An old law still holds for quirky quantum materials

This surprising result is important for understanding unconventional superconductors.


The thermal-to-charge conductivity ratio of various materials is temperature-proportional at absolute zero. This phenomenon is known as the Wiedemann-Franz law.

This so-called Wiedemann-Franz law has remained valid, except in quantum materials, where electrons clump together into an electron soup instead of acting as individual particles. According to experimental observations, there is a significant deviation from the 170-year-old law in these quantum materials.

According to a theoretical argument presented by physicists at Stanford University, the University of Illinois, and the Department of Energy’s SLAC National Accelerator Laboratory, the law should apply roughly to one particular class of quantum material: copper oxide superconductors, or cuprates, which conduct electricity without losing any of it at relatively high temperatures.

Recent work suggests that the Wiedemann-Franz rule should still roughly hold if one looks exclusively at the electrons in cuprates. They propose that other variables, such as vibrations in the atomic latticework of the material, could explain experimental results that break the rule.

According to Wen Wang, the paper’s primary author and a Ph.D. candidate at the Stanford Institute for Materials and Energy Sciences (SIMES) at SLAC, this unexpected finding is crucial to our knowledge of other quantum materials and unconventional superconductors.

Wang said, “The original law was developed for materials where electrons interact with each other weakly and behave like little balls that bounce off defects in the material’s lattice. We wanted to test the law theoretically in systems where neither was true.”

For this study, scientists ran simulations based on the Hubbard model. The Hubbard model is now a crucial tool for modeling and explaining systems where electrons stop functioning independently and work together to cause surprising phenomena.

The findings demonstrate that the electronic and thermal conductivity ratio approaches the Wiedemann-Franz law’s predictions when electron transport is the only factor considered.

Wang said, “So, the discrepancies that have been seen in experiments should be coming from other things like phonons, or lattice vibrations, that are not in the Hubbard model.”

SIMES staff scientist and paper co-author Brian Moritz said, “Although the study did not investigate how vibrations cause the discrepancies, somehow the system still knows this correspondence between charge and heat transport amongst the electrons. That was the most surprising result.”

“From here, maybe we can peel the onion to understand more.”

Journal Reference:

  1. Wen Wang, Jixun Ding, Yoni Schattner et al. The Wiedemann-Franz law in doped Mott insulators without quasiparticles. Science. DOI: 10.1126/science.ade3232


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