Fate of Weyl semimetals in the presence of incommensurate potentials

We investigate the effect of the incommensurate potential on Weyl semimetal, which is proposed to be realized in ultracold atomic systems trapped in three-dimensional optical lattices. For the system without the Fermi arc, we find that the Weyl points are robust against the incommensurate potential and the system enters into a metallic phase only when the incommensurate potential strength exceeds a critical value. We unveil the trastition by analysing the properties of wave functions and the density of states as a function of the incommensurate potential strength. We also study the system with Fermi arcs and find the Fermi arcs are sensitive against the incommensurate potential and can be destoryed by a weak incommensurate potential.