Discovered in high-energy physics, the chiral anomaly has recently made way to materials science by virtue of Weyl semimetals (WSM). Thus far, the main efforts to probe the chiral anomaly in WSM have concentrated on electronic phenomena. Here, we show that the chiral anomaly can have a large impact in the A1 phonons of enantiomorphic WSM. In these materials, the chiral anomaly produces an unusual magnetic-field-induced resonance in the effective phonon charge, which in turn leads to anomalies in the phonon dispersion, optical reflectivity, and the Raman scattering.Introduction.-A major recent development in quantum materials has been the discovery of threedimensional Weyl semimetals (WSM) 1 . These materials contain Weyl nodes, i.e. topologically robust points of contact in momentum space between two nondegenerate and linearly-dispersing electronic bands. Weyl nodes are characterized by a quantum number called chirality, referring to the parallel or anti-parallel locking between momentum and spin. WSM have their low-energy electrodynamics governed by pairs of Weyl nodes with the Hamiltonian

Motivated by an apparent paradox in [X-L. Qi, E. Witten, S-C. Zhang, Phys. Rev. B 87 134519 (2013)] we use the method of gauged Wess-Zumino-Witten functionals to construct an effective action for a Weyl fermion with a Majorana mass that arises from coupling to a charged condensate.We obtain expressions for the current induced by an external gauge field and observe that the topological part of the current is only one-third of that that might have been expected from the gauge anomaly. The anomaly is not changed by the induced mass gap however. The topological current is supplemented by a conventional supercurrent that provides the remaining two-thirds of the anomaly once the equation of motion for the Goldstone mode is satisfied. We apply our formula for the current to resolve the apparent paradox, and also to the chiral magnetic effect (CME) where it predicts a reduction of the CME current to one third of its value for a free Weyl gas in thermal equilibrium. We attribute this reduction to a partial cancelation of the CME by a chiral vortical effect (CVE) current arising from the persistent rotation of the fluid induced by the external magnetic field.

Weyl semimetals display unusual electronic transport properties when placed under magnetic fields. Here, we investigate how magnetic fields alter the dynamics of long wavelength lattice vibrations in these materials. To that end, we develop a theory for the phonon dispersion, which incorporates contributions from chiral and nonchiral Landau levels, electron-phonon interactions, electron-electron interactions, and disorder. We predict (i) a magnetic-field-induced hybridization between optical phonons and plasmons, (ii) avoided crossings between pseudoscalar optical phonons and electronic excitations originating from nonchiral Landau levels, (iii) a sharp dependence of the sound velocity on the relative angle between the sound propagation and the magnetic field. We compare our results to recent theoretical studies on the signatures of the chiral anomaly in phonon dynamics.