Strong enhancement of superconductivity on finitely ramified fractal lattices

TL;DR

This study shows that certain fractal lattices, like the Sierpinski gasket, can significantly enhance superconductivity and critical temperature, unlike other fractals such as the Sierpinski carpet.

Contribution

It reveals how fractal geometry, especially the ramification properties, can influence and potentially improve superconducting properties in lattice models.

Findings

Sierpinski gasket enhances $T_c$ and phase coherence

Sierpinski carpet shows no significant effect

Fractal ramification affects superconductivity

Abstract

Using the Sierpinski gasket (triangle) and carpet (square) lattices as examples, we theoretically study the properties of fractal superconductors. For that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard model with attractive on-site potential and employ the Bogoliubov-de Gennes approach and the theory of superfluid stiffness. For the case of the Sierpinski gasket, we demonstrate that fractal geometry of the underlying crystalline lattice can be strongly beneficial for superconductivity, not only leading to a considerable increase of the critical temperature $T_c$ as compared to the regular triangular lattice but also supporting macroscopic phase coherence of the Cooper pairs. In contrast, the Sierpinski carpet geometry does not lead to pronounced effects, and we find no substantial difference as compared with the regular square lattice. We conjecture that the qualitative difference between these cases is caused by different ramification properties of the fractals.