripe and identify the musician." The group, which Zhang said has been "obsessed" with the problem since 2023, simulated a single partially filled stripe in two standard models of cuprate physics, the extended Fermi-Hubbard model and the t-J model, using the density-matrix renormalization group, a numerical method that handles strongly interacting electrons in one and quasi-one dimension with high precision. They paired it with a "perfect sampling" technique borrowed from quantum gas microscopy experiments, which let them take snapshots of the simulated electrons the way an experimentalist photographs ultracold atoms in an optical lattice.

The musician turned out not to be an electron pair in the usual sense. "The pairing inside a stripe is carried by objects called spinon singlets, pairs of magnetic defects with opposite chirality that fit together like the two interlocking halves of a yin-yang symbol," Zhang said. A spinon is a disturbance in the pattern of electron spins on the lattice, a kind of topological kink in the magnetic order. Two of them with opposite handedness bind into a singlet, and that bound object carries the d-wave sign structure, the four-lobed cloverleaf pattern in which the pairing amplitude flips sign between perpendicular directions, that is the signature of cuprate superconductivity.

The critical test was to break it. When the researchers switched off the magnetic interaction that binds spinons together, the singlets dissolved and the d-wave pattern disappeared. When they restored the interaction, both came back. "This is strong evidence of causality, not just a beautiful coincidence," Zhang said. The implication, in his words, is that "stripes are not just passive backgrounds for superconductivity; they are active factories that produce the elementary pairing units." Science magazine listed the mechanism of high-temperature superconductivity among its 125 biggest open questions in 2005 and again in 2021.

The paper comes with a falsifiable prediction. In a follow-up preprint, the team calculates that scanning tunneling microscopy should see a subtle shift of two lattice constants between the positive-energy and negative-energy spatial patterns inside a stripe. "We have received preliminary positive feedback from experimental groups regarding this prediction," Zhang said. A more direct confirmation would come from cold-atom simulators, where ultracold atoms in optical lattices emulate the Hubbard model directly. "If an experimentalist can photograph a spinon singlet in an optical lattice, it would be the smoking gun that validates the entire scenario," he said.

What the work does not yet do is explain a bulk superconductor. A single stripe pairing locally is not the same as a macroscopic phase-coherent state across millions of stripes at finite temperature. "Turning that local dance into a global superconducting state is still the next mountain to climb," Zhang said, though he noted the simulations already show hints of spinon singlets tunneling between neighboring stripes, "which could be the bridge that turns local pairing into global superconductivity." Mapping that inter-stripe coherence is the group's next project.