Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals

We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields ( E and B ) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in- | B | terms in set-ups where the tilt-axis is not perpendicular to the plane spanned by E and B . The advantage of the emergence of the linear-in- | B | terms is that, unlike the various | B | 2 -dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response from π to 2 π , when we consider their dependence on the angle θ between E and B ; and (2) lead to an overall change in sign of the conductivity depending on θ , when measured with respect to the B = 0 case.