Unconventional superfluidity of superconductivity on Penrose lattice

Using the attractive Hubbard model as an example, we theoretically investigate the gap function, superfluid density, and superconductivity (SC) transition temperature on the semiperiodic Penrose lattice. First, we clarify that the gap function, density of states, and superfluid density positively correlate to the extended degree of single-particle states around the Fermi energy. Second, we confirm that the paramagnetic component of the superfluid density does not decay to zero in the thermodynamic limit, which is completely different from periodic systems. Regardless of the scaling, the difference between diamagnetic and paramagnetic currents remains stable, consistent with recent experimental results showing that although the superfluid density is lower than that of a periodic system, the system has bulk SC. Third, we find that the superfluid density and SC transition temperature can be boosted with the increase in disorder strength, which should be general to quasicrystal but unusual to periodic systems, reflecting the interplay between the underlying geometry and disorder.