How a Flat Band Makes a Pair of Electrons Tiny express
In a superconductor, electrons pair up like dancers holding hands. Usually, the distance between them, the pair size, depends on how fast they move and how strongly they are bound. But sometimes the dance floor almost disappears, and there's nowhere to move. This happens in materials with flat electronic bands: electrons nearly freeze, and the usual rules stop working.
Physicists have found a new way to measure the size of such pairs using the quadrupole moment — something like the charge distribution inside the pair. The big surprise: when time-reversal symmetry is broken (for example, by a magnetic field), the Berry curvature comes into play — a geometric property of the electron's wave, akin to the curvature of space for its internal state. It can squeeze the pair to the limit, setting the minimum possible size.
Applying the theory to rhombohedral graphene, a layered material made of carbon with flat bands, the scientists saw that it is precisely the Berry curvature that determines the pair size. The calculated values matched the coherence lengths known from experiments: about 30–50 nanometers. For comparison, that's hundreds of times smaller than the thickness of a human hair. Thus, the geometry of wave functions directly governs superconductivity at the microscopic level.
In rhombohedral graphene, the Berry curvature can make Cooper pairs so small that they would fit inside a virus.
In Peter Watts's novel Blindsight, superconducting carbon-based structures exist under extreme conditions — reminiscent of graphene systems where the geometry of electron waves plays a key role.