The team knew the material was made like a layered cake, with layers of superconducting copper oxide alternating with spacer layers. At higher temperatures, oxygen atoms tend to roam around in the spacer layer. But when temperatures drop, they settle down. These oxygen atoms — and the electrons they bring to what would otherwise be vacancies — are thought to contribute to the drop in resistance that accompanies superconductivity. But until now, no one had been able to see the structure with high resolution.
Bianconi and his team got a shock when they realized the pattern formed by the once-roaming oxygen atoms was fractal. The pattern looked the same at the 1-micrometer scale as it did at the 400-micrometer scale.
This self-similarity was completely unexpected in superconductors, Bianconi says. “We were very astonished. We couldn’t believe our eyes,” he says. “This is not an area where we expected to see a fractal pattern.”
Their analysis also revealed that the superconductor is a “scale-free” network, meaning its structure obeys the same mathematics as can be used to describe connections within the internet and some social networks. “I find it plainly mysterious,” says condensed matter physicist Jan Zaanen of Leiden University in the Netherlands. “It is telling us something very deep.”
The researchers also found that the greater the length scales at which the pattern persisted – or the more complete its “fractality” – the higher the maximum temperature at which the crystal could superconduct. Bianconi speculates that the scale-free distribution of the interstitial oxygen helps preserve the “quantum coherence” of electrons in the crystal. Superconductivity is thought to depend on this property, which breaks down as temperature rises.