Extended Hubbard model on fractals: d-Wave superconductivity and competing pairing channels

TL;DR

This study investigates how fractal geometries influence superconducting pairing symmetries in the extended Hubbard model, revealing that fractal boundaries selectively enhance or suppress different pairing channels.

Contribution

It demonstrates that fractal structures act as a filter for pairing symmetries, altering the stability of superconducting states compared to regular lattices.

Findings

d-wave superconductivity is destabilized on the Sierpiński carpet.

Extended s-wave pairing is strongly enhanced at high and low fillings.

Hybrid s+d+id states show critical temperature enhancement on the Sierpiński gasket.

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.