Quantum-geometric superconductivity in quasicrystals with critical states

We investigate the superfluid weight, which is a key quantity characterizing superconductors, in quasicrystals with critical states. Microscopically, the superfluid weight consists of a conventional contribution depending on the effective mass, and a quantum-geometric contribution arising from interband effects. In topological-flat-band superconductors, where Wannier functions cannot be exponentially localized, the conventional contribution is suppressed, making the quantum-geometric contribution dominant. Some quasicrystals, on the other hand, possess critical states that are neither exponentially localized nor fully extended. We calculate the quantum-geometric contribution to the superfluid weight of quasicrystals within a real-space formalism and reveal that the quantum-geometric contribution is enhanced in quasicrystals hosting critical states.