When cooled strongly, a uranium-telluride crystal stops resisting current. Before that happens, at a slightly higher temperature, its resistance can still be measured — and it tells about the shape of the invisible paths along which electrons run.
These paths form a surface in momentum space — like a map showing all allowed velocities of particles. For most metals, such a map looks like a smooth sheet. For uranium-telluride, it turned out to be wavy: the edges of the sheet are raised and lowered, like corrugated cardboard. When the magnetic field is tilted, electrons running along this corrugated surface alternately speed up and slow down — and the metal's resistance oscillates steadily.
The authors built a model of the surface from quantum calculations and solved the equation describing how electrons scatter off the crystal lattice. It turned out that the calculated resistance oscillations almost exactly reproduce recent measurements: when the field is tilted away from the crystal axis, the resistance first rises, then falls, then rises again. The match is direct proof that the surface is indeed wavy, not smooth.
The model also yields another conclusion: the current is carried mainly not by electrons but by holes — empty spots left by electrons. These holes scatter off the lattice less often and therefore travel farther. To test this, the physicists calculated how the Hall voltage (the transverse response to current and field) should change when the field is tilted. If a future experiment shows the predicted pattern, the hole hypothesis will be confirmed.
The corrugated Fermi surface (the surface of allowed electron states) resembles a sheet of corrugated cardboard: if you run your finger over it, you can feel repeating bumps. In a metal, such bumps make electrons periodically change speed as the magnetic field rotates.
In Greg Egan's novel 'Schild's Ladder', physicists explore exotic states of matter where electron surfaces acquire unusual topology — somewhat like the wavy surface of uranium-telluride.