Graphene, a two-dimensional carbon crystal, has long tantalized physicists with the hope of high-temperature superconductivity. Its electrons obey the relativistic equation of Paul Dirac, racing at tremendous speed, barely noticing each other. Yet this very “weightlessness” becomes a curse: at the charge neutrality point, where a Bose–Einstein condensate of Cooper pairs could arise, the density of states vanishes. To force electrons to pair up, an attraction so strong is required that it is unattainable in real materials. It seemed graphene was doomed to remain a perfect insulator of superconducting dreams.

The idea, recently proposed and backed by powerful numerical simulations, sounds paradoxical: to give birth to global quantum coherence, one must introduce chaos. Remove a few carbon atoms (vacancies) or attach hydrogen, and the electronic spectrum transforms. Instead of a smooth conical dispersion, a sharp peak in the density of states at the Fermi level emerges, as if electrons hit “reefs” and form a stagnant zone. This zone resembles a flat band, well-known from moiré heterostructures, but arises from disorder. The classical theories of John Bardeen and Lev Landau taught us to fear disorder as the enemy of coherence, yet here it becomes its creator. Imagine a spiderweb: a perfect sheet without a single tear is just a smooth film. But once holes appear, the threads around them begin to intertwine into a complex pattern. So too do the electronic wave functions around defects cease to be localized; they acquire a multifractal nature, extending across the entire sample. Their superposition forms an entangled network, reminiscent of a hologram: each defect carries an imprint of the whole crystal. In this quantum web, even an infinitely weak attraction forces electrons to pair up.

Self-consistent calculations based on the Bogoliubov–de Gennes equations, a kind of quantum-field detective, revealed: with a vacancy concentration of just 4%, the critical coupling constant drops fivefold, and the superconducting gap grows linearly with attraction, as in flat-band systems. Yet the most striking feature is that this gap is inhomogeneous: concentrated around defects, but the phase coherence is anchored across the entire lattice. The key to order from chaos lies in the geometric superfluid weight $D_s$—a purely quantum characteristic born not from kinetic energy but from the topology of the wave functions. In the web of defects, each thread quivers in unison with the overall vibration, and this dance persists up to temperatures of tens of kelvins, as predicted by the Berezinskii–Kosterlitz–Thouless criterion. Vortices, the eternal wanderers of the two-dimensional world, here fall into vacancy traps and freeze, like boats moored at a dock, unable to destroy the supercurrent. In other words, the entropy of vortices, which in two dimensions disrupts superconducting order, is vanquished by the elegant geometry of quantum states.

The discovery overturns the notion of how to create quantum materials. The traditional path — growing perfectly pure crystals, spending years on perfection. The new route — engineering controlled disorder, transforming cheap graphene into a superconductor. Horizons are already visible: flexible superconducting electronics, sensors based on pseudogap states, even quantum-thermodynamic devices where quantum-thermodynamic effects may help optimize the transition temperature. The immediate tasks are to account for structural relaxation of defects, competition with magnetism, and, most importantly, to verify the predictions experimentally via scanning tunneling microscopy, which can “see” the superconducting gap with interferometric precision. This work is not merely a calculation but an invitation to a new way of thinking: a defect is not a flaw but a tool; disorder does not destroy but creates. The quantum web awaits its weaver, and perhaps our technological civilization will learn to spin superconducting threads from chaos, just as a spider spins its web — at night, in the dark, following strict mathematical laws.