A Working theory of high temperature superconductors finds magnetism as the quantum glue and is able to predict properties

Physicists have identified the “quantum glue” that underlies a promising type of superconductivity — a crucial step towards the creation of energy superhighways that conduct electricity without current loss.

Superconductivity arises when two electrons in a material become bound together, forming what is called a Cooper pair. Groundbreaking experiments performed by Freek Massee and Milan Allan in Davis’s group were analyzed using a new theoretical framework developed at UIC by Morr and graduate student John Van Dyke, who is first author on the report. Their results pointed to magnetism as the force underlying the superconductivity in an unconventional superconductor consisting of cerium, cobalt and indium, with the molecular formula CeCoIn5.

“For a long time, we were unable to develop a detailed theoretical understanding of this unconventional superconductor,” said Morr, who is principal investigator on the study. Two crucial insights into the complex electronic structure of CeCoIn5 were missing, he said: the relation between the momentum and energy of electrons moving through the material, and the ‘quantum glue’ that binds the electrons into a Cooper pair.

PNAS – Direct evidence for a magnetic f-electron–mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5

Those questions were answered after the Davis group developed high-precision measurements of CeCoIn5 using a scanning tunneling spectroscopy technique called quasi-particle interference spectroscopy. Analysis of the spectra using a novel theoretical framework developed by Morr and Van Dyke allowed the researchers to extract the missing pieces of the puzzle.

The new insight allowed them to explore the 30-year-old hypothesis that the quantum glue of superconductivity is the magnetic force. Magnetism is highly directional, Morr said. “Knowing the directional dependence of the quantum glue, we were able, for the first time, to quantitatively predict the material’s superconducting properties using a series of mathematical equations,” he said. “Our calculations showed that the gap possesses what’s called a d-wave symmetry, implying that for certain directions the electrons were bound together very strongly, while they were not bound at all for other directions,” Morr said.

Directional dependence is one of the hallmarks of unconventional superconductors. “We concluded that magnetism is the quantum glue underlying the emergence of unconventional superconductivity in CeCoIn5.”

The finding has “lifted the fog of complexity” surrounding the material, Morr said, and was only made possible by “the close collaboration of theory and experiment, which is so crucial in advancing our understanding of complex systems.” “We now have an excellent starting point to explore how superconductivity works in other complex material,” Morr said. “With a working theory, we can now investigate how we have to tweak the system to raise the critical temperature — ideally, all the way up to room temperature.” –


In heavy-fermion materials, the magnetic moment of an f-electron atom, such as Ce, is screened via the Kondo effect resulting in the splitting of a conventional light band into two heavy bands within few millielectron volts of the Fermi energy. For decades it has been hypothesized that Cooper pairing and superconductivity of the resulting heavy electrons are mediated by the f-electron magnetism. By extracting the magnetic interactions of CeCoIn5 from heavy-fermion scattering interference, and by then predicting quantitatively a variety of characteristics expected for unconventional superconductivity driven by them, we provide direct evidence that the heavy-fermion Cooper pairing in this material is indeed mediated by f-electron magnetism.


To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands Eα,βk with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5 then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.

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