A team from Institut Quantique has identified what appears to be a new quantum limit for electrons.
Photo : Photo : Martin Blache - UdeS
Published today in the journal Nature, the study co-led by Professor Louis Taillefer reveals that, in some metals, the time that elapses between two successive electron collisions is given by Planck’s constant – the fundamental unit of the quantum world.
In principle, the resistance of a metal to the passage of an electric current is a well understood physical phenomenon. At low temperatures, it is partly caused by the collisions of electrons with each other, which leads to the loss of some of the energy they carry. It’s a bit like two bumper cars losing speed when they collide. The standard theory predicts that the electrical resistance decreases as the square of the temperature when temperature tends to absolute zero.
But it turns out that in some so-called “strange” metals, resistance varies linearly with temperature, which is quite unexpected.
“It’s very moving, this mystery,” says Louis Taillefer. “This line is superbly simple – except that it shouldn’t exist! Observed with my own eyes here in Sherbrooke, first in a copper oxide and then in an organic conductor, linear resistance has never ceased to fascinate me. Because the linearity is perfect, down to T = 0, we sense that we are touching something deep.”
In 2019, Taillefer’s team discovered, using a simple model, that the time between one collision and the next for an electron is the same for all copper oxides (“cuprates”) showing this linear resistance. This universal time is determined by Planck’s constant divided by the thermal energy, and that’s all.
“This universal aspect, linked to Planck’s constant, shows that we are touching on something fundamental,” adds the researcher.
It was still necessary to demonstrate by direct measurement that this time is indeed “Planckian”. This is what Taillefer’s team has just done, in collaboration with Prof. Brad Ramshaw’s team at Cornell University, as described in their article Linear-in temperature resistivity from an isotropic Planckian scattering rate published this week. To do this, they placed a cuprate sample in an intense magnetic field to deflect the path of electrons in this strange metal, and measured the variation of the resistance, directly related to the collision time of electrons.
Gaël Grissonnanche carried out this project first as a postdoc at Sherbrooke and then as a postdoc at Cornell. The measurements were performed in the strongest static magnetic field in the world, at the National High Magnetic Field Lab in Tallahassee, USA.
“It was a real tour de force. Before Gaël, we had never done this kind of measurement.” explains Prof. Taillefer. “He achieved not only the highly accurate experimental measurements, with PhD students Yawen Fang (Cornell) and Anaëlle Legros (Sherbrooke), but also the elaborate data analysis, with his postdoc colleague Simon Verret (Sherbrooke), which allowed them to extract the collision time.”
“This is an experimental technique that I have been developing for many years now,” said Brad Ramshaw, an Assistant Professor at Cornell University who co-led the study, “but it was Gaël who really took it to the next level. There is enormous complexity in the level of analysis that goes into this experiment, but out the other side emerges such a simple and intuitive result. It’s really physics at its best – beautiful simplicity from great complexity.”
The time that Grissonnanche and collaborators extracted not only has the Planckian value, but this holds for all directions of electron motion – it is said to be isotropic.
“ The “Planckian” time is very short or “fast” if you prefer, it is the fastest time allowed by quantum mechanics. What we are showing today is that in a strange metal, no matter which direction the electrons choose to travel, they undergo collisions at the most intense rate possible, they have no way to escape. This was as dazzling as it was unexpected, because there is nothing isotropic about the other properties of these materials. This appeared to us as a missing piece at the heart of this phenomenon,” explains Gaël Grissonnanche. “It is only through this isotropy that we can explain the universal nature of the phenomenon in the different families of strange metals. Another fascinating aspect is that although in this study we are focusing on the infinitely small, it turns out this same Planckian time also seems to apply to black holes – huge objects!”
This research was done in a close collaboration between Sherbrooke and Cornell, fostered by CIFAR and its Quantum Materials Program, of which both Taillefer and Ramshaw are part.
“The beautiful part of this story is that this success is the result of a tremendous collaborative effort over several years with impeccable mechanics. It began with the bringing together of the expertise of the Quebec group and the American group within CIFAR, and it was done with passionate students and postdocs who were able to play their part wonderfully within this grand project,” says Gaël Grissonnanche. “Personally, I remember the incredible opportunity to have shared a whole year with my colleague and friend Simon Verret, a postdoc in Prof. André-Marie Tremblay’s group in Sherbrooke, a year during which we built all the algorithmic machinery necessary to extract the juice from our experiments. Such a rapprochement between theorist and experimentalist is rare but so fruitful”.
Ramshaw says that their use of this “algorithmic machinery” is just getting started. “One of the biggest surprises for those of us working in the field is that this approach to the data analysis works at all. This opens up new ways to solve previously unsolvable problems—something that Gaël is already working on for the next generation of experiments.”
This research was supported in part by the Canada First Research Excellence Fund, CIFAR, the Natural Sciences and Engineering Research Council of Canada (NSERC), the Gordon and Betty Moore Foundation’s EPiQS Initiative, the National Science Foundation and the European Research Council.