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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17362 |
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Table of Contents:
- Fractal structures such as the Sierpiński gasket have been predicted to enhance the critical temperature 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 dramatically alters the competition between pairing channels: the predominant d-wave superconducting dome at half filling of the square lattice becomes unstable for the carpet, while at high and low fillings extended s-wave pairing gets strongly enhanced. We attribute this to geometric frustration of sign-changing order parameters by the fractal boundary structure. On the triangular Sierpiński gasket, hybrid s+d+id states show critical temperature enhancement comparable to that previously observed for pure s-wave pairing. Our results demonstrate that fractal geometry acts as a selective filter for pairing symmetries, with the compatibility between order parameter structure and lattice topology determining which channels are stabilized or suppressed.