In a chunk of magnet, an electron behaves like a ship with a heel: even in dead calm, its trajectory curves to the side. This is the anomalous Hall effect — motion with a transverse drift without an external magnetic field.

Previously, it was thought that it all came down to how the electron's own rotation (spin) affects its motion. But the theories of Schrödinger and Pauli missed a deeper reason. The full description by Dirac in fundamental physics shows that the electron itself possesses a built-in path curvature (Berry curvature). It’s as if a vessel had an asymmetric hull and couldn’t sail straight.

The magnitude of the heel is given by the constant 1/(2m²c²), where m is the electron mass, c is the speed of light. In magnetically ordered crystals, where all spin-"compasses" point the same way, time symmetry is broken. This creates an additional electric field: that very anomalous signal. Surprisingly, such curvature exists even for a stationary electron. Practically, it promises electronics without bulky magnets: current can be controlled using the material’s internal curvature.