Graphene, a sheet of carbon one atom thick, behaves like a calm water surface, until superconductivity appears. Then, unusual waves ripple across it, like the circles from a thrown stone: pairs of electrons move without friction. But in a special chiral state, these waves twist in one direction, like water swirling down a bathtub drain.
The authors calculated how these waves are affected by the curvature of the energy landscape — the Berry phase effect. Each quasiparticle carries a tiny magnetic compass, and the Berry curvature makes the needle turn as it moves. In rhombohedral graphene, the layers are shifted so that the energy relief is distorted, and quasiparticles can develop their own Fermi surface — a region in momentum space where they live. Then the familiar picture breaks down: thermal conductivity deviates from strict quantum steps, and transverse spin and orbital currents are sharply enhanced.
This anomalous transport of heat and spin is like a crowd in the subway that suddenly starts swirling into a vortex, even though each person is walking straight. In graphene, this vortex can be induced simply by passing a current or creating a temperature difference. This opens the way to devices where heat and magnetic moments are controlled without magnets — by the geometry of the material alone.
The Berry curvature is named after the English physicist Michael Berry, who in 1984 showed that a particle's wave function can accumulate a geometric phase when parameters are changed slowly. This idea led to the understanding of many anomalies in solids, including the quantum Hall effect.