Physicists Heated the Electrons in Twisted Graphene by 20 Degrees While the Crystal Around Them Stayed Near Absolute Zero. The Resistance Jumped by Thousands of Ohms Anyway, Which Means the Electrons Are Blocking Themselves.

When a metal warms up, its electrical resistance usually goes up too, and physicists have argued for a century about why. Are the current-carrying electrons being scattered by vibrations of the atomic lattice, or are they crashing into one another? A standard measurement cannot say, because heating a sample heats the electrons and the crystal together, and the two fingerprints land on top of each other in the same resistance curve.

Researchers at the National University of Singapore's Institute for Functional Intelligent Materials have now pulled the two apart in twisted bilayer graphene, the two-sheet carbon stack that hosts superconductivity when the layers are rotated by about 1.1 degrees. In a paper published Aug. 13 in Nature Communications, the team used terahertz radiation to heat the electrons alone while leaving the lattice almost untouched. The resistance climbed by several kilohms in devices near the magic angle. The electrons, in other words, were getting in their own way.

"Conventional transport measurements heat the electrons and the lattice together, so their fingerprints are superimposed," said Denis Bandurin, the assistant professor who led the study. "We wanted to separate those two temperatures and ask what the electrons themselves were doing."

The team built tiny bar-shaped devices of twisted graphene sandwiched in insulating hexagonal boron nitride, with graphite gates to dial the number of charge carriers and metal antennas to funnel 0.14-terahertz radiation into the carbon. Each photon at that frequency carries just 0.6 millielectronvolts, far too little to kick electrons between energy bands. Instead the radiation jostles the carriers already present. They share the energy among themselves within femtoseconds and settle into a hot electronic state before any meaningful heat leaks to the lattice. At full power the electrons reached about 20 kelvin above the crystal, which was held near 2 kelvin. Separate heat-flow tests capped the lattice warming below 1 kelvin, and electrical-noise measurements confirmed the two systems stayed thermally decoupled.

The comparison with a control device made from a single sheet of ordinary graphene is what gives the result its force. Heating the single sheet's electrons produced almost no change in resistance, exactly as expected when phonons, the lattice vibrations, are what limit the current. In twisted graphene, the resistance shot up. "When the lattice stays cold and the resistance still rises sharply, the response is tied primarily to the hotter electronic system," said doctoral student Artur Shilov, the paper's first author.

A second finding was stranger. In devices twisted farther from the magic angle, resistance rose with the square of temperature, the classic signature of electron-electron collisions in a Fermi liquid, at carrier densities as low as 100 billion per square centimeter. That should not happen. Electrons colliding in a clean metal conserve their total momentum, like billiard balls on a frictionless table, so their collisions alone cannot slow the current. Something has to absorb momentum, either the lattice through umklapp scattering or collisions between different carrier bands, and at such dilute densities both of those channels are geometrically closed off.

The team's explanation leans on what makes twisted graphene odd. Its Dirac-like bands break Galilean invariance, so velocity and momentum are no longer simply proportional, and the moiré pattern leaves electrons scattered across several distorted "valleys" in the band structure. Collisions between valleys, the researchers propose, can change electron velocities enough to sap the current even while total momentum is conserved. Theory led by Dmitrii Maslov at the University of Florida, with Joshua Covey and Alessandro Principi of the University of Manchester, predicted a T-squared coefficient between 0.005 and 0.5 ohms per kelvin squared depending on screening. The measured value, about 0.1, sits inside that window.

"We are proposing a mechanism that is compatible with both the band structure and the size of the observed effect," Maslov said. "The microscopic picture is not closed. The method helps us rule out some explanations and shows us where the remaining question lies." The technique should transfer to other moiré materials and low-density quantum systems where the two kinds of heating have never been told apart.