Electrons obey social distancing in 'strange' metals

A Cornell University-led collaboration has used state-of-the-art computational tools to model the chaotic behavior of Planckian, or "strange," metals. This behavior has long intrigued physicists, but they have not been able to simulate it down to the lowest possible temperature until now.

The team's paper, "Linear Resistivity and Sachdev-Ye-Kitaev (SYK) Spin Liquid Behaviour in a Quantum Critical Metal with Spin-1/2 Fermions," published July 22 in the Proceedings of the National Academy of Sciences. The study's lead author is doctoral student Peter Cha.

Leading the collaboration is Eun-Ah Kim, professor of physics in the College of Arts and Sciences, who is interested in the social phenomena of electrons and how they interact as a society, with all the complications that entails.

Like people, electrons have different innate tendencies. In metals, electrons are independently minded and mostly roam freely. In insulators, electrons are stuck in a fixed position. Between these metal and insulator phases exists the strange case of Planckian metals. In Planckian metals, electrons dissipate energy at the fastest possible rate allowed by the fundamental laws of quantum mechanics. They have a high level of chaotic behavior and electrical resistivity.

Imagine a congested road with slow-moving traffic. The vehicles are heading in the same general direction, but they are sluggish and their movement is restricted. This is the plight of electrons in Planckian metals. Now compare that with electrons in a superconductor, which is the most organized, coherent state possible, a superhighway with huge numbers of electrons rushing along in lockstep, without resistance or scattering. For more than three decades, scientists have been puzzled that Planckian metals can switch into high-temperature superconductors. This inexplicable behavior appears to be somehow related to the individualistic electrons' desire to distance themselves from each other.

"Just as we have social distancing recommendations at the order of our governor, electrons have social distancing recommendations at the order of Mother Nature," Kim said. "But exactly how this social distancing order resulted in this particular, maximally chaotic behavior has been a mystery. How do you go from the mandate of, okay, you're all repelling each other, to this particular form of chaotic, incongruent behavior? It suggests there is something in this very confusing state that is a seed for a very organized state."

Kim's research group collaborated with scientists at the Flatiron Institute, an internal research division of the Simons Foundation in New York City, who specialize in computational quantum physics. Together, they created the first-ever model of Planckian behavior down to the lowest possible temperature, absolute zero (zero degrees Kelvin or -273.15 degrees Celsius). This marks the quantum critical region when one state of matter transitions to another.

By adjusting the ratio between the electrons' urge to bounce around (kinetic energy) and the strong social interactions that lock the electrons into position according to their spins (interaction energy), which is essentially a mandate for social distancing, the researchers tuned the system to the verge of transition between an ordinary metal and an interaction-driven insulator. When the social distancing is stronger, the system enters a spin glass insulator state, in which immobile electrons are only represented by their loosely aligned spins. But when kinetic energy dominates, the system enters a Fermi liquid metal state.

"We found there is a whole region in the phase space that is exhibiting a Planckian behavior that belongs to neither of the two phases that we're transitioning between," Kim said. "This quantum spin liquid state is not so locked down, but it's also not completely free. It is a sluggish, soupy, slushy state. It is metallic but reluctantly metallic, and it's pushing the degree of chaos to the limit of quantum mechanics."

The model is minimalist by design, allowing the researchers to identify the most basic ingredients for Planckian metal behavior. This will provide a template for building more complicated models that can capture even more elusive phenomena, such as high-temperature superconductivity. And maybe even more than that.

"The universes and societies of electrons that we study are not only a subject of curiosity and intellectual satisfaction," Kim said. "They're also a subject that makes a difference in the society. We can change society -- revolutionize society -- by understanding new materials, new kinds of states. The discovery of semiconductors led to the transistor. And we cannot imagine what the world would be like today if there were no transistors."

The research was supported by the U.S. Department of Energy and the Simons Foundation.