We study the geometric contribution to the superfluidity in quasicrystals in which the conventional momentum-space quantum geometric tensor cannot be defined due to the lack of translational invariance. Based on the correspondence between the momentum and magnetic flux, we propose a general framework to define the quantum metric in flux space and reveal its contribution to the superfluid weight in quasicrystalline superconductors. As an application, we investigate the attractive Hubbard model on various extrinsic and intrinsic quasicrystals with flat-energy spectra. In the weak-coupling limit, we reveal the geometric origin of the superfluid weight in quasicrystals with flat-energy spectra and establish its connection to the quantum metric in flux-space. Moreover, by analyzing the spread of Wannier functions, we propose a general fluctuation mechanism that explains how quasiperiodicity modulates the integrated flux-space quantum metric. Our theory provides a general way to examine the effect of the quantum geometry in systems lacking translational symmetry.

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• Flat bands
• Superconductivity
• Superfluid density
• Quasicrystals
• Hubbard model
• Mean field theory
• Tight-binding model
• Wannier function methods