Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals

Weyl superconductivity is a topological phase in three-dimensional crystals in which the Weyl equation describes quasiparticle excitation near band-touching points in momentum space called Weyl nodes. For quasicrystals which lack translational symmetry, a theory of Weyl superconductivity has not been established, in spite of recent extensive studies on quasicrystalline topological phases. Here, we demonstrate the occurrence of quasicrystalline Weyl superconductivity by extending the definition of Weyl superconductivity to periodically stacked, two-dimensional superconducting quasicrystals. We identify quasicrystalline Weyl nodes—topologically protected point nodes in one-dimensional momentum space corresponding to the stacking direction—in terms of a topological invariant given by a change in the Bott index in quasicrystalline layers. We find that these Weyl nodes exist in pairs and that Majorana zero-energy modes protected by the nonzero Bott index between a pair of quasicrystalline Weyl nodes appear on surfaces. These Majorana zero modes form an infinite number of arcs in momentum space, densely and quasiperiodically distributed as a function of momentum in the direction of surfaces within each quasicrystalline layer. In Ammann-Beenker (Penrose) quasicrystals, the quasiperiodicity of Majorana arcs is governed by the silver (golden) ratio associated with the quasicrystalline structure.