Dynamical piezomagnetic effect in time-reversal-invariant Weyl semimetals with axionic charge density waves

Charge density waves (CDWs) in Weyl semimetals (WSMs) have been shown to induce an exotic axionic insulating phase in which the sliding mode (phason) of the CDW acts as a dynamical axion field, giving rise to a large positive magnetoconductance [Wang, Phys. Rev. B 87, 161107(R) (2013)PRBMDO1098-012110.1103/PhysRevB.87.161107; Roy, Phys. Rev. B 92, 125141 (2015)PRBMDO1098-012110.1103/PhysRevB.92.125141; J. Gooth, Nature (London) 575, 315 (2019)NATUAS0028-083610.1038/s41586-019-1630-4]. In this work, we predict that dynamical strain can induce a bulk orbital magnetization in time-reversal (TR)-invariant WSMs that are gapped by a CDW. We term this effect the "dynamical piezomagnetic effect"(DPME). Unlike in J. Gooth et al. [Nature (London) 575, 315 (2019)NATUAS0028-083610.1038/s41586-019-1630-4], the DPME introduced in this work occurs in a bulk-constant (i.e., static and spatially homogeneous in the bulk) CDW, and does not rely on fluctuations, such as a phason. By studying the low-energy effective theory and a minimal tight-binding (TB) model, we find that the DPME originates from an effective valley axion field that couples the electromagnetic gauge field with a strain-induced pseudogauge field. In particular, whereas the piezoelectric effects studied in previous works are characterized by 2D Berry curvature, the DPME represents the first example of a fundamentally 3D strain effect originating from the Chern-Simons 3-form.