Electrons in metals try to behave like obedient motorists, but they end up
more like bumper cars. They may be reckless drivers, but a new Cornell-led
study confirms this chaos has a limit established by the laws of quantum
mechanics.
The team's paper, "T-Linear Resistivity From an Isotropic Planckian
Scattering Rate," written in collaboration with researchers led by Louis
Taillefer from the University of Sherbrooke in Canada, published July 28 in
Nature. The paper's lead author is Gael Grissonnanche, a postdoctoral fellow
with the Kavli Institute at Cornell for Nanoscale Science.
Metals carry electric current when electrons all move together in tandem. In
most metals, such as the copper and gold used for electrical wiring, the
electrons try to avoid each other and flow in unison. However, in the case
of certain "strange" metals, this harmony is broken and electrons dissipate
energy by bouncing off each other at the fastest rate possible. The laws of
quantum mechanics essentially play the role of an electron traffic cop,
dictating an upper limit on how often these collisions can occur. Scientists
previously observed this limit on the collision rate, also known as the
"Planckian limit," but there is no concrete theory that explains why the
limit should exist, nor was it known how electrons reach this limit in
strange metals. So Ramshaw and his collaborators set out to carefully
measure it.
"Empirically, we've known that electrons can only bounce into each other so
fast. But we have no idea why," said Brad Ramshaw, the Dick & Dale Reis
Johnson Assistant Professor in the College of Arts and Sciences, and the
paper's senior author. "Before, the 'Planckian limit' was just kind of
inferred from data using very simple models. We did a very careful
measurement and calculation and showed that it really is obeyed right down
to the fine details. And we found that it's isotropic, so it's the same for
electrons traveling in any direction. And that was a big surprise."
The researchers focused their study on a copper oxide-based high-temperature
superconductor known as a cuprate. Working with collaborators at the
National High Magnetic Field Laboratory in Tallahassee, Florida, they
introduced a sample of cuprate metal into a 45-tesla hybrid magnet—which
holds the world record for creating the highest continuous magnetic
field—and recorded the change in the sample's electrical resistance while
shifting the magnetic field's angle. Ramshaw's team then spent the better
part of two years creating numerical data analysis software to extract the
pertinent information.
Surprisingly, they were able to analyze their data with the same relatively
simple equations used for conventional metals, and they found the cuprate
metal's electrons obeyed the Planckian limit.
"This approach that we used was supposed to be too naïve," Grissonnanche
said. "For scientists in the field, it is not obvious a priori that this
should work, but it does. So with this new discovery, we have killed two
birds with one stone: we have extended the validity of this simple approach
to strange metals and we have accurately measured the Planckian limit. We
are finally unlocking the enigma behind the intense motions of electrons in
strange metals."
"It doesn't seem to depend on the details of the material in particular,"
Taillefer said. "So it has to be something that's almost like an overriding
principle, insensitive to detail."
Ramshaw believes that other researchers may now use this calculation
framework to analyze a wide class of experimental problems and phenomena.
After all, if it works in strange metals, it should work in many other
areas.
And perhaps those strange metals are a little more orderly than previously
thought.
"You've got these wildly complicated microscopic ingredients and quantum
mechanics and then, out the other side, you get a very simple law, which is
the scattering rate depends only on the temperature and nothing else, with a
slope that's equal to the fundamental constants of nature that we know," he
said. "And that emergence of something simple from such complicated
ingredients is really beautiful and compelling."
Such discoveries may also enable deeper understanding of the connections
between quantum systems and similar phenonmena in gravitation, such as the
physics of black holes—in effect, bridging the dizzyingly small world of
quantum mechanics and their "dual" theories in general relativity, two
branches of physics that scientists have been trying to reconcile for nearly
a century.
Reference:
Grissonnanche, G., Fang, Y., Legros, A. et al. Linear-in temperature
resistivity from an isotropic Planckian scattering rate. Nature 595, 667–672
(2021).
https://doi.org/10.1038/s41586-021-03697-8
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