Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings

In this paper, we investigate the theory of dynamical axion string emerging from chiral symmetry breaking in three-dimensional Weyl semimetals. The chiral symmetry is spontaneously broken by a charge density wave (CDW) order which opens an energy gap and converts the Weyl semimetal into an axion insulator. Indeed, the phase fluctuations of the CDW order parameter act as a dynamical axion field $\theta({\vec{x}},t)$ and couples to electromagnetic field via $\mathcal{L}_{\theta}=\frac{\theta(\vec{x},t)}{32\pi^2} \epsilon^{\sigma\tau\nu\mu} F_{\sigma\tau} F_{\nu\mu}.$ Additionally, when the axion insulator is coupled to the background geometry/strain fields via torsional defects, i.e., screw dislocations, there is a novel interplay between the crystal dislocations and dynamical axion strings (i.e., vortices of the CDW order parameter). For example, the screw dislocation traps axial charge, and there is a Berry phase accumulation when an axion string is braided with a screw dislocation. In addition, a cubic coupling between the axial current and the geometry fields is non-vanishing and indicates a Berry phase accumulation during a particular three-loop braiding procedure where a dislocation loop is braided with another dislocation and they are both threaded by an axion string. We also observe a chiral magnetic effect induced by a screw dislocation density in the absence of chemical potential imbalance between Weyl points and describe an additional chiral geometric effect and a geometric Witten effect.