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

Abstract

Fractal structures such as the Sierpiński gasket have been predicted to enhance the critical tem- perature 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 dramat- ically 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.

Figures (9)

• Figure 1: $U-V$ phase diagram of the extended Hubbard model on the square (left) and Sierpinski carpet (right) lattices at half-filling.
• Figure 2: Phase diagrams of the thermodynamic limit of the square lattice at the left, a square lattice flake with side $N_{x}=N_{y}=27$ at the center, and the $G=3$ Carpet at the right.
• Figure 3: Phase diagrams of the thermodynamic limit of the triangular lattice at the left, an equilateral triangle flake with triangular lattice base with side $N_{x}=33$ at the center, and the $G=4$ Sierpiński gasket at the right.
• Figure 4: Phase diagrams of the thermodynamic limit of the honeycomb lattice at the left, an equilateral triangle flake with honeycomb base at the center, and the $G=4$ Sierpiński gasket at the right.
• Figure 5: Profiles of the order parameter for the different geometries/pairing states at $T=0.001$ and $\mu = -2.7$, $\mu = 1.15$, and $\mu = 1$ shown in panels (a)--(c) respectively. Circular markers shows on-site superconductivity and the edge color corresponds to the extended component.