In a long corridor, a crowd of people tries to keep as far apart as possible. In a spacious hall, they would simply spread out, but here the walls squeeze them so tightly that they have to move single file, coordinating every step. Electrons in graphene layers twisted by a tiny angle behave in a similar way. Their motion is confined to nearly flat energy bands where strong interactions reign.

In such cramped conditions, electrons can organize in different ways. Sometimes they form a fractional insulator — a state where charge flows only along the edges, and inside, an order emerges reminiscent of a liquid of particles with fractional charge. But the authors of the new work discovered another participant: an anti-insulator, the mirror image of the former. Both states compete for electrons, yet their confrontation does not destroy the system; instead, it gives birth to something new. Two scattering channels, acting together, create an effective attraction between electrons, and the corridor suddenly turns into a superconductor — a material that transmits current with zero loss.

The researchers built a phase diagram — a map of states as a function of interaction strength and geometric parameters. Near the fractional insulator, they found a region of superconductivity, and at other settings, a charge density wave, where electrons gather into periodic clumps. Thus, geometry, usually staying behind the scenes, steps into the spotlight and dictates which collective behavior electrons will choose.