Quantum-geometric origin of superfluid weight in quasicrystals with critical states

A distinctive feature of many quasiperiodic systems is the presence of critical states that are neither extended nor exponentially localized. We investigate the geometric effect on the superfluid weight in quasiperiodic systems with critical states at zero temperature. We employ both real-space and momentum-space approaches to superfluid weight in quasicrystals, which allows us to separate the conventional and quantum geometric contributions. We find that the superfluid weight is dominated by the geometric contribution in quasiperiodic systems with critical states. This finding reveals a fundamental interplay between superconductivity and critical states in quasicrystals.