If you shape a material into a fractal pattern, it can totally change how it carries electricity.
March 19, 2026
Original Paper
Extended Hubbard model on fractals: d-Wave superconductivity and competing pairing channels
arXiv · 2603.17362
The Takeaway
Using a Sierpiński carpet geometry (a recursive pattern of squares), physicists found they could selectively 'filter' superconductivity. The fractal's unique geometry suppresses the standard electrical behavior of the crystal while stabilizing more exotic quantum states that wouldn't normally exist.
From the abstract
Fractal structures such as the Sierpiński gasket have been predicted to enhance the critical tem- perature of s-wave superconductivity compared to regular crystals while maintaining macroscopic phase coherence of Cooper pairs. Here we extend this analysis to order parameters with non-trivial symmetry by studying the extended Hubbard model with nearest-neighbor attraction on fractal lattices. Using Bogoliubov-de Gennes mean-field theory, we find that the Sierpiński carpet dramat- ically alters th