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A long, narrow pan, and a thin pancake sets in uneven stripes. For decades, scientists saw a similar picture when modeling the behavior of electrons in superconductors — materials that conduct electricity without loss. They used elongated "cylinders," and the result was always the same: rigid magnetic "stripes" that were thought to hinder superconductivity.

The authors of the new study took a wide "pan"—a square lattice of 24×24—and saw something completely different. The real material resembles not a frozen pattern but boiling milk: magnetic regions (a kind of "puddles" with special properties) constantly move, merge, and split. This dynamic collective behavior is the key to the puzzle. Static stripes turned out to be merely a side effect of the shape, an artifact of the boundaries.

And there's more. The scientists saw that adding "holes" (removing electrons) and adding electrons act completely differently. Holes, like hot oil, actively melt the magnetic order, and superconductivity flourishes when about 15–20% of electrons are lost. Electrons, on the other hand, preserve rigid magnetic barriers, and superconducting "streams" flow only through narrow cracks between them, reaching a maximum at 10% excess. This asymmetry is a long-standing puzzle, and now it has a simple explanation at the atomic scale.

In the end, without adjusting parameters, the researchers obtained the famous "superconducting dome"—a graph showing under what conditions superconductivity arises. Their curve perfectly matched experimental data, down to fine details. This proves that pure quantum mechanics of electrons in a square lattice (the Hubbard model) by itself gives rise to high-temperature superconductivity. The key to the recipe is to give magnetic "puddles" the freedom to dance.