A thin film of zirconium nitride lies on a magnesium oxide substrate. Its thickness is two-tenths of a micron, like a spider's web, but inside it quantum life is boiling. When cooled to half a kelvin, superconductivity does not disappear all at once: it breaks up into rare islands that still hold on amid the disorder.

This disorder is created by zirconium vacancies and extra nitrogen atoms. They break the perfect lattice, and the superconducting state cannot cover the entire sample. What remains are isolated regions, like puddles after rain. Around them is normal metal, which does not conduct current without resistance.

Measuring the resistance in a magnetic field, the researchers noticed that the curves for different temperatures do not converge at a single point, but spread into a broad zone. Such a signature indicates a Griffith singularity. But the scaling, the law by which resistance depends on field and temperature, turned out to be two-dimensional. As if the superconducting islands lined up in flat sheets, even though the material itself is three-dimensional.

The effective critical exponent zν grew with decreasing temperature and diverged toward zero. Its dependence on the field was described by an activation law with an exponent of 0.7–0.8, close to the value of 0.61 from simulations for two-dimensional systems. The data fell onto two branches in activation scaling coordinates, as expected for a plane.

The rare superconducting regions in the three-dimensional material apparently connect into a percolation network, like paths between puddles. This network is effectively two-dimensional, so the scaling also yields two dimensions. The sea of disorder did not swallow the islands: it linked them into a thin conducting film inside the volume.

Today this is pure knowledge. It deepens the understanding of quantum phase transitions in disordered superconductors, but direct applications are not yet visible. However, it is now clear that even in the cubic lattice of zirconium nitride, disorder can draw two-dimensional pictures. Islands in the sea are not just a metaphor, but an accurate portrait of a quantum state.