Weyl points in a quasicrystal stack 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. It relies on driving a topological phase transition by tuning the vertical crystal-momentum, forcing gap closures at the critical points. We illustrate our theory in a 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. We establish the Weyl-point character of the band closings by a number of distinct signatures, including via the local Chern marker, the bulk dispersion, and the density of states. Interestingly, we also uncover an analogue of Fermi arcs in the quasicrystalline setting, manifested by densely distributed lines in the Fourier-resolved spectrum, in one-to-one correspondence with the Bragg peaks of the structure factor. Possible experimental realizations and connections to the recently observed band crossings in a stack of chalcogenide quasicrystals will also be discussed.