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 from the University of Groningen after an in-depth review of recent literature on metals. They analyzed over 30 metals and show that a simple formula can provide a more systematic classification of metals. Their analysis was published in Physical examination B August 29.
Metals conduct electricity, but not all in the same way. Scientists differentiate between several classes of metals with names such as “correlated”, “normal”, “strange” or “ad”. Metals in these classes differ, for example, in how their resistivity reacts to increasing temperatures. “We were interested in metals that could go from conductor to insulator and vice versa,” explains Beatriz Noheda, professor of functional nanomaterials at the University of Groningen. She is Scientific Director of the CogniGron Research Center, which develops materials-centric systems paradigms for cognitive computing. “To this end, we would like to make materials that can not only be insulators or conductors, but can also change between these states.”
By studying the literature on the resistivity of metals, she and her colleagues found that the demarcation between the different classes of metals was not clear. “So we decided to look at a large sample of metals.” Qikai Guo, a former postdoctoral researcher in the Noheda team and now at the School of Microelectronics at Shandong University, China, and their colleagues at the University of Zaragoza (Spain) and CNRS (France) used the change in resistivity with increasing temperatures as a tool to compare over 30 metals, partly based on literature data and partly based on their own measurements.
“The theory states that the resistivity response is driven by electron scattering and that there are different scattering mechanisms at different temperatures,” says Noheda. For example, at very low temperature, there is a quadratic increase, which would be the result of electron-electron scattering. However, some materials (“strange” metals) exhibit strictly linear behavior that is not yet understood. Electron-phonon scattering was thought to occur at higher temperatures, resulting in a linear increase. However, diffusion cannot increase indefinitely, which means that saturation must occur at a certain temperature. “Yet, some metals show no saturation in the measurable temperature range and these have been labeled as ‘bad’ metals,” says Noheda.
When analyzing the responses of different types of metals to increasing temperatures, Noheda and his colleagues encountered something unexpected: “We could fit all datasets with the same type of formula.” This turned out to be a Taylor expansion, in which the resistivity r is described as r = r0 + One1T+A2J2 + One3J3…, where T is the temperature, while r0 and different A values are different constants. “We found that just using a linear term and a quadratic term produces a very good fit for all metals,” says Noheda.
In the article, it is shown that the behavior of different types of metals is determined by the relative importance of A1 and one2 and by the magnitude of r0. Noheda says, “Our formula is a purely mathematical description, without any physical assumptions, and depends on only two parameters.” This means that the linear and quadratic regimes do not describe different mechanisms, such as electron-phonon and electron-electron scattering, they simply represent the linear (by incoherent dissipation, where the phase of the electron wave is changed by scattering) and non-linear (where the phase is unchanged) coherent contributions to scattering.
In this way, a formula can describe the resistivity of all metals, whether normal, correlated, bad, strange or otherwise. The advantage is that all metals can now be classified in a simpler and more transparent way for non-specialists. But this description also brings another reward: it shows that the low-temperature linear dissipation term (called Planckian dissipation) occurs in all metals. This universality is something that others have already hinted at, but this formula clearly shows that it is.
Noheda and his colleagues are not metal specialists. “We were coming from outside the field, which meant we had a fresh look at the data. What went wrong, in our opinion, was that people searched for meaning and mechanisms related to linear terms and quadratics. Perhaps, some of the conclusions extracted in this way need to be revised. It is well known that the theory in this area is incomplete. Noheda and his colleagues hope that theoretical physicists will now find a way to reinterpret some of the previous results thanks to the formula they found. “But in the meantime, our purely phenomenological description allows us to compare metals of different classes.”
Exotic electron-electron interactions deemed unnecessary for conduction in nickelates
Qikai Guo et al, Phenomenological classification of metals based on resistivity, Physical examination B (2022). DOI: 10.1103/PhysRevB.106.085141
Provided by the University of Groningen
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