A crystal is like a row of soldiers on a parade ground: every atom is in its place, and electrons march through it in neat waves. An amorphous material is like a crowd at a train station, where there is no order, just a jostling throng. In such a crowd, an electron usually gets stuck quickly, like a person trying to push through a dense mass of people.
In the new experiment, researchers took a two-dimensional sheet of carbon atoms bonded into a disordered network, monolayer amorphous carbon, and measured how electronic states are distributed within it. At low energies, electrons indeed get trapped: their waves decay within a few atoms. But at the center of the energy band, exactly at zero energy, a strange state emerges: the electron is not tied to a location, yet it does not propagate as in a crystal. It resembles a swimmer in a sea where waves chaotically diverge and converge, creating patches of calm water and zones of strong currents.
The authors suggest that this state is protected by a hidden symmetry that survives even in complete disorder. In mathematics, it is described by the Wess–Zumino–Witten topological term, but the essence is simpler: in a network of sp²-bonded carbon, a semblance of chirality randomly survives. It's as if in a crowd, each person could turn only in one direction. Such a condition is enough to keep electrons from getting stuck at the center of the spectrum.
This work shows for the first time that even in a completely disordered two-dimensional system, a critical point can exist where electrons are nearly free. Previously, such behavior was seen only in crystals with impurities, where order still exists. Here, there is no order at all, and yet an island of conductivity survives.
Monolayer amorphous carbon is the same carbon as in graphite or graphene, but its atoms are arranged without any pattern, like scattered coins. It remains strong and flexible, and its electronic properties can be tuned by the degree of disorder.