Chiral anomaly, charge density waves, and axion strings from Weyl semimetals

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We study dynamical instability and chiral symmetry breaking in three-dimensional Weyl semimetals, which turns Weyl semimetals into ``axion insulators.'' Charge density waves (CDWs) are found to be the natural consequence of chiral symmetry breaking. The phase mode of this charge density wave state is identified as the axion, which couples to an electromagnetic field in the topological $\ensuremath{\theta}\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$ term. One of our main results is that ``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.