Title: Fate of Weyl semimetals in the presence of incommensurate potentials,
Abstract: 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.