Tunneling chirality Hall effect in type-I Weyl semimetals

We propose a tilt-assisted chirality Hall effect in the normal metal-superconductor (NS) junctions based on the time-reversal broken type-I Weyl semimetals. It is found that the chirality-contrasting skew reflection occurs at the NS interface due to the tilt of the Weyl cones, which is responsible for the nonzero transverse chirality Hall currents. Distinct from the Hall effect induced by the Berry curvature, we further illustrate that the transverse chirality current here is determined by the symmetry of the tilt. Specifically, both the transverse chirality Hall current and the transverse charge Hall current may occur when the tilt breaks the mirror symmetry ($\mathcal{M}$). However, a pure transverse chirality Hall current with zero net charge is present when the tilt breaks $\mathcal{M}$ symmetry but preserves the combined $\mathcal{MC}$ symmetry, where $\mathcal{C}$ represents the $\mathbb{Z}_2$ exchange symmetry.