  We study dynamical instability and chiral symmetry breaking in three
dimensional Weyl semimetals, which turns Weyl semimetals into "axion
insulators". Charge density waves (CDW) is found to be the natural consequence
of the chiral symmetry breaking. The phase mode of this charge density wave
state is identified as the axion, which couples to electromagnetic field in the
topological $\theta{\bf E}\cdot{\bf B}$ term. One of our main results is that
the "axion strings" can be realized as the (screw or edge) dislocations in the
charge density wave, which provides a simple physical picture for the elusive
axion strings. These axion strings carry gapless chiral modes, therefore they
have important implications for dissipationless transport properties of Weyl
semimetals with broken symmetry.
