Quasicrystalline Weyl superconductors

We theoretically investigate Weyl superconductivity in quasicrystals. Crystalline Weyl superconductors have stable point nodes characterized by the Chern number in the Brillouin zone. The point nodes are called Weyl nodes. Since quasicrystals lack the Brillouin zone, we cannot directly use the Chern number for their topological characterization. Nevertheless, we show that Weyl superconductivity can be realized in quasicrystalline layers stacked periodically. Because vertical momentum can be defined in the quasicrystalline systems due to the periodicity, Weyl nodes can be characterized by a change in the Bott index in the vertical momentum space. We demonstrate quasicrystalline Weyl superconductivity by using a stack of two-dimensional superconducting quasicrystals under an external magnetic field. We also show that quasicrystalline Weyl superconductors host Majorana surface states because of the nonzero Bott index.