Quasicrystalline Weyl points and dense Fermi-Bragg arcs

We introduce a general mechanism for obtaining Weyl points in a stack of 2D quasicrystals, which can be extended to any stack of aperiodic layers. To do so, we drive a topological phase transition with the vertical crystal-momentum as the tuning parameter, which leads to gap closures at the critical points. We illustrate this in a simple 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. We establish the presence of Weyl points via the local Chern marker, projected band structure and density of states. Interestingly, we also uncover an analogue of Fermi arcs in the quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed lines connecting the band degeneracies at the same Fourier momenta as the Bragg peaks. We also discuss connections to the recently observed band crossings in a stack of chalcogenide quasicrystals and the prospect of a fully quasicrystalline Weyl system. The flexibility of our proposal opens the way for the realization of other gapless topological phases in aperiodic platforms, thereby significantly expanding the scope of topological band theory.