Tilt induced vortical response and mixed anomaly in inhomogeneous Weyl matter

We propose a non-dissipative transport effect and vortical response in Weyl semimetals in the presence of spatial inhomogeneities, namely a spatially varying tilt of the Weyl cones. We show that when the spectrum is anisotropic and tilted due to spatial lattice variations, one is confronted with generalized quantum anomalies due to the effective fields stemming from the tilt structure. In particular, we demonstrate that the position-dependent tilt parameter induces local vorticity, thus generating a chiral vortical effect even in the absence of rotation or magnetic fields. As a consequence, it couples to the electric field and thus contributes to the anomalous Hall effect.