Quasiperiodic Pairing in Graphene Quasicrystals

We investigate the superconducting instabilities of twisted bilayer graphene quasicrystals (TBGQCs) obtained by stacking two monolayer graphene sheets with 30° relative twisting. The electronic energy spectrum of the TBGQC contains periodic energy ranges (PERs) and quasiperiodic energy ranges (QERs), where the underlying local density of states (LDOS) exhibits periodic and quasiperiodic distribution, respectively. We found that superconductivity in the PER is a simple superposition of two monolayer superconductors. This is because, particularly near the charge neutrality point of the TBGQC, the two layers are weekly coupled, leading to pairing instabilities with a uniform distribution in real space. On the other hand, within the QER, the inhomogeneous distribution of the LDOS enhances the superconducting instability with a nonuniform distribution of pairing amplitudes, leading to quasiperiodic superconductivity. Our study can qualitatively explain the superconductivity in recently discovered moiré quasicrystals, which show superconductivity in their QER.