Interplay of fractal geometry and symmetry of the superconducting order parameter.

Fractal structures such as the Sierpinski gasket have been theoretically predicted to enhance the critical temperature of superconductivity, as compared with regular crystals, while maintaining the macroscopic phase coherence of the Cooper pairs. Before, the analysis was performed for the s-wave attractive Hubbard model. In our work, we considerably extend this study and consider different types of superconducting pairing symmetries, such as and dx2 −y2 , d+id, and take into account the possibility of emergence of charge-density. We perform the Hartree-Fock mean-field decoupling for the extended attractive Hubbard model, and solve self-consistently the Bogoliubov-de Gennes equations. In this way, we compute spatial profiles of different order parameters and the superfluid density, and obtain phase diagrams of the Hubbard model on the Sierpinski carpet and gasket, showing that fractal geometry leads to considerably different phase diagrams than that of regular lattices, and can lead both to strong suppression and strong enhancement of superconductivity.