High-angular-momentum topological superconductivities in twisted bilayer quasicrystal systems

The electron states in the quasicrystal (QC) are hot topics recently. While previous attentions were focused on such intrinsic QCs as the Penrose lattice, the recent "twistronics" provides us with a new type of QC, i.e., the extrinsic QC, including the 30 degrees-twisted bilayer graphene and 45 degrees-twisted bilayer cuprates as two synthesized examples, unifiedly dubbed as TB-QC. Here we build an efficient microscopic framework to study electron electron interaction driven superconductivities (SCs) in these extrinsic QCs, and find that their nature sits in between those of crystals and intrinsic QCs. Remarkably, our microscopic calculations on the three exemplar TB-QCs reveal various novel topological SCs carrying high angular momenta and high Chern numbers protected by their unique QC symmetries, absent in conventional crystalline materials. The nature of SCs in these extrinsic QCs is also fundamentally different from those in intrinsic QCs in the aspect of pairing-symmetry classifications and topological properties.