A sheet of graphene one atom thick is twisted at a small angle, and it starts behaving like a layered pie with layers slightly rotated relative to each other. At a certain twist angle, this material becomes a superconductor: electrons begin to move in pairs, like dancers in a waltz, without losing energy. But what exactly happens inside has remained a mystery.

In the new work, scientists peered into this 'dance' using two different tools: tunneling spectroscopy, which takes a 'snapshot' of electronic states, and measurements of superfluid stiffness — how strongly the superconducting state resists changes. It turned out that electron pairs do not form a simple uniform sea but a density wave with finite momentum — a so-called pair density wave state. It's as if the dancers moved not in a circle but in waves rolling onto the shore.

Moreover, these same excited electrons affect superfluid stiffness: at low temperatures, it is suppressed roughly as the square of the temperature. The scientists predict that by changing the electron density or applying an electric field, one could enhance the residual current at zero voltage while simultaneously weakening the stiffness. This provides a direct way to test the theory in future experiments.