Extended Hubbard model on fractals: d-Wave superconductivity and competing pairing channels
Abstract
Fractal structures such as the Sierpi\'nski 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 Sierpi\'nski 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 Sierpi\'nski 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.
Keywords
Cite
@article{arxiv.2603.17362,
title = {Extended Hubbard model on fractals: d-Wave superconductivity and competing pairing channels},
author = {Robert Canyellas and Mikhail I. Katsnelson and Andrey Bagrov},
journal= {arXiv preprint arXiv:2603.17362},
year = {2026}
}