Magnetovortical and thermoelectric transport in tilted Weyl metals

Abstract

We investigate how tilting affects the off-diagonal, dissipationless response of a pair of chirally imbalanced Weyl cones to various external perturbations. The pair of chirally imbalanced Weyl cones can be described as a chiral electron fluid, that can flow with a velocity field that contains vorticity. Upon applying an external magnetic field, we obtain the so-called magnetovortical linear-response matrix that relates electric and heat currents to the magnetic field (chiral magnetic effect) and the vorticity (chiral vortical effect). We show how this reponse matrix becomes anisotropic upon tilting the cones and determine its non-analytic long-wavelength behavior, as well as the corresponding AC response. In addition, we discuss how the tilt dependence of the electronic (or density-density) susceptibility introduces anisotropy in the dispersion relation of the sound-like excitations in the fluid of chiral fermions, which are known as chiral magnetic waves. In the case of an externally applied electric field and a temperature gradient, we find a Hall-like response in the electric and heat current density that is perpendicular to both the tilting direction and the perturbations. As the tilting direction forms a time-reversal symmetry breaking vector, a non-zero (heat) orbital magnetization manifests itself. We calculate the magnetization currents microscopically and elucidate how to subtract these contributions to obtain the transport currents.