Our theoretical understanding of how metals conduct electricity is incomplete. The current taxonomy seems too vague and contains too many exceptions to be convincing. This is the conclusion reached by materials scientists at the University of Groningen after a thorough study of the recent literature on metals. They analyzed more than 30 metals and showed that a simple formula could provide a more systematic classification of metals.Their analysis was published in *Physical Review B* August 29.

Metals conduct electricity, but not all conduct electricity in the same way. Scientists use names such as “relevant,” “normal,” “strange,” or “advertising” to distinguish several classes of metals. For example, metals in these classes differ in the way their resistivity responds to an increase in temperature. “We are interested in metals that can change from conductors to insulators and vice versa,” explains Beatriz Noheda, Professor of Functional Nanomaterials at the University of Groningen. She is the Scientific Director of the CogniGron Research Center, which develops materials-centric systems paradigms for cognitive computing. “To do this, we want to make materials that can not only be insulators or conductors, but can also change between these states.”

**unexpected**

While studying the literature on metal resistivity, she and her colleagues found that the boundaries between different classes of metals are not well defined. “So, we decided to look at a large number of metal samples.” Guo Qikai (former postdoctoral researcher in Noheda’s team, now at the School of Microelectronics, Shandong University, China) and colleagues from the University of Zaragoza (Spain) and CNRS (France) More than 30 metals were compared using the change in resistivity with increasing temperature as a tool, based partly on literature data and partly on their own measurements.

“The theory states that the resistivity response is determined by the scattering of electrons, and that different scattering mechanisms exist at different temperatures,” explains Noheda. For example, at very low temperatures, a secondary increase was found, said to be the result of electron-electron scattering. However, some materials (“strange” metals) exhibit strictly linear behavior, which is currently unknown. Electron-phonon scattering is thought to occur at higher temperatures, which results in a linear increase. However, scattering cannot increase infinitely, which means that saturation should occur at a certain temperature. “However, some metals do not exhibit saturation over a measurable temperature range, and these are called ‘bad’ metals,” Noheda said.

When analyzing the response of different types of metals to temperature increases, Noheda and her colleagues encountered something unexpected: “We could fit all datasets with the same type of formula.” It turned out to be a Taylor expansion, where The resistivity r is described as r = r_{0} + a_{1}T + A_{2}Ton^{2} + a_{3}Ton^{3}…where T is the temperature and r_{0} And the various A values are different constants. “We found that using only linear and quadratic terms was sufficient to produce very good fits for all metals,” explains Noheda.

**more transparent**

In the paper, it is shown that the behavior of different types of metals is determined by the relative importance of A_{1} and a_{2} and the size of r_{0}“Our formulation is a purely mathematical description, without any physical assumptions, and depends only on two parameters,” Noheda said. This means that the linear and quadratic schemes do not describe different mechanisms, such as electron-phonon and electron-electron Scattering, they simply represent the linear (through incoherent dissipation, where the phase of the electron wave is changed by scattering) and non-linear coherent (phase-invariant) contributions to scattering.

In this way, one formula can describe the resistivity of all metals – whether they are normal, correlated, bad, strange or otherwise. The advantage is that all metals can now be classified in a simple way that is more transparent to non-experts. But this description also has another payoff: it shows that a linear dissipation term at low temperatures, known as Planck dissipation, occurs in all metals. This generality is something others have already hinted at, but this formula makes it clear that it is.

Neither Noheda nor her colleagues are metal experts. “We come from outside the field, which means we have a whole new perspective on the data. In our view, what’s going wrong is people looking for meaning and linking mechanisms to linear and quadratic terms. Perhaps, some conclusions are based on this Theories extracted in this way need to be revised. Theories in this field are notoriously incomplete. Noheda and her colleagues hope that theoretical physicists will now find a way to reinterpret some of the previous results, thanks to the formula they discovered. “But at the same time, our purely phenomenological description does allow us to compare different classes of metals. ”

Exotic electron-electron interactions are not required for conduction in nickelates

**More information:**

Qikai Guo et al., Resistivity-Based Phenomenological Classification of Metals,

*Physical Review B*(2022). DOI: 10.1103/PhysRevB.106.085141

Courtesy of the University of Groningen

**Citation**: Metals Revisited Reveals a ‘Strange’ Similarity (September 7, 2022), Retrieved September 8, 2022, from https://phys.org/news/2022-09-fresh-metals- reveals-strange-similarity.html

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