Asymmetric thermal transport in strained Weyl semimetals due to axial anomaly

We show that strained Weyl semimetals exhibit a directional asymmetry of the heat transfer along the strain axis. The forward/backward asymmetry of the thermal conductivity appears as a result of the axial anomaly, which leads to the emergence of unidirectionally propagating ``chiral'' sound modes. The chiral phonons modify, in a directionally asymmetric manner, the spectrum of the acoustic lattice vibrations, and both types of phonons contribute to the thermal asymmetry of the material. We estimate the magnitude of the effect and discuss its possible experimental detection.